1.2.1 Force

A foundation concepts in physics, a force may be thought of as any influence which tends to change the motion of an object. A force can be described as the push or pull upon an object resulting from the object’s interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects. When the interaction ceases, the two objects no longer experience the force. Forces only exist as a result of an interaction.

There are four fundamental forces in the universe: the gravity force, the nuclear weak force, the electromagnetic force, and the nuclear strong force in ascending order of strength. In mechanics, forces are seen as the causes of linear motion, whereas the cause of rotational motion is called a torque. The action of forces in causing motion is described by Newton’s Laws.

Force is a quantity which is measured using the standard metric unit called the Newton. A Newton is abbreviated by a “N”. To say “10.0 N” means 10 Newtons of force. One Newton is the amount of force required to give a 1 kg mass an acceleration of 1 m/s².

Force = mass x acceleration
F = m x a = 1 kg x 1 m / s²

A force is a vector quantity—it has both magnitude and direction. To fully describe the force acting upon an object, you must describe both the magnitude (size or numerical value) and the direction. Thus, 10 Newtons is not a full description of the force acting upon an object. In contrast, 10 Newtons downwards is a complete description of the force acting upon an object; both the magnitude (10 Newtons) and the direction (downwards) are given.

A torque is a special form of force that turns an axle in a given direction. It is sometimes called a rotational force. You can create a torque by pushing on a rod or lever that rotates an axle. Likewise, a torque on an axle can result in a linear force at a distance from the center of the axle.

Torque equals force multiplied by moment arm. Pushing on a rod that rotates an axle can create a torque on that axle. Likewise, a torque on an axle can result in a linear force at a radius from the center.

The relationship between torque and force is:

T = FR
or
F = T/R

where
T is the torque in newton-meters
F is the force (Newtons)
R is the radius or distance from the center to the edge (meters)
R is also sometimes called the moment arm. The force, F, is applied perpendicular to the radius, lever or moment arm.

1.2.2 Work

Work refers to an activity involving a force and movement in the direction of the force.
A work is done on an object when the force acts on it in the direction of motion or has component in the direction of motion.
In order to accomplish work on an object there must be a force exerted on the object and it must move in the direction of the force.
Work = Force x distance moved in direction of force
Work is measured in joules (J ). The formula for this is:

J = N x m

Where force is measured in Newtons and distance in meters.

For a constant force F which moves an object in a straight line from x1 to x2, the work done by the force

Work = force x (x2-x1)

Mathematically, work can be expressed by the following equation:

W = F x d x cos Θ

where F is the force, d is the displacement, and the angle (theta) is defined as the angle between the force and the displacement vector. Perhaps the most difficult aspect of the above equation is the angle “theta.” Theta is defined as the angle between the force and the displacement.

• A force acts from the right on an object and it is displaced to the right. In such an instance, the force vector and the displacement vector are in the same direction. Thus, the angle between F and d is 0 degrees.
• A force acts from the left on an object and it is displaced to the right. In such an instance, the force vector and the displacement vector are in the opposite direction. Thus, the angle between F and d is 180 degrees.
• A force acts upward on an object as it is displaced to the right. In such an instance, the force vector and the displacement vector are at right angles to each other. Thus, the angle between F and d is 90 degrees.

For the more general case of a variable force F(x) which is a function of x, the work is still the area under the force curve, and the work expression becomes an integral.

Work is not done when there is no motion or when the force is perpendicular to the motion.
Let us apply the work equation to determine the amount of work done by the applied force in each of the three situations described below.

Diagram A Answer:
W = (100 N) x (5 m) x cos (0 degrees) = 500 J
The force and the displacement are given in the problem statement. It is said (or shown or implied) that the force and the displacement are both to the right. Since F and d are in the same direction, the angle is 0 degrees.

Diagram B Answer:
W = (100 N) x (5 m) x cos (30 degrees) = 433 J
The force and the displacement are given in the problem statement. It is said that the displacement is to the right. It shows that the force is 30 degrees above the horizontal. Thus, the angle between F and d is 30 degrees.

Diagram C Answer:
W = (147 N) x (5 m) x cos (0 degrees) = 735 J

1.2.3 Energy

Energy is the capacity for doing work. You must have energy to accomplish work – it is like the “currency” for performing work. In the process of doing work, the object which is doing the work exchanges energy with the object upon which the work is done. When the work is done on the object it gains energy. The energy acquired by the objects upon which work is done is known as mechanical energy.

Mechanical energy is the energy which is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position.

Mechanical energy = Kinetic energy + Potential energy
Potential Energy PE = mass of the object x acceleration of gravity x height of the object

PE = m x g x h
g represents the acceleration of gravity (9.8 m/s/s on Earth)

Kinetic Energy is depend on two variables: the mass and the speed

The following equation is used to represent the kinetic energy (KE) of an object.

KE = 1/ 2 x m x v ²

1.2.4 Power

Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation.

Power = work / time = (force x displacement) / time

The standard metric unit of power is the Watt. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a Watt is equivalent to a Joule/second. For historical reasons, the term ‘horsepower’ is occasionally used to describe the power delivered by a machine. One horsepower is equivalent to approximately 750 Watts.

Most machines are designed and built to do work on objects. All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects. Thus, the power of a machine is the work/time ratio for that particular machine. The power rating relates to how rapidly the engine can accelerate the car.

2.4.1 First angle and third angle projections

In the First angle method of projection, the object is assumed to be placed in the first quadrant and the three views are drawn on the horizontal, vertical and side plane as mentioned above. Then, the vertical plane and the side plane are rotated by 90 degrees to form a single plane surface which shows all three views. In the same manner, in the third angle projection, the object is placed in the third quadrant, the three views are drawn and the vertical and side planes rotated by 90 degrees to form a single plane surface showing the three views.

The assumption made by the draftsman, whether first angle or third angle, is clearly recorded in the title block of the drawing. The symbols used for these two systems are given in Figures 2.8 and 2.9.

The three views of the object given in Figure 2.10 are shown in Figures 2.11 and 2.12 respectively.

• Front view: Drawn looking straight at the front of the object.
• Side view: The left side of the object is drawn toward the right side view of the object and vice versa.
• Plan View: The top of the object is drawn toward the bottom view of the object and vice versa.

Both first angle and third angle projections are quite popular and used widely in the industry. Figure 2.13 is an example of third angle projection.

2.5.1 Isometric projection

In isometric projection, the two axes are at 60 degrees to the vertical axis and the measurements along these two axes can either be scaled from measurements on actual objects or they can be actual measurements if the space permits. The isometric projection of a cube is shown below in Figure 2.15.

2.5.2 Oblique projection

In this method, the two axes are at right angles to each other and the third axis is at 45 degrees to them. The oblique projection of a cube is shown in Figure 2.16.

2.6.1 Sectional views

The views of the object drawn after cutting it by a plane are called sectional views. Sectional views are drawn to clarify the interiors or hidden details on a multi-view drawing of an object. The observer imagines that the object is cut by a plane (cutting plane) and that the part of object nearer to the observer is removed from the view exposing the interiors of the object where a cut has been taken.

The sectional view usually replaces one of the principal views (plan, front view or side view) depending upon position of cutting plane. However it is not a rule and the sectional view many times supplements the other view to give the clear idea about the external as well as the internal details of the object. Hidden lines are omitted in the sectional views to avoid the confusion between dotted lines and hatching lines. However in the portion where the object is not cut, we follow the normal convention that the hidden lines are dotted.
The spokes and the ribs of a wheel are not sectioned in the plane of the wheel even though it may cut them. (Spokes are thin wire-like elements which hold the rim and the wheel hub together whereas the ribs are the strengthening or reinforcing parts of the wheel).

It is also conventional drawing practice not to take sections on keys, key ways, nuts, bolts and other fasteners in the assembly in which they are used.

A separate sectional view giving the cross sectional details of the spoke, rib or key, etc. can be drawn to supplement the sectional view of wheel and hub or shaft.

Types of sectional views

Types of sectional views are as follows:

• Full section view
• Half section view
• Rotated section view
• Removed section view
• Allied section view
• Offset section
• Partial section
• Assembly section
• Pictorial section

Each one of these is explained below with an illustration.

Full section view
This is the simplest type of section in which the cutting plane cuts the object in two and half the object nearer to the observer is removed. This section is very useful for the parts or assemblies which are symmetrical about the center line. This is illustrated in Figure 2.18 (a).

Half section view
In this case two cutting planes placed at 90 degrees to each other cut the object halfway through We remove one quarter of the object which is cut from the main object exposing two half surfaces of the object at 90 degrees to each other. This section is very useful and elegant way of showing the interior portion of a symmetrical object. This is shown in Figure 2.18 (b).

Note the thick lines in Figure 2.18 (a) and dotted lines in Figure 2.18 (b) on the right half of the views showing the internal details of the object. The other half of is identical in both sectional views. Also note the hatching on the exposed cut area. It is conventional to do the hatching of such surfaces to highlight the fact that the area is a cut area. The hatching also indicates the material of the cut area. Details of hatching are given later. Further, note that other outside views are not affected while drawing a sectional view.

Rotated or revolved sectional view
This sectional view is used to show the uniform shape of object from end to end. See Figure 2.19. Here the object is a square pipe with a rectangular cavity all through. This is shown by revolving the cross section of the pipe drawn along the length itself of the pipe itself.

Removed section
This sectional view is used to show the variable shape of an object from end to end. This is shown in the lower portion of Figure 2.19. Here the object is a circular pipe in the middle portion, with different cross sections for the end portions as shown. Such parts are not uncommon in mechanical engineering.

Aligned section
These views are drawn to show the shape of features that do not align with vertical and horizontal center lines of the object (see Figure 2.19).

Here the cutting plane is aligned to pass through the holes of the flange which are located at 45 degrees to vertical and horizontal planes. Hence a vertical or horizontal cross section would not have revealed these holes.

2.14.1 Bolts

A bolt consists of an integral head at one end, unthreaded portion in the middle and threaded portion at the other end. The bolt will pass through the hole in the two parts to be fastened and a nut will be used on the threaded portion of the bolt to fasten the two parts together. A typical bolt is shown in Figure 2.29.

Depending upon the shape of the bolt head, the bolts are known as hexagonal headed bolt, square headed bolt, cup headed bolt (provided with a snug or square neck), T-headed bolt, etc.

2.14.2 Nuts

A nut has to be used with a bolt or a stud to fasten the two parts together. It will have internal threading. When tightened on the threaded portion of bolt or stud. It will draw the two parts together and tighten them. A typical nut is shown in Figure 2.30.

Depending upon the external shape of nut, the nuts are called hexagonal nut, square nut, flanged nut, dome nut, etc

2.14.3 Screw fastener

A screw fastener will have threaded portions on both ends. It is threaded permanently in one part. After placing the other part such that screw passes through other part with corresponding holes in it, the two parts are tightened with a nut that is placed on threaded end of the screw. Instead of a nut, the screws may have just a slot for tightening it if the tightening loads are less.

2.14.4 Bolt and nut assembly

A typical bolt and nut assembly is given in Figure 2.31.

2.14.5 Washers and locking arrangements

During the operation of the machine, the fastening of the bolt and nut can become loosened due to vibration, heat, etc. To prevent this, a washer is normally used before tightening the nut and locking it with a split pin after tightening. Spring washers and the use of two nuts tightened in opposite directions are some other methods of locking.

3.2.1 Elasticity

When some external forces act on a body, the internal forces in the material resist any deformation from these external forces. When the external forces are removed, the material regains original shape and size, this property is known as elasticity. Elasticity is measured by elastic modulus that is called as Young’s modulus. The modulus is measured in MPa (mega Pascals)
A material is said to be perfectly elastic if there are no residual stresses left on removal of external load.

3.2.2 Plasticity

When we load a material with a tensile load, the length of the material increases. The higher the load, the higher the extension will be. But a stage comes when the material extension becomes disproportionately large even for small increase of load. This is termed as plasticity. Bearing materials such as brass, bronze, etc. exhibit this property. Lead is a good example of a plastic material.

3.2.3 Ductility

Ductility can be defined as how easily a material can be drawn into thin wires or rolled into thin sheets. Mild steel, steel, copper and brass are highly ductile. Cast iron has very poor ductility. Ductility can also be defined as a measure of ability to deform plastically without fracture. Characteristics of ductility are large elongation, area reduction and fracture strain.

3.2.4 Brittleness

Lack of ductility is brittleness. The material breaks into pieces under impact or under a tensile load. Cast iron is an example of a brittle material.

3.2.5 Malleability

When a material can be hammered into thin sheets or small bars without cracking it is known as malleability. Gold is the most malleable metal. Cast iron has poor malleability. Mild steel is highly malleable and is used in manufacturing corrugated iron sheets.

3.2.6 Toughness

Toughness is when a material resists fracture when acted upon by force. When such a material fractures, it exhibits considerable local deformation. Mild steel, copper and aluminum are remarkably tough. This is also the measure of ability to absorb energy. It is measured in J/m³

3.2.7 Hardness

A hard material resists scratching (abrasion) or penetration by other materials. It is also a property by virtue of which a material cuts or produces a scratch on another material that is less hard. Diamond is hardest of all known materials. Glass is also very hard but it is very brittle. There are three important scales of measure of hardness (Rockwell, Brinell, Vickers).

3.2.8 Wear resistance

Property to resist abrasion is wear resistance. Quenched and tempered nickel-chromium steel has a very high degree of wear resistance. This material is used for gears, sprockets, cams, rollers, etc.

3.2.9 Fatigue resistance

Resistance of a material to repeated cyclic stresses is fatigue resistance. Breaking of a wire when it is subjected to repeat bending in opposite directions is a good example of fatigue. Fatigue resistance is very important for aircraft parts.

3.2.10 Corrosion resistance

Resistance of a material to withstand chemical action of oxidizing agents, acids and alkalis is known as corrosion resistance. Wrought iron exhibits high resistance to corrosion. Similarly, stainless steel is a good corrosion resistant material.

3.2.11 Heat resistance

This is a property by virtue of which a material retains its strength and other properties at high temperature.

3.2.12 Creep resistance

This property is combination of heat resistance and resistance to high pressure.

3.2.13 Weld ability

This is the property by virtue of which two parts can be welded together

3.2.14 Harden ability

This is when a metal is capable of being hardened by some heat treatment. Steel can be hardened by heating to about 1300°C and quenching in a cool medium like air, oil or molten lead. Mild steel however cannot be hardened.

3.2.15 Porosity

This is the property of having pores between adjacent particles. The ratio of volume occupied by the pores to the total volume of the body is a measure of its porosity.

Sometimes there could be more than one material which will satisfy all the requirements of design, however the cost may be the consideration for choosing one amongst them. Sometimes none of the material would meet all requirements and then selection of material becomes a compromise between what is required and what is available.

3.2.1 Solid solution strengthening

Homogeneous mixtures of two or more kinds of atoms in solid state are called a solid solution which is analogous to liquid solution such as sugar in water. There are two types of solid solutions:

• interstitial solid solution
• substitutional solid solution

In the interstitial solid solution, the atoms of solute occupy the interstitial spaces of the solution whereas in the substitutional solid solution, the atoms of solute substitute the atoms of solvent, either in an ordered pattern or in a disordered pattern. Ideally, the solute and solvent atoms are randomly distributed in disordered substitutional solid solution. Properties of an alloy in solid phase are not the averaged properties of the component metals in pure state. It is found that the hardness generally increases to a maximum at around 50 % of each metal whereas the strength increases gradually towards a value dictated by stronger component. In general, greater the amount of solute, higher will be the hardness and strength, for example brass with 30% zinc will be harder and stronger as compared to brass with 10% zinc.

3.2.2 Strengthening by grain size reduction

Mechanical properties of materials depend on arrangement of grains, their shapes and in particular, their size. Grain size directly controls the extent of slip interference by adjacent grains and affects the properties of strength, toughness, ductility and fatigue of metals. Fine grained steel have higher strength, modulus of rupture and better fatigue resistance. Compared to the coarse grained steel, fine grained steel exhibits greater tensile strength. It also has better machine finish, better crack resistance and better deep drawing capability. On the contrary, coarse grained steel will have better hardening ability, forge ability and better high temperature creep strength.

Grain size is important for non ferrous materials. Grain size may be regulated by the factors such as:

• rate of solidification from liquid phase
• plastic deformation followed by an appropriate heat treatment.

3.2.3 Strengthening by thermal processing – heat treatment

Heat treatment of metals is basically an operation or combination of many operations that involve heating and cooling of metals or alloys in the solid state to produce certain desired properties. The process of heat treatment is thus processing of material with definite and controlled temperature changes that involve:

• heating to a pre-determined temperature
• soaking at that temperature till the structure becomes uniform
• cooling at predetermined rate to cause formation of desirable structures for desired properties.

Heat treatment results in one or many of the following advantages

• improved mechanical properties such as tensile strength, toughness, hardness, ductility, heat resistance, shock resistance, resistance to corrosion.
• improved technological properties such as machinability, forge ability, workability
• relieving of internal stresses that develop in hot and cold working of metals.
• change of grain size

The various methods of heat treatment are:

• annealing
• normalizing
• hardening
• tempering
• diffusion coatings

Annealing

Various methods of annealing are:

• full annealing
• process annealing
• spheroidise annealing
• Full annealing consists of:
• heating the steel to just above the critical point (40 to 50 degrees higher), the higher the carbon content, the higher the annealing temperature will be
• holding at that point for considerable time (not less than 3 to 4 minutes per millimetre of section)
• slow cooling (at a rate of 150-200° C per hour for carbon steels and 30 to 100°C for alloy steels)

Process annealing

This is used to restore the ductility property suffered during cold working of steels. Annealing is done usually at 500-700° C.

Spheroidise annealing

Annealing is done at 730-770°C. This process is useful for producing bearing steels with globular pearlite structure.

Normalizing

Normalizing is used for eliminating coarse grained structure, remove internal stresses and to improve mechanical properties suffered during cold working of steel. In this process heating is at 30-50°C above the annealing temperature and cooling is done in air.

Hardening

Hardening followed by tempering is done to develop wear resistance and improve strength, elasticity, ductility and toughness. Heating is done at 1100 to 1300 deg C (25 to 50 % higher than the temperature used for carbon structural steels and cooling is done in a current of air/oil or molten salts depending on the requirement of steel structure to be produced.

Induction hardening
This is a very effective surface hardening method. Typical areas of application are surface hardening of bearing areas of crankshaft, camshaft, axles and similar wearing surfaces.

The process consists of passing a very high frequency current of about 2000 Hertz through a copper inductor block which acts as a primary coil of a transformer. The block is placed around the surface to be hardened without directly touching the surface. The eddy currents and hysteresis losses generate the heating effect. The hardening temperature is about 750-760°C for 0.5 % carbon steel and 790-800°C for alloy steel. The heated areas are then quenched immediately by water sprays. Induction hardening is accomplished by extremely rapid heating and rapid quenching of surface which has no effect on interior core.

Flame hardening
Heating of metal surface with oxy-acetylene flame is known as flame hardening. This is also based on the principle of rapid heating and cooling of wearing surface. The flame is directed to the wearing area without heating the remainder area. This method is quick and convenient and does not affect the toughness or ductility property of the other portion. This does not require any furnace for heat treatment hence it is useful for large parts.

Precipitation hardening (also called age hardening)
Precipitation is the decomposition of a solid solution into two phases of different composition – the precipitate and the solid solution. Precipitation hardening is the process of hardening an alloy by precipitation of a constituent from a supersaturated solid solution by heating to an elevated temperature. This is sometimes called age hardening. While precipitation hardening takes place at elevated temperatures, age hardening takes place at room temperatures.

Tempering

Steel after quenching is hard and brittle, with large internal stresses. These shortcomings are rectified by the process of tempering. Tempering treatment consists of re-heating the steel after hardening to temperatures below the critical line, holding it there for considerable time (not less than 4 to 5 minutes for each millimeter of section) and then slow cooling.

Diffusion coatings

Diffusion coating or metallic cementation is the process of impregnating the surface of steel with aluminum, chromium, silicon, boron, beryllium and other elements. This is accomplished by heating and holding the steel parts in direct contact with one of these elements that may be in solid, liquid or gaseous state. This imparts the metal properties of heat resistance, wear resistance and corrosion resistance.

3.2.4 Strain hardening

If a specimen that has been overstrained to above the yield point is allowed to rest or age before retesting, the yield point returns at a higher stress. This process which is accompanied by hardening due to increased stress is known as strain ageing or strain-age hardening.

3.2.5 Cold working

If there is a plastic deformation of considerable extent, strain hardenings will invariably result. This is a cumulative process. If a piece of metal is bent back and forth several times, yield stress is increased after each cycle of bending and unbending. In the end the piece may be brought back to original shape but it would have undergone considerable strain hardening. This is known as cold working. Plastic working at temperatures that are 30–50 % of melting temperatures is called cold work. This results in considerable increase in hardness, yield point and strength of cold worked metals. These changes are also accompanied by a marked decrease in ductility and slight decrease in density.

3.3.1 Stress and strain on a body

All external forces on a body constitute a ‘load’ on the body. The effect of load is to produce tension, compression, shear, bending or twisting of the body depending on the nature of force. A body subjected to external load will deform, yield or break depending upon the magnitude of load; its cross-sectional dimensions and the nature of material. This is shown in Figure 3.1.

In Figure 3.1, P is the load applied along the axis of the object. It is tensile in Figure 3.1(A) and compressive in Figure 3.1(B). In the first case the body will elongate and in second case the body will shorten.

When the load is applied, the body exerts internal resistance to the deformation. A steady state is reached when the applied load and the internal resistance become equal. In this steady state, the internal resistance per unit cross-sectional area of the body (perpendicular to the direction of applied load) is known as stress, and the resultant deformation expressed as a fractional change with respect to original size is known as strain. Since stress load must balance the applied load, we have

sA₀=P    or    s=P/A₀

Where
s = the normal stress, N/m² (Newtons per square meter)
P = the applied load, N (Newtons)
A₀ = the original cross-sectional area.

The load applied along the axis of the component could be tensile or compressive and the stress will accordingly be called tensile stress or compressive stress. Thus for example if a tensile load of 100 N is applied along the axis of a component with a cross sectional area of one square meter, then normal tensile stress will be 100/1=100 N/ m².

Under the effect of the external load, the body will deform. If the external load is tensile, the body will elongate and if the external load is compressive, the body will shorten. Thus, if L₀ is originally the length of the body and it deforms by a small amount DL then the strain on the body is given by

e= DL/ L₀

Since strain is just the ratio of two length values it does not have any unit. It is just a number. If the applied load is a shear load, there will be a transverse deformation of the body. This is shown in Figure 3.2. Shear stress is shear force per unit area and is given by

τ =P/A₀

where
τ = shear stress in N/m² ,
P = force applied parallel to upper and lower surface
A₀= cross sectional area of the face prior to deformation.

Due to this shear load the body will deform by a certain angle Θ (theta). This will create a shear strain which is given by

γ = tan Θ

where γ = the shear strain
Θ =angle of deformation in radians

3.4.1 A body under shear load

In the elastic region of the material, i.e. in the region where the material comes back to its original state when the load is removed, the relationship between stress and strain is given by Hooke’s Law: stress is proportional to strain and independent of time. It follows from Hooke’s Law that the ratio of stress to strain is a constant. This constant proportionality is called modulus of the material. If the stress is compressive or tensile, the modulus is called as modulus of elasticicity and if the stress is shear stress, the modulus is called modulus of rigidity. The modulus of elasticity is also called Young’s modulus and is denoted by E. Modulus of rigidity is denoted by G. In case of volumetric distortion, is called a bulk modulus and denoted by G. Volumetric strain is defined as ratio of volume after distortion to original volume before application of load.

When a body is subjected to tensile load, it elongates in the direction of load application but at the same time its cross-sectional area decreases and thus the increase in length results in decease of transverse dimension.

This ratio of lateral strain to axial strain is known as Poisson’s ratio and is denoted by μ

(mu).

3.5.1 Tensile testing of materials

A schematic representation of the apparatus used to conduct the tests for determining tensile stress and measuring tensile strain is shown in Figure 3.3.

The tensile testing machine essentially consists of the unit for applying tensile load to the test specimen and a measuring device for measurement of load applied on the test specimen. The test specimen is machined to standard dimensions and attached to the jaws of tensile testing machine. Before commencing the test, two gauge marks are made on the specimen usually at 50 mm or 200 mm apart according to size of test piece. The specimen can be either round or flat and the ends either plain, threaded, shouldered or with pin arrangement. A typical test specimen is shown in Figure 3.4; the test specimen is deformed under the action of tensile load on it. Load is slowly increased in steps and the deformation is measured by an accurate mechanical, electrical or optical device.

The load and deformation readings are taken at each step. The test may be continued until fracture. The data is then plotted as load versus elongation.

3.5.2 Hardness testing

It is difficult to define hardness as a distinct property because it is closely associated with material structure, composition and other mechanical properties. Hardness may represent the ability of the material to resist scratching, abrasion, cutting, or penetration. Sometimes hardness is measured by the ability of the material to absorb energy under impact loads. Hardness as measured by resistance to abrasion is also a measure of wearing quality of material. Therefore hardness is not an independent characteristic of mechanical properties. It determines the same properties as in other testing methods, for example, tension tests but under different loading conditions.

3.5.3 Testing techniques

In the process of determination of hardness, a small indenter is forced into the surface of the material to be tested, under controlled conditions of loading and rate of application. The indenter is a steel ball or a diamond cone. The indenter first overcomes the resistance of the material to elastic deformation and then a small amount of plastic deformation. Upon deeper indentation of the tip, it overcomes large plastic deformation. This is very simple, rapid and non-destructive test and therefore it is very popular in industrial applications The three most important and most commonly used methods of determining hardness of a material are the Brinell hardness test, the Rockwell test and the Vickers test. Knoop microhardness test and Rockwell superficial tests are also used in some cases.

Brinell hardness test

This is the most commonly used test in the industry for measurement of hardness of iron and steel material. In this test, a hardened steel ball of 10 mm diameter is used for indenting under a load of 5000 to 30000 N or 5 mm ball with load of 7500 N. The load is maintained for 10-15 seconds and diameter of the impression is measured after the test. Then Brinell Hardness Number is obtained by the equation:

where

BHN = Brinell Hardness number

P = Load applied

D = Diameter of ball in mm (10 mm)

d = Diameter of indent, mm

In practice, BHN corresponding to particular value of indent is measured from a table since D is fixed (10 mm).

Rockwell hardness test

This test is based upon the indentation of a hard tip into the test piece under the action of two consecutively applied loads: initial and final. A conical shaped diamond with 120° apex angle and 0.2 mm radius is used to make indentations for hard materials. For soft materials, a hardened steel ball of 1.5 mm diameter is used. The Rockwell hardness number is the difference between the indentation from the final load and initial load of 100 N. The load is applied and maintained for 15 seconds and then released.

Vickers hardness test

This test is similar to Brinell hardness test. However the test uses a square based diamond pyramid with an angle of 136 degrees between opposite faces. The hardness number is given by the formula:

VHN = 1.8544 x P/d²

Where
P is the load applied and d is diagonal of the impression of indenter in millimeters. Details of indenter and formulae for calculation of hardness are given in Table 2.1. Comparison between the hardness numbers from different methods is given in Figure 2.5.
Measured hardness numbers are relative (not absolute or with any units). This should be kept in mind while comparing the values obtained by different techniques.

3.6.1 Elastic deformation

Any material subjected to load will deform, yield or break depending upon the magnitude of load, nature of material and its cross-sectional dimension. The load may be a tensile, compressive or shear load. The deformation will increase as the load increases. As the deformation starts, the body starts resisting the deformation by internal forces counteracting the external forces.

The moment the load increase stops, the deformation remains unchanged and body remains in a state of equilibrium, resulting from external and internal forces. If the body comes back to its un-deformed original shape and size when the load is removed, the deformation that had taken place is called elastic deformation. But if the body does not come back to original size and shape, then it is said to have deformed beyond elastic limit and deformation is called plastic deformation.

The elastic deformation is linear for most of the metals. Which means deformation is proportional to load applied. Some metals show a non-linear deformation still within elastic limit. Grey cast iron, many polymers and concrete show this non-linear behavior. In case of linear or nearly linear deformation, the relationship between strain and stress is given by Hooke’s Law which is:

E = s / e

Where

E is called modulus of elasticity or Young’s modulus which is given in giga Pascals (Gpa). For most typical metals value of this modulus ranges from 45 Gpa to 407 Gpa.

s is stress level given by s = P / A and

e is strain level given by e = dL / L₀

P is tensile load applied on the body , in Newtons (N),

A is original cross sectional area of the test specimen in m²,

dL is increase in length in meters

L₀ is original length of the test specimen, in meters

If the load is shear load instead of tensile load, shear stress is proportional to shear strain in the elastic limit of shear or at low values of shear. The constant of proportionality in this case is called modulus of rigidity (G) which is expressed in gigaPascals. Thus we have the following relationships for elastic shear:

G = t/q

t = P / A₀ and

q = tan^-1(g)

where

G = modulus of rigidity or shear modulus, in GPa,

t = shear stress , in N/m²

  = P / A₀ , in N/m²

P = instantaneous shear force applied parallel to upper and lower surfaces, in N

A₀ = cross sectional area of each of the faces prior to deformation, in m²

q = angle of deformation in radians

g = shear strain (no units)

  = tan (q)

Bulk modulus K is defined similarly.

3.6.2 Poisson’s ratio

When a metal is strained in one direction, there are corresponding strains in all other directions. Thus, if an object is strained along longitudinal direction, strains will be developed along the lateral direction also. The ratio of lateral strain to axial (longitudinal) strain is known as Poisson’s ratio, and is denoted by μ . When the axial strain is tensile, the lateral strains are compressive and when axial strains are compressive, the lateral strains are expansive. Hence, lateral strains are always opposite in sign to the sign of axial strain. This means if a body elongates in one direction, its dimension is reduced in another direction perpendicular to it. The value of Poisson’s ratio varies from metal to metal and is usually between 0.3 to 0.6.

3.6.3 Stress-strain diagrams

The relationship between stress and strain is usually shown on a plot of stress versus strain, stress on vertical axis (ordinate) and strain on horizontal axis (abscissa). It is common practice to prepare the plots of load applied versus strain generated. The load applied could be tensile, compressive, shear, and the strain could be elongation, compression, deflection, or twist. A typical stress-strain diagram is shown in Figure 3.6.

True stress and true strain

Conventional definitions of stress and strain are:

Stress = Load applied / original cross sectional area

Strain = increase or decrease of size / original size.

These conventional definitions are sufficient and acceptable for most of the engineering applications. However sometimes it is necessary to use the ‘true values’ in the deformed state instead of original values. In this case, ‘true stress’ will be load per unit of ‘true cross sectional area’ and ‘true strain’ is integral of the ratio of an incremental change in length to instantaneous length of the sample.

Both conventional as well as ‘true’ values are used in engineering practices. The conventional values are useful and are used in elastic region or the linear region whereas ‘true’ values are used in plastic region. Use of each one has its own advantages and disadvantages. So far, we have studied only linear region of stress-strain diagram. As the load increases, the specimen will start yielding. From this point, the characteristic of stress- strain relationship becomes non-linear. This is shown in Figure 3.7. In this figure the region O-A is the conventional linear region where stress is proportional to load.

Different regions of stress-strain diagram

If the stress is increased further, the material starts yielding. This region is shown as region A-B in the diagram. In this region strain increases as stress increases as in conventional region O-A, but the rate of increase is higher. In the region B-C there is considerable elongation but very little increase of stress. This zone is the plastic zone of yielding. A perfectly plastic material will not require any further increase of stress for further increase of strain, the material just keeps elongating without much increase of stress.

After this point, further elongation takes place only with additional stress which is due to a phenomenon called strain hardening. This is the region C-D shown in the diagram. Strain hardening takes place because of the change in crystalline structure of material that occurs during yielding, resulting in increased resistance of material to further deformation. The material will now reach a breaking point at point D with increasing load. The corresponding stress value is called ultimate stress. Hereafter, without any increased stress, the material keeps elongating and rupture occurs at point E.

The curve C-E^’ is the ‘true’ stress-strain diagram. Notice that along this curve, the stress is increasing even beyond ultimate stress point unlike the ‘conventional’ stress-strain diagram which uses original length and original area for stress and strain calculations.

Modulus of elasticity E is the slope of the stress-strain curve in the linear region O-A and the point A is called the proportionality limit beyond which the linear relationship fails to exist.

The stress at which the yielding of the material takes place with no noticeable increase of tensile force is called yield strain.

If a body comes back to its un-deformed original shape and size when the load is removed, the deformation that had taken place is called elastic deformation. But if the body does not come back to original size and shape, then it is said to have deformed beyond elastic limit and deformation is called plastic deformation.

In case of linear or nearly linear deformation, the relationship between strain and stress is given by Hooke’s Law (see Section 3.6.1). Shear modulus G and bulk modulus K are defined in a similar way.

If an object is strained along longitudinal direction, strains will be developed along the lateral direction also.

3.7.1 Ferrous alloys

Metals with iron as a predominant constituent are called ferrous alloys. The important ferrous alloys are:

• pig iron
• cast iron
• wrought iron
• carbon steel
• alloy steel

Ferrous alloys are produced in the largest quantity amongst all metal types because iron ore is abundantly available in the crust of the earth. Its extraction, refining, alloying and fabrication are also very economical. It is very versatile and can be alloyed in different combinations giving a large spectrum of properties. The only disadvantage of ferrous alloys is that they are susceptible to corrosion.

Pig iron

Pig iron is the raw material for all iron and steel products. This is obtained from chemical reduction of iron ore in a blast furnace by a process called as smelting. The main raw materials required for pig iron are:

• Iron ore: carbonates, hydrates or oxides of iron
• Coking coal: high quality coking coals
• Flux, limestone or dolomite. This lowers the melting point and promotes removal of ash, sulphur and residues of burnt fuel.

Pig iron contains about 3-4.5 % carbon. The high amount of carbon makes it very hard and brittle which makes it unsuitable for any commercial use.

Cast iron

Pig iron when re-melted and refined becomes cast iron. It contains 3-4.5% carbon and other alloying elements particularly silicon, sulphur, manganese and phosphorous are also present in negligible quantities. There are varieties of cast iron based upon the conditions in which carbon exists. The most common varieties are gray cast iron, white cast iron, malleable cast iron, chilled cast iron, alloy cast iron and mechanite cast iron. Grey cast iron is ductile, white cast iron is brittle and malleable cast iron is very tough. These are widely used varieties of cast iron.

Wrought iron

This is highly refined iron with less than one percent of carbon and a small amount of slag that gives the metal a peculiar fibrous structure. Wrought iron also possesses non-corrosive and better fatigue characteristics. It is tough, malleable and ductile. It can be forged and welded. It is used for the manufacture of bolts and nuts, chains, crane hooks, railway couplings, pipe and pipe fittings, plates, sheets, bars and boiler tubes, etc.

Carbon steel

Carbon steel contains carbon up to 1.5% distributed throughout the mass of metal. There is no free carbon in the form of graphite. Carbon steels are classified according to the carbon content as

• Low carbon or mild steel with 0.05 to 0.3 % carbon
• Medium carbon steel with 0.3 to 0.6 % carbon
• High carbon steel with 0.6 to 1.5 % carbon
• Tool steel with1.0 to 1.5 % carbon

Alloy steel

Many properties of the steel can be improved by addition of certain other elements such as chromium, nickel, manganese, silicon, vanadium, molybdenum, tungsten, phosphorous, copper, titanium, zirconium, cobalt and aluminum. These elements may be used separately or in different combinations to obtain different characteristics in the steel. Various reasons for alloying could be to improve and to produce fine grained steel, for example:

• wear resistance
• corrosion resistance
• electrical properties
• mechanical properties such as tensile strength, elasticity, ductility etc
• harden ability and hardness
• machinability
• weld ability
• high temperature resistance

3.7.2 Non-ferrous alloys

Metals and alloys that do not contain iron as a base are known as non-ferrous metals and alloys. The important characteristics of non-ferrous metals are:

• Susceptibility to corrosion
• Low density
• Good formability
• Softness and facility of cold working
• High electrical conductivity
• Special magnetic properties
• Attractive colors
• Fusibility and ease of casting

However they have lower melting points, low strength at higher temperatures and higher shrinkage as compared to ferrous metals. The main non-ferrous metals and alloys are:

• Copper and its alloys
• Aluminum and its alloys
• Magnesium and its alloys
• Titanium and its alloys
• Lead and its alloys
• Zinc and its alloys
• Nickel and its alloys

Copper and its alloys

Copper is extracted from the ore called pyrites and has a distinctive red color. It is relatively soft, malleable, ductile and flexible but very tough and strong. It is a very good conductor of electricity, second only to silver. Copper can be easily cast, forged, rolled or drawn into wires. Its melting point is 1083° C. It is useful for making pipes, tubes, munitions, etc.

There is a wide range of metals with which copper can be alloyed. Some of these alloys are explained below.

• Copper-aluminum alloy (aluminum bronze): contains 6% aluminum and 10% copper. Useful for decoration purposes and imitation jewelry.
• Copper-tin alloy (tin bronze): 5-25 % tin and 75-90 % copper. Hard, wear-resistant. Can be cast, rolled, stamped, and drawn into wires, rods, sheets. Better corrosion resistance as compared to brasses. Useful for pump fittings, hydraulic linings, utensils, bearings, bushes.
• Copper zinc alloy (brass): As much as 50 % zinc. Can be cast, hot forged, cold forged, cold rolled into sheets, drawn in wires, extruded through dies. Melting point 800-1000°C, Non corrosive, soft, ductile. It has high tensile strength, good fusibility, and good surface finish. It is poor conductor of electricity.
• Copper-nickel alloy (Monel metal): 60% nickel, 38% copper and a small amount of aluminum or manganese. It is white, tough, and ductile. Can be welded, soldered or brazed. It has good corrosion resistance, high strength at elevated temperatures. Can be heat treated.
• Copper-tin-antimony alloy (babbit metal): This is tin based white metal with 88 % tin, 8 % antimony and 4 % copper. It is soft, has low coefficient of friction and little strength. It is ideally suited for bearings and is commonly used with cast iron box for high pressure and loads.
• Copper-tin-phosphorus alloy (phosphor bronze): Wrought phosphor (93.7 % Copper, 6 % tin, 0.3 % phosphorous) increases strength, ductility and soundness of casting. It has good wear resistance, high elasticity, and resistance to salt water corrosion.
• Copper-silicon-manganese/zinc alloy (Silicon bronze): Copper 96%, Silicon 3%, Manganese/Zinc 1%. Good corrosion resistance, high strength when cast, rolled, stamped, forged, pressed either hot or cold. It can be welded by all usual methods. Used in boilers, tanks, stoves etc for high strength and good corrosion resistance.
• Copper, zinc, lead and little manganese (Manganese bronze): This alloy is highly resistant to corrosion .It is stronger and harder than phosphor bronze. Used for bushes, plungers, feed pumps, worm gears.
• Copper, tin zinc, (Gun metal) 88 % Copper, 2 % Zinc 10 % tin. The metal is very strong, resistant to water and atmospheric corrosion. Used for boiler fitting, bushes, bearings, glands etc.
• Copper and tin (Bell metal): Copper 80% and tin 20%. Hard and resistant to surface wear. Used for making bells, gongs and utensils.

Aluminum and its alloys

Aluminum is produced from aluminum oxide ore (alumina) which is etracted from the mineral bauxite. It is silvery white in color; very light (2.7gm/cm³ compared to steel density of 7.9 gm/cm³), it is a non corrosive metal and used very extensively in aircraft and in automobiles components. Even though it is weak and soft in its pure form, its alloys are hard and rigid. Aluminum alloys can be easily formed, turned, cast, forged and die cast.

Its high resistance to corrosion and toxicity makes it suitable for cooking utensils. It is a good electricity conductor and therefore used for power transmission. It is also good conductor of heat. It has high ductility. It can be easily beaten into foils. A pure aluminum foil has a high reflecting power and used for reflectors, mirrors and telescopes. Water and air has practically no effect on it. The melting point of aluminum is sufficiently high (658°C) but lower compared to ferrous metals and alloys.

Even though aluminum is a soft and weak metal, its alloys are hard and strong while retaining the lightness. Aluminum alloys could be cast or wrought and age hardened. Duralumin (3.5 –4.5 % Cu, 0.4-0.7 % Mn, 0.4-0.7 % Mg) and Y-alloy (3.5-4.5 % Cu, 1.8-2.3 % Ni, 1.2-1.7 % Mg) are good examples of aluminum alloy. Y-alloy retains its strength at high temperature and is very useful for pistons and aero-engines.

Magnesium alloys

These are lightest amongst all structural alloys (1.7 gm/cm³), relatively soft and elastic (elastic modulus of 45 Gpa), difficult to deform at room temperature. It has a low melting temperature (651°C). It is chemically unstable and susceptible to corrosion in marine environments. It can be easily cast or wrought. Main alloying elements are aluminum, zinc and manganese. This alloy is extensively used for aircraft structures, missile, light luggage, chain saws, power tools, steering wheels and columns, seat frames, audio-video equipment, computer communication equipment, etc.

Titanium alloys

These alloys are comparatively heavy (4.5 gm/cm³), have high melting point (1668°C), are extremely strong (1400 MPa). They are highly ductile and can be easily forged or machined. It has high chemical reactivity with other materials at elevated temperatures. These alloys are having strong corrosion resistance. The cost of manufacturing is very high. Its use is limited aircraft structures, space vehicles, and the petroleum and chemical industries.

Lead and its alloys

Lead is heaviest of all common metals, extracted from an ore called galena that is actually lead sulphate. It has bluish grey color and dull metallic lustre. It is very soft, malleable and ductile metal and can be rolled very easily. It resists corrosion even in acidic environment. Therefore it is used in water pipes, roof covering, sheathing of electrical cables, construction of chemical plants, batteries, etc. Melting point is 327°C. Lead alloyed with tin forms solders. When alloyed with small percentage of arsenic, it is used to produce bullet heads.

Zinc and its alloys

Zinc is obtained from zinc ore ‘blended (zinc sulphide)’ and ‘calamine (zinc carbonate)’.

Zinc is a fairly heavy, bluish white metal. It has good corrosion resistance and is very cheap. Its melting point is 419° C.

Method of applying zinc coating is known as galvanizing. Brass is the most widely used copper zinc alloy. (This is already explained above in copper alloys).

Muntz metal is 40% zinc and 60% copper. Strong, hard, more ductile than brass. It is excellent for temperatures around 700-750° C but not for cold working.

Nickel and its alloys

It is obtained from the nickel sulphide ore. It is tough, silver colored, harder than copper, strong as copper but less ductile. It is malleable, weldable, magnetic metal. Common nickel alloys are monel metal, german silver, nichrome, nimonics.

The important ferrous alloys are pig iron, cast iron, wrought iron, carbon steel and alloy steel. Pig iron contains about 3-4.5 % carbon. The high amount of carbon makes it very hard and brittle which makes it unsuitable for any commercial use. Pig iron when re-melted and refined becomes cast iron. It contains 3-4.5 % carbon and other alloying elements particularly silicon, sulphur, manganese and phosphorous. Wrought iron is highly refined iron with less than one percent of carbon and a small amount of slag that gives the metal a peculiar fibrous structure. Carbon steel contains carbon up to 1.5 % distributed throughout the mass of metal. There is no free carbon in the form of graphite. Many properties of the steel can be improved by addition of certain other elements such as chromium, nickel, manganese, silicon, vanadium, molybdenum, tungsten, phosphorous, copper, titanium, zirconium, cobalt or aluminum.

Copper-aluminum alloy (aluminum bronze) contains 6 % aluminum and 10 % copper. It is useful for decoration purposes and imitation jewelry. Copper-tin alloy (tin bronze) contains 5-25 % tin and 75-90 % copper. It is hard and wear-resistant. It can be cast, rolled, stamped, drawn into wires, rods, sheets. It has better corrosion resistance as compared to brasses. It is useful for pump fittings, hydraulic linings, utensils bearings, bushes. Copper zinc alloy (brass), Copper-nickel alloy (Monel metal), Copper-tin-antimony alloy (babbit metal), Copper-tin-phosphorus alloy (phospher bronze), copper-silicon-manganese/zinc alloy (Silicon bronze), Copper, tin zinc (Gun metal), Copper and tin (Bell metal) are important copper alloys.

Aluminium alloys like duralumin and Y-alloys and magnesium, titanium and zinc alloys are also commercially very useful alloys.

3.8.1 Failure and Deterioration of materials

There are three possible modes of failure of a material:

• Failure from fracture
• Failure due to fatigue
• Failure due to creep

Fracture failures

Failure of a material by stress induced separation into two or more parts/pieces is known as failure from fracture. The stress levels during fracture are normally uniform (static) (i.e. constant or changing very slowly with time) and temperatures are low compared to melting point of the material. The stresses in fracture failure could be tensile, compressive, shear or torsional. Shear or torsional failures are more often the cause for fracture failure than tensile or compressive stresses.

Shear stress induced fracture failure could be a pure shear fracture or a cleavage fracture. A shear fracture is characterized by gray and fibrous fractured surface whereas a cleavage fracture is characterized by bright and granular fractured surface due to reflection of light from the flat cleavage surfaces.

Fracture failure occurs in three steps:

• Crack initiation
• Crack propagation
• Fracture failure

A fracture is preceded by plastic deformation and absorption of strain energy in the fractured material. If the plastic deformation and energy absorption is minimal we call it a brittle fracture failure. The rate of crack propagation is very large in this case. A brittle fracture could also take place due to cleavage along crystal planes. If there is significant plastic deformation and energy absorption before failure then it is termed as ductile failure. The rate of crack propagation is slow in this case. A detailed comparison between the characteristics of ductile failure and brittle failure is given in Table 3.2.

Fracture profiles

Fracture profiles are categorized into three groups:

• Highly ductile fracture in which the specimen necks down to a point
• Moderately ductile fracture after necking
• Brittle fracture without any/much plastic deformationThese three fracture profiles are shown in Figure 3.8 below

Fatigue of metals

When the load on a part is unsteady (increasing and decreasing continuously and randomly with time) the life of the part (time before failure) is reduced considerably compared to its life under steady loading. This phenomenon is known as fatigue and the failure under such unsteady conditions of loading is termed as fatigue failure.

Fatigue failure can take place at a stress level that is considerably lower than the yield stress level for a static steady load. Fatigue is a very important consideration for machines which are subjected to continuous cyclic loading such as springs, gear teeth, valves, turbine blades, aircraft, gas engines, bridges, etc.

The importance of the fatigue failure can be judged from the statistics that 80 to 90 % of total failures in high speed machines are due to fatigue.

Fracture caused by a fatigue is brittle fracture even in ductile materials. There is no noticeable plastic deformation at the fractured surface. The surface is generally perpendicular to the direction of applied stress. One surface of the material in which fatigue failure has taken place is smooth and polished while the other looks jagged and rough. This indicates alternate loading in the region of fatigue failure. The fatigue failure usually takes place suddenly (without warning) and is catastrophic.

Fatigue strength is a structure sensitive property, which is affected by factors such as surface condition, temperature, roughness, porosity, foreign inclusions (slag, oxides), etc. These factors can reduce the fatigue life by as much as 20 %.

Fatigue failure, like fracture failure, occurs in three steps:

• Crack initiation
• Crack propagation and
• Final failure in fatigue

Fatigue life is normally specified by the total number of cycles to fatigue. Thus, the number of cycles for fatigue failure N_f is given by

N_f = Ni + Np

Where Ni is the number of cycles for crack propagation and Np is number of cycles for crack propagation before failure.

Creep and stress rupture of metals

Creep is defined as slow and progressive deformation of a material with time at constant stress levels. Properties of most of the engineering materials do not exhibit any change of stress levels at room temperature over long time duration. However at elevated temperatures, strength depends on strain rate as well as time duration. Many materials exhibit visco-elastic behavior over a period of time. Thus a material subjected to constant load at elevated temperatures for long time duration will creep. Once creep sets in, material will show reduction in cross sectional area (called necking) and strain rate keeps increasing with time till rupture and possibly a rupture failure takes place.

Creep failure is an important phenomenon for steam and chemical plants which operate at high temperatures of 450 to 550°C, boilers, ovens, gas turbines, supersonic jets, rockets, missiles, and nuclear plants all working at very high temperatures. Creep failures or ruptures are easy to identify due to the deformation (necking) that occurs. The failures may appear ductile or brittle.

The increase of strain of a metal as a function of time is shown in Figure 3.9 for a material subjected to constant load under high temperature condition. It will be observed that there are three distinct stages of creep.

The first stage of a creep, known as primary creep, is a region of decreasing creep rate. This is primarily the period of transient creep. During this period deformation takes place and resistance to creep increases until the beginning of second stage. The second stage of a creep, known as secondary creep, is a region of nearly constant creep rate or steady creep rate. The third stage, known as tertiary creep is the region accelerated creep rate. This occurs due to necking. It will end at the point of creep fracture.

Testing for creep

This test is conducted on a tensile test specimen with constant load application, maintaining a constant temperature. The specimen is placed in an electric furnace and heated to the required temperature. The strain is measured over a period of time. Strain is plotted against time. The slope of strain versus time curve gives the creep rate. The test is continued until creep failure i.e. ruptures. The creep rate is calculated separately in the three stages as explained above.

Testing for stress ruptures

Stress rupture is same as failure in creep. Rupture is measured by the breaking strength of material that is assessed by tests conducted up to breaking failure.
Breaking strength = Pf / A0
where Pf is the load at breaking failure and A0, the original cross-sectional area of specimen.

The stress rupture test is similar to Creep test except that stresses used are higher than in creep test. Test data is plotted as stress versus time. The test is conducted at different temperatures similar to the creep test. The stress rupture line shows a change of slope which is due to structural changes in the material. A typical plot of rupture test is shown in Figure 3.10.

Notice that rupture stress levels are lower for higher temperatures. Also note that the stress and time scales for the graph are logarithmic scales. The relationship is linear on these scales and becomes non-linear if drawn on a normal uniform scale. Lastly note that at very low levels of temperatures the slope is almost without a kink indicating that there is hardly any structural change in the material.

3.9.1 Direct corrosion

This corrosion is the result of chemical reaction between materials particularly metals and corrosive solutions such as acids. Acid pickling used to clean metal surfaces and etching are the results of chemical attack and are good examples of direct corrosion. To control direct corrosion, inhibiting chemicals are added in the corrosive solution

3.9.2 Electrochemical corrosion

This is the most common type of corrosion that takes place at room temperature. This is the result of reaction of metals with water or aqueous solution of salts, acids or bases. The reaction involves transfer of electrons from one surface to another. In all these cases, electricity flows from areas of one metal surface to other areas through the solution (known as the electrolyte). There must be some potential difference between the two metal surfaces for flow of electricity between them.

The metal surfaces develop anodic and cathodic characteristics because of structural and chemical inhomogeneities exising in the metals. Current flows from anode to cathode and in this process anode is corroded because of flow of ions from metal to solution. The rate of reaction depends upon the amount of current flow and the nature of electrolyte.

3.9.3 Galvanic corrosion

If a metal electrode of higher potential is connected to another of lower potential, both kept in an electrolyte, current will flow through the connecting wire. This arrangement is known as galvanic cell. Galvanic corrosion also takes place if two dissimilar metals are in electrical contact with each other and they are exposed to electrolyte.

3.9.4 High temperature corrosion

High temperature corrosion is known as oxidation and is a dry corrosion. Oxide films and scale are formed on metal surface at high temperature causing corrosion such as rusting of ferrous alloys.

3.9.5 Factors influencing the rate of corrosion

The rate of corrosion depends on the current flowing from cathode to anode. This is influenced by many parameters which are associated either with nature of metal used as electrodes or with the environment to which it is exposed. Some of them are:

• electrode potential of the metal. Usually anodic material corrodes faster.
• chemical inhomogeneities e.g. inclusions, impurities, etc.
• physical inhomogeneities e.g. regions of high residual stress
• passivity of the metal i.e. formation of thin film of oxide.
• ion concentration i.e. pH value. Acidic solutions cause faster corrosion.
• nature and concentration of other ions and degree of agitation
• increased temperature increases higher corrosion.

There are many types of corrosion, for example:

• Uniform corrosion: corrosion which is uniform over given surface and relatively superficial.
• Pitting: a localized corrosion through electrochemical reaction
• Crevice corrosion: occurs in cracks or crevices formed between mating surfaces of metal assemblies and takes the form of pitting or etched patches.
• Fretting and selective corrosion: local surface discolorations and deep pits.
• Stress corrosion: a combination of tensile stress and corrosive environment causes failure of metal structures. The stress may be residual or applied. The rate of stress corrosion depends on stress level, corrosive agent, time and temperature of exposure, structure of the metal, amount of plastic strain, etc.
• Erosion corrosion: the acceleration of corrosion by simultaneous abrasion by the turbulent flow of gases or liquids e.g in condenser tubes, piping, etc.

The methods of controlling and preventing corrosion depend on economic considerations and practical situations. Some of the important methods are:

• Use of high purity metals and special alloy additions
• Modification of corrosive environment
• Application of inhibitor
• Cathodic protection

Protective coatings to stop corrosion, like paints, plastics, bitumen or pitch are very common.

Metallic coatings are applied by various processes such as electroplating, cladding, hot dipping, high temperature diffusion, metal spraying and vacuum deposition. Classes of corrosion are:

• direct corrosion
• electro-chemical corrosion
• galvanic corrosion
• high temperature oxidation

4.3.1 Planar force systems

When all forces are acting only in one plane (for example XY, or YZ, or XZ plane only in Figure 4.2), these are called planar forces.

The coordinate system for analysis

• X-axis: horizontal direction
• Y-axis: vertical direction
• Z-axis: normal to the plane (or perpendicular to this page you are looking at)

Planar Static Equilibrium

There are three equations of static equilibrium:

• The sum of the forces in the x-direction is equal to zero
• The sum of the forces in the y-direction is equal to zero
• The sum of the moments about the z-axis is equal to zero

4.3.2 Forces and moments

A force is an action that changes, or tends to change, the state of motion of the body upon which it acts.

Some books also quote a definition of Force as ‘an agent, which produces or tends to produce, destroy or tends to destroy motion’. It is a vector quantity that can be represented either mathematically or graphically.

A complete description of a force includes its:

• Magnitude
• Direction
• Point of application

According to Newton’s Second Law of Motion, the applied force or impressed force is directly proportional to the rate of change of momentum. Mathematically it can be put as

• F = M x a
• F = k x M x a

Where:
F = Force acting on a body,
M = Mass of the body,
a = Acceleration,
k = Constant of proportionality

Force is measured in Newtons (abbreviated to N). It can be defined as the force, while acting upon a mass of one kilogram, produces an acceleration of 1 m/s² in the direction of which it acts. Thus:

1 N = 1 kg x 1 m/s²
= 1 kg/m/s²

When a 1 kg body is accelerating at 9.81 m/s² the force acting on the body is 9.81 N. A 1 kg mass, attracted towards the earth with an acceleration of 9.81 m/s² experieces a 1 kilogram force, briefly written as Kgf. Thus:

1 Kgf = 1 Kg x 9.81 m/s²
= 9.81 Kg m/s²
= 9.81 N (since 1N = 1 Kg/m/s² )

Kilogram force (Kgf) is also known as Gravitational or Engineers’ Unit of Force.

Concept of Moments

The concept of moments is the turning effect produced by a force, on the body, on which it acts. In other words, the tendency of force to cause a body to pivot, spin or rotate about an axis or a point. The moment of the force is equal to the product of the force and the perpendicular distance of the point, about which the moment is required, and the line of action of the force (see Figures 4.4 and 4.5).

Mathematically

Moment of a Force at “A” = Force x Distance
= F x l

4.3.3 Concept of Couples

A couple is defined as two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance (see Figure 4.6). The fact that the forces are equal in magnitude and opposite in direction means they cause rotation.

The magnitude of the couple (i.e. moment of couple) is the product of one of the forces and the arm of the couple.

Mathematically at point Y, Moment of Couple formed at ‘Y’ can be put as
Mo = F x d

4.3.4 Common Types of Loads

There are various types of forces essential to consider during any mechanical design. Component size, their supports and many other design factors depend on the quantity and the type of the load. Figure 4.7 shows some typical types of loads.

Support Reaction Forces

According to the Newton’s Third Law there is always a reaction to any action. When a load is applied on any machine or its part it is balanced by the support reactions. Calculation of correct support reactions is important while designing. There can be various reactions at a single support, dependent upon the force, its type, point of application and type of support.

Beam Support Conventions

Figure 4.9 shows a beam (here you can see a pipe supported on roller [which can slide left or right]) supported on roller where the reaction will be purely acting perpendicular to the applied vertical force. Any force applied from the side i.e. left to right will cause reaction in terms of movement. If the roller is supporting the beam at some angle then the reaction ‘RB’ will be in angle to the support B.

As shown in Figure 4.10, if a beam is supported in the fashion as shown, the reactions at the point B will be Rbx in X direction and RBy in Y direction (vertically upward direction).

Figure 4.11 shows a fixed support beneath the beam which results in reaction as shown (due to the weight of beam).

4.5.1 Gears

Gears act like levers and are mainly used to transmit the power or rotary motion between two shafts. Gears can change the direction in which a force is applied; or increase or reduce a force or the distance over which a force is applied. When a definite velocity ratio is required, gears are used, as in the case of watch mechanism. A gear drive is also provided when the distance between driver and follower is very small.

Gears work in teams. Two gears working together are called a gear train. The gear on the train to which the force is first applied is called the driver. The final gear on the train to which the force is first applied is called the driven gear. Any gears between the driver and the driven gears are called the idlers.

Gear Trains

A gear train is the arrangement of gears in a gear box to achieve the required speed reduction or higher speed and torque or power. In industry a maximum of 5 stages of reductions are used, except some exceptional cases which are specially designed to achieve some special purpose requirement of speed and higher torque.

A gear train is a set or system of gears arranged to transfer rotational torque from one part of a mechanical system to another. Two are shown in Figure 4.14.

Gear trains consists of:

• Driving gears: attached to the input shaft.
• Driven gears: attached to the output shaft
• Idler gears: interposed between the driving and driven gear in order to maintain the direction of the output shaft the same as the input shaft or to increase the distance between the drive and driven gears. A compound gear train refers to two or more gears used to transmit motion.

Types of Gears

Spur gears have teeth parallel to the axis of rotation and are used to transmit motion to a parallel shaft (Figure 4.15a).

Helical gears have teeth inclined to the axis of rotation. They are not as noisy as spur gears, and cause some thrust loads. Sometimes used for nonparallel shafts. The double helical gears are known as herringbone gears.

When two non-intersecting and non-parallel (i.e. non-coplanar shafts) are connected, the gear arrangement is called a skew bevel gearing or spiral gearing. This type of gear have line of contact, the rotation of which about the axes generate the two pitch surfaces known as hyperboloids.

Bevel gears (Figure 4.15b) have teeth formed on conical surfaces and transmit motion between intersecting shafts.

Worm gears (Figure 4.15c) are used when high speed ratios (e.g. more than 3) is required. The worm gearing is essentially a form of spiral gearing in which the shafts are usually at right angles. This type of gearing has the disadvantage of low efficiency.

In internal gearing the gears of two shafts mesh internally as shown in Figure 4.15e. The larger gear is called an annular wheel and the smaller one is pinion. Both gears rotate in same direction.

Rack and pinion gears are used predominantly to convert rotary motion into linear motion. If we look at Figure 4.15 d and e, we will notice that the two gears are meshed in a line. The straight line gear is called as rack and the circular one as pinion.

The rack and pinion arrangement is commonly found in the steering mechanism of cars or other wheeled, steered vehicles. This arrangement provides a lesser mechanical advantage than other mechanisms such as recirculating ball, but much less backlash and greater feedback, or steering “feel”. The use of a variable rack was invented by Arthur E. Bishop, to improve vehicle response and steering “feel” on-centre, and was fitted to many new vehicles after he created a hot forging process to manufacture the racks, thus eliminating any subsequent need to machine the form of the gear teeth.

Gear Terminology

Figure 4.16 shows the terms used when discussing gears. In closer detail:

• Pitch Circle: is an imaginary circle which by pure rolling action, would give the same motion as the actual gear.
• Pitch circle diameter: the diameter of the pitch circle. The size of the gear is usually specified by the pitch circle diameter.
• Pitch surface: the surface of the rolling discs which the meshing gears have replaced at the pitch circle.
• Addendum: the radial distance of a tooth from the pitch circle to the top of the tooth.
• Dedendum: the radial distance of a tooth from the pitch circle to the bottom of the tooth.
• Addendum circle: the circle which is concentric to the pitch circle and passes through the top of the teeth.
• Dedendum Circle: Also called the root circle, passes or is drawn through the bottom of teeth.
• Circular pitch: the distance measured on the circumference of the pitch circle from a point of one tooth to the corresponding point on the next tooth. It is usually denoted by Pc.
• Pc= π x D / T , where
• D= Diameter of the pitch circle, and T = Number of teeth on the wheel
• Or Pc / π = D/T
• Whole depth: the radial distance from the addendum and the dedendum circle of a gear. It is equal to the sum of the addendum and dedendum.
• Working depth: the radial distance from the addendum circle to the clearance circle. It is equal to the sum of addendum of two meshing gears.
• Tooth Thickness: the width of the tooth measured along the pitch circle.
• Width of space: the width of space between the two adjacent teeth measured along the pitch circle.
• Face and Flank of tooth: Face is the surface of the tooth above the pitch surface and Flank is below the pitch surface.
• Top Land: the surface of the top of the tooth.
• Fillet Radius: The radius which connects the root circle to the profile of tooth.
• Other terms you may come across when talking about gears are:
• Diametral pitch: the ratio of number of teeth to the pitch circle diameter in millimeter. It is denoted by Pd, mathematically
•        Pd = T/ D
•             = π / Pc
• Module: the ratio of number of teeth to the pitch circle diameter in millimeters to the number of teeth. It is usually denoted by “m”. Mathematically,
•         Module, m = D/T
• The recommended series of modules are 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, and 50.
• Clearance: In two meshing gears, clearance is the radial distance from top of the tooth of one gear to the bottom of the tooth of second gear. A Circle passing through the top of the meshing gear is a clearance circle
• Backlash: the difference between the width space and the tooth thickness, measured on the pitch circle.
• Pressure Angle: the angle between the common normal to two gear teeth at the point of contact and the common tangent at the pitch point.

Speed Ratios

Figure 4.17 shows two wheels; one wheel with radius “r” and a bigger wheel with radius “R”. Let us consider that a Force “F” acting tangentially at two wheels shows that the velocity component at two wheels will be equal. We can put this mathematically as:

Ti = Force x radius
= F x r and
To = F x R

if ‘Vi’ and ‘Vo’ are velocity components, therefore

Vo/Vi = R/r or
N = R / r

If ‘T’ & ‘t’ are the number of teeth on the bigger and smaller gear, respectively, and we have seen that R / r = T / t , therefore N = T / t.

The above figure 4.18 shows that in order to have a constant angular velocity ratio for all positions of the wheels, P must be the fixed point for the two wheels. In other words the common normal at the point of contact between a pair of teeth must always pass through the pitch point. This is fundamental condition which must be satisfied while designing the profiles for the teeth of gear wheels, known as the Law of Gearing.

N total = R1/R2 x R2/R3 x R3/R4 x … Rn-1/Rn
N total = N1 x N2 x N3 … Nn

Now consider a case of ‘N’ numbers of gear i.e. a Gear train with N numbers of gears meshed together such as that shown in Figure 4.19.

Gear Forms, Systems and Materials

Gear Form
The two types/forms of teeth which are commonly used are cycloidal and involute.

• Cycloidal teeth: a cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line. When a circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epi-cycloid. On the other hand, if a circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypo cycloid.
• Involute Teeth: an involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping or by a point on a taut string which is unwrapped from a reel.

Gear/Tooth System:
The tooth system is a standard which specifies the relationships involving addendum, dedendum, working depth, tooth thickness, and pressure angle.

The following four systems of gear teeth are commonly used in practice.

• 14.5 degree Composite system used for general purpose gears. It is stronger but has no interchangeability .The tooth profile of this system has cycloidal curves at the top and bottom and involute curve at the middle portion. The teeth are produced by formed milling cutters or hobs.
• The tooth profile of 14.5 degree Full depth Involute system was developed for use with gear hobs for spur and helical gears.
• The 20 degree Full depth Involute system results in a stronger tooth because of increase in pressure angle from 14.5 to 20 degree which increases/widens the tooth at base.
• 20 Degree Stub Involute systems have a strong tooth to take heavy loads.

If the point of contact between the two teeth is always on the involute profiles of both the teeth (of two meshing gears) then interference may be avoided. The minimum number of teeth on the pinion which will mesh with any gear (also rack) without interference are shown in Table 4.2.

Material

For gear manufacture the material selection mainly depends upon the strengths and service condition like wear and noise. The gears may be manufactured from metallic materials like cast iron, steel and bronze or non-metallic materials like wood, rawhide, compressed paper and synthetic resins like nylon.

Due to its ease in producing complicated shapes, cast iron is widely used for manufacturing gears. Good wearing strength and excellent machinability are added advantages of cast iron. Cast iron is used when smooth action is not that important.

Plain carbon steel or alloys steel are used when high strength of gears is required. It is common practice to heat-treat the steel when toughness and tooth hardness are required at the same time.

4.5.2 Flexible Machine Elements (Belts and Chains)

Belts and chains fall into the category of flexible machine elements that can transmit power from one shaft to another by means of pulleys which may rotate at the same or different speeds depending upon the size of follower pulley. The advantages are that they can transmit power over long distances, and can absorb shock loads and have relatively low cost.

The amount of power transferred depends upon following factors:

• Velocity of the belt
• The tension under which the belt is placed on the pulleys.
• The arc of contact (indirectly the area of contact and slippage factor) between the belt and follower pulley.
• The conditions under which the belt is used. (They do not have infinite life, hence must be replaced at the first signs of wear.)

To use the belts efficiently:

• Belts must be inspected regularly.
• Can be used for synchronizing (timing) purposes.
• Can drive more than one shaft at a time.
• Belts can slip and hence the centre distances must be correct (belts are supplied in standard sizes).
• Belt tensioners can be used to supply tension without adjusting the centre distances.

Figure 4.19 shows a belt and pulley system.

Types of Belts

Although there are many types of belts (customized as per requirement) used in industries, the following are the most important types of belts:

• Flat belt: The flat belt is mostly used in factories and workshops, where moderate amount of power is to be transmitted, from one pulley to another when two pulleys are not more than 8 meters apart.
• V-Belt: This type is used when two pulleys are near to each other and where a great amount of power is to be transmitted. The pulleys used in this case have slots of V shape on it. The cross sectional dimension of V belts have been standardized by manufacturers, with each section designated by a letter of the alphabet or in numbers for sizes.
• Circular belt or rope: It is the same as a flat belt drive however is used when the center distance between two pulleys is greater than 8 meters and large amount of power is to be transmitted. Rope drives use either fiber rope or wire rope. Fiber ropes are used when the distance between two pulleys is about 60 meters, whereas wire ropes are used when pulleys are up to 150 meters apart.
• Timing Belts: A timing belt is made up of rubberized fabric with steel wire to take tension load (Figure 4.20). It has teeth as shown in Table 4.5. The teeth are fitted into special grooves/slots on the pulley. The belts are generally coated with nylon fabric. A timing belt does not stretch or slip and consequently transmit power at a constant angular velocity ratio. The efficiency of this belt is around 97-99 percent. These belts don’t require any lubrication and are quieter than chain drives.

• Flat Belt Joints: The ends of open belts are joined together to form a closed loop when an endless belt is not available and the ends are joined together by one of the following methods:
• Cemented joints: These joints are made by manufacturers and are preferred over other joints due to their reliability and strength.
• Laced joints: Formed by punching holes in a line across the belt leaving a margin between the edge and the holes. Rawhide is used for lacing the two ends together to form a joint.
• Metal lace joints: Are like a staple connection. The points are driven through the flesh side of the belt and clinched on the inside.
• Hinged joint: Metal hinges may be fastened at the belt end and connected by a steel or fiber pin.
• These forms of joints are illustrated in Figure 4.21.

Types of Flat Belt Drives

• Open Belt Drive: In this arrangement the shafts are arranged parallel and rotating in same direction (Figure 4.22). In the case of large center distances the tight side should be lower one.

• Crossed or twist belt drive: The crossed or twist belt drive is used for parallel shafts which are rotating in opposite direction (Figure 4.23). To avoid the belt rubbing against itself, a maximum distance of ‘20 x width’ is maintained as a rule of thumb and the belt is rotated with the maximum speed of 15m/sec.

• Quarter turn belt drive: When the shafts are arranged as shown in Figure 4.24, i.e. perpendicular to each other, and require rotation in one direction, quarter turn belt drives are used. The pulley width is always kept 50% more than belt width (minimum 1.4 times belt width). If the distance between two pulleys or shaft is more then a guide pulley is used to guide the belt.

• Compound belt drives are used to drive more than one shaft or if the distance between driver and driven is more and a step down or step up of rpm is required. The efficiency of such drive is always less than a simple drive due to more slippage at every stage (Figure 4.25).

• Belt drive with Idler Pulleys: This type of drive is used for high velocity ratio and when the required belt tension cannot be obtained by other means. If in a parallel shaft, the driven pulley is smaller in diameter (i.e. when the application demands higher speeds in multiples of input speed), the angle of contact becomes less, and hence to increase the angle of contact in smaller pulley, idler pulleys are used as shown in Figure 4.26.

• Stepped and Cone Pulley drives: As shown in Figures 4.27 and 4.28, a stepped or cone pulley drive is used to change the speed of the driven shaft without stopping whilst the main or driving shaft revolves at constant speed. This is accomplished by shifting/changing the belt from one step to another or by shifting the position in the cone type of pulley.

• Fast and Loose Pulley drive: A fast and loose pulley drive, as shown in Figure 4.29 is used when the driven or machine shaft is to be started or stopped whenever desired without interfering with the driving shaft. A loose pulley runs freely over the machine shaft and is incapable of transmitting any power.

Velocity Ratio, Slip and Length of Belts

Velocity ratio is the ratio between the velocities of the driver and the follower (see Figure 4.30).

Let d = diameter of driver
D = diameter of follower
N1 = Speed of driver in r.p.m
N2 = Speed of driven/follower in r.p.m
Considering zero slippage of belt.

Therefore, the length of belt passing over the driver in one minute is
= π x d x N1 (assuming belt thickness negligible)

And the length of belt passing over the driven in one minute
= π x D x N2

Since the length of belt passing over the driver and follower is same or equal, then
π x d x N1 = π x D x N2

And Velocity ratio N1/N2 = D/d

If we assume thickness of belt as t then
Velocity Ratio, N1/N2 = (D+t / d+t)

In the case of a compound belt drive, where four pulleys (d1,d2,d3,d4) come into play then Velocity ratio will be:
N4 / N1 = speed of last driven/speed of driver
N4 / N1 = product of diameters of drivers/product of diameters of driven
Therefore, N4/N1 = (d1 x d3/d2 x d4)

Sometimes in belt drives the friction between pulley and belt is not sufficient to hold the belt. This may cause some forward motion of pulley without carrying belt. This is called belt slip and is generally expressed as a percentage.

Let S1 & S2 is the slip over the driver as well as driven pulley respectively

Then, Velocity of belt passing over the driver per second will be
V = (π x d x N1/60) – [( π x d x N1/60) x S1/100]
= π x d x N1/60 (1 – S1/100)

Velocity of belt passing over the driven/follower per second will be
V = π x D x N2/60 (1 – S2/100)

Therefore, π x D x N2/60 = v – v(S2/100)
= v (1- S2/100)

Hence, π x D x N2/60 = π x d x N1/60 (1 – S1/100) x (1- S2/100)

Therefore N2 / N1 = d/D x (1 – S1/100 – S2/100 )
N2 / N1 = d/D x (1 – (S1+ S2)/100 )

Now S1 + S2 = S (Total percentage of slip)
Therefore N2/N1 = d/D (1 – S/100)

If Thickness ‘t’ of Belt is considered then,
N2/N1 = (d+ t) / (D+ t) x (1 – S/100)

L = √ [4C² – (D – d)² ] + ½ (DΘ_D + dΘ_d)

where L is Length of Belt

L = π /2 (d + D ) + 2C + (d – D)²/ 4C , in terms of pulley Diameters .

4.5.3 Chains and sprockets

Advantages:

• Constant speed ratio
• No slippage or creep is involved.
• Longer life. Can handle heavy loads.
• It has ability to drive a number of shafts from a single power source.

Disadvantages:

• More expensive
• Heavier when has to transfer heavy loads.
• Requires lubrication (e.g. drip feed).
• Lubrication is available but is expensive

Chains (Figure 4.31) generally have a long life if used under proper conditions. ANSI has standardized roller chains. Figure 4.32 shows the nomenclature of roller chains. Pitch is the linear distance between the centers of roller. The width is the space between the inner link plates. The chains are manufactured in single, double, triple and quadruple strands. The dimensions of standard sizes are listed in Table 4.6.

Figure 4.34 shows a sprocket driving a chain in anti-clockwise direction. Denoting the chain pitch by p, the pitch angle Y, pitch diameter of the sprocket by D, then
Sin Y/2 = p/2 / D/2 or
D = p / sin(Y/2)
Since Y = 360 / N , where N number of sprocket teeth
D = p / sin (180/N)
The angle Y, through which the link swings as it enters contact, is called the angle of articulation.

4.5.4 Couplings

Couplings are used to transmit torque between two shafts, mainly to connect the shafts which are parallel to each other and in the same axis causing both to rotate in unison, at the same speed. Numerous types of couplings are on the market according to required torque or power to be transmitted. Some are rigid, others are flexible. Couplings protect the equipment from overload, and insulate driver from driven equipment.

Flexible couplings are used to compensate for minor amounts of misalignment and random movement between the two shafts.

Flexible couplings are rigid in torsion and flexible in bending. They are used when there is possibility of minor misalignment between two shafts which are connected to transmit power at the same speed. These couplings are suitable for conditions of vibration and shock. Excessive loads would bear on shafts and bearings without flexible couplings.
Bearings would fail prematurely and performance would suffer without couplings. These types of coupling are suitable for lower torque at higher speeds.

Flange coupling

Figure 4.36 shows a protected Flange Coupling with two separate cast iron flanges (may be made of machined steel). Each half is mounted on the shaft end and keyed to it. Generally one part will have a projected portion and the other a corresponding recess. This helps to bring the shafts in line and to maintain alignment. The flanges are coupled together by means of bolts and nuts.

Flange couplings are available in three types

• Unprotected type flange coupling
• Protected type flange coupling
• Marine type flange coupling

In a marine type of flange coupling, the coupling is an integral part of the shaft and the two parts are held together by means of tapered headless bolt numbering from 4 to 12 depending on shaft diameter.

Jaw Flex Coupling

This is a light load flexible coupling ideal for connecting directly to induction motors (Figure 4.37).

Oldham Coupling

Precision flexible coupling with large permissible parallel misalignment and outstanding durability (Figure 4.38).

Neo-Flex Coupling

This is no lubrication long-life flexible coupling ideal for medium and high speeds, and in situations subject to heavy vibration or impact (Figure 4.39).

Bellows Coupling

Compact, precision coupling made from high quality stainless steel bellows structure combines simplicity with non-backlash features (Figure 4.40).

4.5.5 Bearings

Bearings are manufactured to take pure radial loads, pure axial loads, or combination of both. The terms rolling contact bearing, anti friction bearing and rolling bearings are all used to describe the main load which is transferred through elements in rolling contact rather than in sliding contact. This section will deal with various types of bearings one by one.

Figure 4.42 shows an arrangement of a motor when a pulley is mounted and two other pulleys are mounted parallel to the shaft of motor and connected by either rope, belt (Vee or Flat) or chain and sprocket. The direction of rotation may be clockwise or anticlockwise. The main point of consideration is of type of load acting on the pulley which contains bearings as rolling element.

Here the loads acting on the pulley (or bearings) due to tension in belt is a Radial type (that is, acting in the direction of the radius of the pulley or bearing).

Consider the case of a man sitting on a revolving chair as shown in Figure 4.43.

Here the type of load (weight of man) acting on the base or the bearing in the base is acting perpendicular to the radius of base or bearing. This type of load is called a thrust load.

Plain/Bush Bearings

When surfaces rotate or slide, the sliding friction causes heat. This reduces component life and efficiency. Friction can be reduced by lubrication that keeps the surfaces apart. Selection of the correct bearing material is critical. Lubrication also dissipates heat and maintains clean contact between the surfaces. In a plain bearing relative motion is by sliding. In rolling element bearings, the motion is rolling. The load on the bearing can be a radial or axial (thrust) load. Material must have a low coefficient of friction, be able to conduct heat away from the bearing, as well as be wear and impact resistant.

Plain bearing can be classified as:

• Direct lined bearings: Housings are lined directly with bearing material by means of metallurgical bonding. Limited by manufacturing possibilities.
• Insert liners: Consist of a liner inserted into a previously machined housing
• Solid inserts: Wholly machined from suitable material
• Lined inserts: Have a backing material (cast iron, steel, copper alloy) and lined with bearing material
• Thick-walled, medium-walled, thin walled inserts
• Wrapped bushes: Pressed from flat strip of bronze, or steel lined with bearing material. Supplied as standard bushes.

Plain Bearing material

White metals:

• A range of lead or tin base alloys covered by British Standards.
• Low melting point alloys, suitable to bond with almost any surface.
• Good corrosion resistance.

Others:

• Copper lead alloys, lead bronze, tin bronze (phosphor bronze), aluminum base alloys.
• Metallic porous metal bearings manufactured by powder metallurgy.
  • Fine powders are mixed and compressed in moulds.
  • The effect is a “metal sponge” that can be impregnated with lubricating oil.

Plain Bearing Mounting is classified into three main groups:

• Journal bearings: the supporting pressure of the bearing is at right angles to the shaft axis (Figure 4.44).

• Pivot bearings: the supporting pressure is parallel to the shaft axis (Figure 4.45).

• Collar bearing: the supporting pressure is largely parallel to the axis of the shaft, but the shaft passes through the bearing so that it also supports pressure at right angles to the shaft (Figure 4.46).

Bearing types

There are many different types of standardized bearings on the market:

• Deep groove ball bearing
• Self-aligning ball bearing
• Angular contact ball bearing
• Cylindrical roller bearing
• Needle roller bearing
• Spherical roller bearing
• Taper roller bearing
• Thrust ball bearing
• Spherical roller thrust bearing
• Spherical plain bearing
• Double row angular contact thrust bearing

Figure 4.47 shows the four main components of ball bearing: outer ring, inner ring, the rolling elements or steel balls, and the separator.

Deep groove ball bearings (Figure 4.48):

• Single row deep groove most popular.
• Simple, non-separable.
• Little maintenance, high speeds.
• Cannot accommodate misalignment.

Self-aligning ball bearings (Figure 4.49):

• Two rows of balls with common raceway.
• Permits minor displacement of shaft in the housing.
• Suitable for applications where misalignment can arise.

Angular contact ball bearings (Figure 4.50):

• Line of action of the load and contacts between balls and raceway is at an angle.
• Suitable to carry combined loads.
• Single row for axial load in one direction.
• Double row for axial load in either direction.
• Also suitable for precision applications.

Cylindrical roller bearings (Figure 4.51):

• Rollers guided between integral flanges.
• Two parts can be separated.
• Easier to mount and dismount.

Needle roller bearings (Figure 4.52)

• For applications where radial space is limited and high load-carrying capacity is required in relation to height these bearings are used.

Spherical roller bearings (Figure 4.53)

• Two rows of rollers on a spherical raceway.
• Self-aligning, heavy-duty type bearing.

Taper roller bearings (Figure 4.54)

• Suitable for combined loads.
• Separable design, two parts can be mounted separately.
• Axial loads in one direction only.
• Radial loads gives rise to an induced axial load which must be counteracted.

Thrust ball bearings (Figure 4.55)

• For axial loads.
• Must have a certain axial load to prevent sliding.

Spherical roller thrust bearings (Figure 4.56)

• Can carry radial load as well.
• Has a self-aligning feature.
• Permits limited angular misalignment

Considerations for selecting a bearing

• Available space
• Space limited by machine’s design.
• Deep groove ball bearings selection for small diameter shafts.
• Cylindrical or spherical roller bearing (or deep groove) for larger applications.

Bearing loads

• Magnitude of load – roller bearings carry greater loads than ball bearings of the same size.
• Direction of load – some carry only radial loads.
• Thrust bearings only suitable for axial load.
• Spherical roller thrust bearings can carry axial and radial loads.
• Angle of contact: the greater the angle the more axial load it can carry.
• Double and single load angular contact bearings are normally used for combined loads.
• Self-aligning ball bearings and cylindrical roller bearings can also be used for combined loads.
• Spherical roller thrust bearings preferred when axial load is dominant.
• Can combine a radial and axial bearing on one shaft.

Figure 4.57 shows a comparison of various bearings according to their radial vs thrust loading capacities. This comparison is based on general considerations.

Misalignment
If a shaft can be misaligned with housing, self-aligning ball bearings (or spherical rollers) can be used (Figure 4.58). Misalignment can be caused by load on shaft.

Speeds

• Limited by temperature
• Low-friction bearings can be used for high speed applications (Figure 4.59).

Precision

• Select bearing and housing with suitable precision when required (Figure 4.60).
• Deep groove, angular contact, cylindrical rollers.

Rigidity

• With machine tools, rigidity is important.
• Cylindrical rollers or taper rollers more suitable (Figure 4.61).

• Axial displacement
• Normally install a locating (fixed) bearing and one non-locating (Figure 4.62).
• Prevents cross-location due to shaft expansion.
• Cylindrical rollers or needle rollers can be used as free bearings.

5.2.1 What is a Standard?

A standard can be defined as a set of technical definitions and guidelines “how to” instructions for designers and manufacturers. Standards, which can run from a few paragraphs to hundreds of pages, are written by experts. Standards are considered voluntary because they serve as guidelines, not having the force of law.

Standards are detailed instructions about how something is to be manufactured, managed, designed, or otherwise handled. The term ‘standard’ is sometimes used interchangeably with the term ‘specification’, although a specification is usually limited to ascertain application whereas a standard has broader, more universal application and often repetitive processes.

Organizations publish their standards; accredits users of standards to ensure that they are capable of manufacturing products that meet those standards; and provides stamps that accredited manufacturers place on their products, indicating that a product was manufactured according to a standard. Organizations cannot, however, force any manufacturer, inspector, or installer to follow their standards. Their use is voluntary.

Standards are developed in different ways through out the world. They can be produced by the government agencies, by trade associations, or by professional associations. Most of the countries have their own national standard organizations like the Canadian General Standard Board (CGSD) or the Bureau of Indian standards (BIS). In the USA the principal standard making body is American National Standard Institute (ANSI), which charters committees and accredits the other groups, to formulate standards. In the international scene, the International Organization for Standardization (ISO) is the primary standard making body.

In order to locate a standard you should (ideally) have the following:

• The name of the publishing organization (e.g., IEEE, ANSI, ASME)
• The standard number
• The title
• The date of the standard
• The subject

The process of standardization began in 1906 when the International Electrotechnical Commission was established. Then, in 1926, in the field of mechanical engineering was established the International Federation of the National Standardizing Associations (ISA) which worked until 1942 when its activity was cut short by the Second World War.

All around the world there are several organizations that define standardization as their main field of activity. We all know the ISO (International Organization for Standardization) because of their standards starting from pen production via bayonet barrels and projection of agricultural equipment to computer processors or the production of CD-ROMs.

5.2.2 What is a code?

A code is a standard that has been adopted by one or more governmental bodies and has the force of law, or when it has been incorporated into a business contract.

5.2.3 International Standards

• ISO – International Organization for Standardization

ISO Online provides access to an online catalog of ISO standards which can be searched by title word and by standard number. Ordering information is also provided. ISO standards can also be ordered through ANSI.

• IEC – International Electrotechnical Commission.

The IEC is the international standards and conformity assessment body for all fields of electrotechnology. The IEC World Wide Web Page at www.iec.ch provides access to an online catalog of IEC standards and other documents.

• ITU – International Telecommunications Union.

The ITU is an international organization within which governments and the private sector coordinate global telecom networks and services, including the coordination, development, regulation and standardization of telecommunications worldwide. The ITU website at www.itu.ch provides information on the standardization activities of the ITU.

7.5.1 Orifice plate

An orifice plate is a device which measures the rate of fluid flow. It uses the same principle namely Bernoulli’s principle which says that there is a relationship between the pressure of the fluid and the velocity of the fluid. When the velocity increases, the pressure decreases and vice versa.

An orifice plate is basically a thin plate with a hole in the middle. It is usually placed in a pipe in which fluid flows. As fluid flows through the pipe, it has a certain velocity and a certain pressure. When the fluid reaches the orifice plate, with the hole in the middle, the fluid is forced to converge to go through the small hole; the point of maximum convergence actually occurs shortly downstream of the physical orifice, at the so-called vena contracta point. As it does so, the velocity and the pressure changes. Beyond the vena contracta, the fluid expands and the velocity and pressure change once again. By measuring the difference in fluid pressure between the normal pipe section and at the vena contracta, the volumetric and mass flow rates can be obtained from Bernoulli’s equation.

The characteristics of orifice plate are:

• Pressures are measured at specified locations.
• 1.5% accuracy
• causes loss of pressure.

7.5.2 Turbine meter

Liquid turbine meter measurement combines the turbine and electronics to measure flow rate within a piping system. The turbine meter is a volumetric measurement device. It functions by sensing the linear velocity of the fluid passing through the known cross sectional area of the meter housing to determine the volumetric flow rate.

The fluid, as it passes through the meter, imparts an angular velocity (RPM) to the rotor, which is proportional to the linear velocity of the flowing fluid. The speed of rotation of the rotor is directly proportional to the volumetric rate.

The development of turbine meters giving accurate measurement over a wide range of flow rates for a large number of fluids, coupled with the advances made in the electronics industry in utilizing the turbine output for flow control and integration, are the reasons for universal acceptance of the turbine principle. It is expensive.

7.5.3 Rotameter

The Rotameter (variable area meter) is named after Rota, one of the European inventors of this flow principle in the beginning of the century. Rota invented the rotating float, which is self-guiding and has less friction in the pipe so that a more precise measurement is possible.

The rotameter is an industrial flow meter used to measure the flow rate of liquids and gases. The rotameter consists of a tube and float. The rotameter is popular because it has a linear scale, a relatively long measurement range, and low pressure drop. It is simple to install and maintain.

The rotameter’s operation is based on the variable area principle. That is, fluid flow raises a float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the float is raised. The height of the float is directly proportional to the flow rate. With liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone.

The float moves up or down in the tube in proportion to the fluid flow rate and the annular area between the float and the tube wall. The float reaches a stable position in the tube when the upward force exerted by the flowing fluid equals the downward gravitational force exerted by the weight of the float. A change in flow rate upsets this balance of forces. The float then moves up or down, changing the annular area until it again reaches a position where the forces are in equilibrium. To satisfy the force equation, the rotameter float assumes a distinct position for every constant flow rate. However, it is important to note that because the float position is gravity dependent, rotameters must be vertically oriented and mounted.

7.6.1 Direct Level Measurement

Direct methods employ physical properties such as fluid motion and buoyancy, as well as optical, thermal, and electrical properties. Direct level measurement does not require compensation for changes in level caused by changes in temperature. Direct level measurements show the actual level of the interface and measure liquid surface.

7.6.2 Indirect Level Measurement

Indirect level measurement involves converting measurements of some other quantity, such as pressure to level by determining how much pressure is exerted over a given area at a specific measuring point, the height of the substance above that measuring point can also be determined. For example, the formula used to determine the height of water in an open tank is:
h = P /0.433 psi
Where:
h = height,
p = pressure indicated on a gage,
0.433 psi = pressure exerted by one square inch of water, one foot high.
For substances other than water, the liquid’s specific gravity (the ratio of the liquid’s density to water’s density) must be factored into the level calculation:
h = P / 0.433 psi (G)
Where:
G = specific gravity

Temperature can also affect the accuracy of indirect level measurement. Substances have a tendency to expand when heated and contract when cooled. Gases are greatly affected by changes in temperature, while solids are affected very little. Because indirect level measurement is sensitive to specific gravity and the effects of temperature, it is necessary to compensate for these factors to ensure accurate measurement.

When selecting a measuring device, it is important to consider the operating parameters and the physical and chemical properties of the process materials.

7.6.3 Float devices

These devices operate by float movement with a change in level. This movement is then used to convey a level measurement. An object of lower density than the process liquid is placed in the vessel, causing it to float on the surface. The float rises and falls with the level, and its position is sensed outside the vessel to indicate level measurement.

Floats can also be used with magnets to detect and indicate level. This type of measurement system uses the attraction between two magnets to follow the level of a process liquid.

7.7.1 Bimetallic strip

Bimetallic thermometers use the differences in thermal expansion properties of metals to provide temperature measurement capability. Stripes of metals with different thermal expansion coefficients are bonded together. When temperature increases, it causes the assembly to bend. When this happens, the metal strip with the large temperature coefficient of expansion expands more than the other strip. The angular position versus temperature relation is established by calibration so that the device can be used as a thermometer.

7.7.2 Resistance temperature devices

Resistive temperature devices capitalize on the fact that the electrical resistance of a material changes as its temperature changes. Two key types are the metallic devices (commonly referred to as RTDs), and thermistors. As their name indicates, RTDs rely on resistance change in a metal, with the resistance rising more or less linearly with temperature.

7.7.3 Thermistors

Thermistors are semiconductors formed from complex metal oxides, such as oxides of cobalt, magnesium, manganese, or nickel. They are available with positive temperature coefficients of resistance (PTC thermistors) and with negative temperature coefficients of resistance (NTC) thermistors. NTC thermistors are used almost exclusively for temperature measurement. Despite the nonlinear nature of thermistors, readout instrument circuits have also been developed to provide a nearly linear output voltage. Thermistors are based on resistance change in a ceramic semiconductor; the resistance drops nonlinearly with temperature rise.

The most common problem related to thermistor accuracy is interchangeability. Thermistor accuracy can also be affected by several mechanical or chemical actions that change its electrical resistance.

7.7.4 Thermocouples

Thermocouples depend on the seebeck effect. That is when a conductor is placed in a temperature gradient, electrons diffuse along the gradient and an emf, or thermo voltage, is generated. The magnitude of the emf depends on the material and also on its physical condition. To measure the generated thermal emf (or Seebeck emf), the circuit must be completed using a second conductor of different material. This is joined to the first conductor at the point of measurement and passes through the same temperature gradient, forming a thermocouple. The thermocouple emf is then the difference between the emfs generated in the two conductors.

In practice, thermocouples have two junctions. One of the junctions is held at the temperature, t₁, to be measured, for example in a furnace. The second reference junction is held at temperature t₂ which is usually the melting point of pure ice. This can be done with real melting ice or electronically, but with some loss of accuracy. The difference in the emfs generated by the two conductors is then given by:

where E is the net emf generated and S_a and S_b are the Seebeck coefficients of conductors a and b.

Many different thermocouple combinations have been used, but only 8 are standardized in IEC 584-1. These include 3 noble metal thermocouples using platinum and platinum-rhodium alloys, widely used for temperature measurement up to 1600 °C. The remaining 5 mainly use nickel-based alloys, which are cheaper and more suitable for industrial use up to about 1200 °C. Other refractory alloys can be used up to and beyond 2000 °C.
The simplicity, ruggedness, low cost, small size and wide temperature range of thermocouples make them the most common type of temperature sensor in industrial use. But potential depends on metal properties and temperature.

7.8.1 Photodiodes

A semiconductor two-terminal component with electrical characteristics that are light-sensitive are called photodiodes.

They are designed to collect and focus the ambient light close to the junction. They are normally biased in the reverse, or blocking, direction; the current therefore is quite small in the dark. When light falls on junction the diode resistance drops and current flows. Photodiodes are used both to detect the presence of light and to measure light intensity.

7.8.2 Phototransistors

All transistors are light sensitive. Phototransistors are specifically designed to take advantage of this important property. Phototransistors are devices with light-sensitive collector-base p-n junction with a large exposed base region. Light entering the base replace the base-emitter current of ordinary NPN transistors. Therefore a phototransistor directly amplifies variations depending on the amount of light. Base current produced is directly proportional to light intensity. Phototransistors are commonly used in light-activated circuits and switches.

7.8.3 Photoresistor

Resistance is a linear function of light intensity. An array of light sensors across a space is often required, e.g. camera.

8.1.1 Pumps – an introduction

A pump is a device used to move liquids/fluids. Pumps are the machines which make many every day tasks possible that we often take for granted. Indeed without pumps our world would be a much different place than we know it today. An early application includes the use of the windmill or watermill to pump water. Today, the pump is used for irrigation, water supply, gasoline supply, air conditioning systems, refrigeration (usually called a compressor), chemical movement, sewage movement, flood control, marine services, etc.

Because of the wide variety of applications, pumps are available in plenty of shapes and sizes: from very large to very small, from handling gas to handling liquid, from high pressure to low pressure, and from high volume to low volume.

A pump moves liquids from lower pressure to higher pressure, and overcomes this difference in pressure by adding energy to the system. A gas pump is generally called a compressor, except in very low pressure-rise applications, such as in heating, ventilating, and air-conditioning, where the operative equipment consists of fans or blowers.

8.1.2 Characteristics of a good pump

A good pump must be:

• Safe
• No risks involved in operation
• Reliable
• Available when required
• Efficient
• Able to Impart energy to fluid

8.1.3 Pump nomenclature

Figure 8.1 shows two images of pumps. Key terms are:

Impeller – An impeller is a circular metallic disc with built-in passages for the flow of fluid. Impellers are generally made of bronze, various plastics, cast iron or stainless steel. The number of impellers determines the number of stages of the pump. A single stage pump has one impeller and is best suited for low head (pressure) service. A two-stage pump has two impellers in series for medium head service. A multi-stage pump has three or more impellers in series for high head service.

Shaft – The shaft transfers the torque from the motor to the impeller during the startup and operation of the pump.

Casing – The main function of casing is to enclose the impeller at suction and delivery ends and thereby form a pressure vessel. The pressure at suction end may be as little as one-tenth of atmospheric pressure and at delivery end may be twenty times the atmospheric pressure in a single-stage pump. A second function of casing is to provide a supporting and bearing medium for the shaft and impeller.

8.1.4 Classification of pumps

The pumps can be broadly classified on the basis of transfer of mechanical energy. Pumps add energy to the liquid by either of two methods, centrifugal force or positive displacement.

Positive Displacement ( PDP ) pumps

• Reciprocating pump
  The reciprocating pump is a positive displacement pump. It sucks and raises the liquid by actually displacing it with piston/plunger that executes a reciprocating motion in a closely fitting cylinder. These pumps are almost become obsolete because of the cost. However, small hand operated pumps such as cycle pumps, football pump, village well pumps and oil drilling pumps etc are widely used. They are best suited for small capacities and high heads. They are classified as follows:
  • Piston / Plunger pumps: Here water is in contact with one side or two side of piston or plunger to force the liquid out of a closed cylinder.
  • Diaphragm pumps: Diaphragms can be used in place of pistons to impart the pumping energy. Diaphragm pumps have the advantage of allowing zero leakage around the piston.

• Rotary pump
  Positive displacement of liquid can also be accomplished by rotary devices such as a vane type rotary pump. Liquid enters the space between the rotor and stator from the inlet on the right. Vanes in the rotor then apply mechanical force directly to the liquid and force it to move in a confined space as the rotor turns:
  • Single rotor
  • Multiple rotor

Dynamic pumps

In dynamic pumps, the increase in fluid energy levels is due to a combination of centrifugal energy, pressure energy and kinetic energy. They are classified as follows:

• Rotary pump
  • Radial flow or Centrifugal pumps: The energy transfer, in a radial flow pump occurs mainly when the flow is in its radial path. They are also called centrifugal pumps.
  • Axial flow pumps: The energy transfer occurs when the flow is in its axial direction.
  • Mixed flow pumps : The energy transfer takes place when the flow comprises radial as well as axial components.

• Special Design pumps
  • Jet pump: A jet pump consists of radial flow pump with jet nozzle at the suction end. It helps to increase the suction lift beyond the normal limit of 8m of water head. It is possible to increase the suction lift up to 60m.
  • Hydraulic ram: This is device with which small quantities of water can be pumped to higher levels from the large quantity of water of low head. It works on the principle of water hammer. When flowing liquid is suddenly stopped, the change in momentum of liquid mass causes a sudden rise in pressure. This pressure is utilised to raise the liquid to higher levels.

8.1.5 Unique advantages of each type

Positive displacement pumps

Positive displacement pumps operate with a series of working cycles where each cycle encloses a certain volume of fluid and moves it mechanically through the pump into the system. Depending on the type of pump and the liquid being handled, this happens with little influence from the back pressure on the pump. While the maximum pressure developed is limited only by the mechanical strength of the pump and system and the driving power available, the effect of that pressure can be controlled by a pressure relief or safety valve.

A major advantage of the P.D. pump is that it can deliver consistent capacities because the output is solely dependent on the basic design of the pump and the speed of its driving mechanism. This means that, if the liquid is not moving through the system at the required flow rate, it can always be corrected by changing one or both of these factors. Positive displacement pumps are suitable for handling highly viscous liquids. They are also self-priming and therefore have the ability to handle liquids with a certain volume of entrained air.

The Piston Pump
The oldest and best known positive displacement pump is the piston pump which uses a piston or plunger to force liquid from the inlet side to the outlet side of the pump. As the piston moves upwards, it will reduce the pressure in the pump body which causes the pressure in the suction line to open the suction valve and permit the liquid to flow into the pump. In the same way, the higher pressure in the discharge line keeps the discharge valve closed. This is called the suction cycle.

When the plunger moves downwards, it increases the pressure in the body which closes the suction valve and opens the discharge valve to force the liquid out of the pump. This is called the ‘discharge cycle’. As the movement of the plunger inside the pump body creates pressure inside the pump, you must ensure that this kind of pump is never operated against a closed discharge valve. All discharge valves must be open before the pump is started, to prevent any fast build up of pressure that could damage the pump or the system.

The Diaphragm Pump
A single diaphragm pump can be similar to the plunger pump except that the up and down motion causing movement of the liquid through the pump is created by a diaphragm instead of a plunger.

Larger models of this kind of pump are used to pump heavy sludge and debris-laden wastes from manholes and catch basins. Smaller models of the same basic design are used as chemical metering or proportioning pumps where a very constant and specific amount of liquid is required.

The Air Operated Double Diaphragm Pump
A more commonly used type of diaphragm pump is the air-operated double diaphragm pump which uses pressurized air to actuate the diaphragms instead of a mechanical device. This is basically two pumps in one where one is on the suction cycle while the other is on the discharge cycle. The air valves alternately pressurize the inside of one diaphragm chamber and exhaust air from the other one.

Internal Gear
Internal gear pumps carry fluid between the gear teeth from the inlet to outlet ports. The outer gear (rotor) drives the inner or idler gear on a stationary pin. The gears create voids as they come out of mesh and liquid flows into the cavities. As the gears come back into mesh, the volume is reduced and the liquid is forced out of the discharge port. The crescent prevents liquid from flowing backwards from the outlet to the inlet port.

External Gear
External gear pumps can also use gears which come in and out of mesh. As the teeth come out of mesh, liquid flows into the pump and is carried between the teeth and the casing to the discharge side of the pump. The teeth come back into mesh and the liquid is forced out the discharge port. External gear pumps rotate two identical gears against each other. Both gears are on a shaft with bearings on either side of the gears.

Vane pump
The vanes – blades, buckets, rollers, or slippers – work with a cam to draw fluid into the pump chamber and force it out of the pump chamber. The vanes may be in either the rotor or stator. The vane-in rotor pumps may be made with constant or variable displacement pumping elements.

Lobe pump
Fluid is carried between the rotor teeth and the pumping chamber. The rotor surfaces create continuous sealing. Both gears are driven and are synchronized by timing gears. Rotors include bi-wing, tri-lobe, and multi-lobe configurations

Screw pump
Screw pumps carry fluid in the spaces between the screw threads. The fluid is displaced axially as the screws mesh.

Single screw pumps are commonly called progressive cavity pumps. They have a rotor with external threads and a stator with internal threads. The rotor threads are eccentric to the axis of rotation.

Multiple screw pumps have multiple external screw threads. These pumps may be timed or untimed.

Centrifugal pump

Centrifugal Pumps are rotodynamic pumps which convert Mechanical energy into Hydraulic energy by centripetal force on the liquid. Typically, a rotating impeller increases the velocity of the fluid. The casing, or volute, of the pump then acts to convert this increased velocity into an increase in pressure. So if the mechanical energy is converted into a pressure head by centripetal force, the pump is classified as centrifugal. Such pumps are found in virtually every industry, and in domestic service in developed countries for washing machines, dishwashers, swimming pools, and water supply.

A wide range of designs are available, with constant and variable speed drives. Horizontal shafts are the most common. Single-stage pumps are usual in the smaller ratings. Pumps with up to 11 stages are in service. A demanding duty is boiler feed, and today’s designs are typically 3-4 stage, with speeds of up to 6000 r/min.

This is how centrifugal pumps operate:

• Liquid is forced into an impeller either by atmospheric pressure, or in case of a jet pump, by artificial pressure.
• The vanes of impeller pass kinetic energy to the liquid, thereby causing the liquid to rotate. The liquid leaves the impeller at high velocity.
• The impeller is surrounded by a volute casing or in case of a turbine pump, a stationary diffuser ring. The volute or stationary diffuser ring converts the kinetic energy into pressure energy.

The main components of a centrifugal pump are as follows:

• Rotating components: an impeller coupled to a shaft
• Stationary components: casing, casing cover, and bearings.
• Stand

After motors, centrifugal pumps are arguably the most common machine, and they are a significant user of energy. Given design margins, it is not unusual for a pump to be found to be over-sized, having been selected poorly for its intended duty. Running a constant speed pump throttled causes energy waste. A condition monitoring test can detect this condition and help size a smaller diameter impeller, either new, or by machining the initial one, to achieve great energy reduction.

Pumps also wear internally, at a rate varying with the liquid pumped, materials of construction and operating regime. Again, condition monitoring can be applied to detect and quantify the extent and rate of wear. It can also help decide when overhaul is justified on an energy-saving basis.

8.1.6 Pump selection

There are certain rules that make it easier to determine the proper pump according to application. The main criteria of the selection of the type of pump are values of discharge (Q), Head (H) and speed (N).

• When the speed is low and it is possible to increase the pump speed it is better to use multi-stage pump; the number of stages are decided on the basis of the head and the type of the pump to be used.
• The type of impeller is another aspect of selection
• Axial flow pumps are employed for very low heads of about six meters and for large discharges.
• Radial pumps are used when the head is high.

The key features that favor selection of PD pump are:

• They can be designed for higher heads than centrifugal pumps.
• They provide constant flow at different heads.
• They have self-priming features.
• More efficient in handling highly viscous fluids.
• Handle low flow, high head situations more efficiently than centrifugal pumps.
• Generally speaking pumps tend to shear liquids more as speed is increased and the centrifugal is a high speed pump. This makes the PD pump better able to handle shear sensitive liquids. Shear rates in PD pumps vary by design but they are generally low shear devices, especially at low speeds. Internal gear pumps, for example, have been used to pump very shear sensitive liquids. It is important to contact the manufacturer for specific information on shear rates and application recommendations
• PD pumps generally can produce more pressure than centrifugals. This will depend on the design of each pump but pressures of 250 psi (580 feet) are not unusual for a PD pump with some models going to over 1000 psi (2,300 feet). This is a significant difference between the two principles. The capability for a PD pump to produce pressure is so great that some type of system overpressure protection is required. So they are used for lifting oils from deep oil wells.
• PD pumps tend to run at lower speeds than centrifugals. This will have an impact on seal life, so PD seals tend to last longer than seals in centrifugal pumps. In addition, to assure adequate seal life a centrifugal will typically require one of the seal flush plans.
• A PD pump, because of its lower shaft speed typically does not need an external flush plan. Also, generally speaking, low speed mechanical devices tend to operate longer than high speed mechanical devices.

The key features that favor selection of a centrifugal pump are:

• For comparable power ratings centrifugals are cheaper.
• Centrifugal pumps deliver liquid at uniform pressure without shocks or pulsations.
• More efficient in handling high flow rate – low head conditions.
• They can be directly connected to motor drive without the use of gears or belts.
• No danger of over-pressurization.
• They can handle liquids with some solids in suspension.
• Installation and maintenance is easier and cheaper.

As illustrated in Figure 8.11, at low rate of flow and high total head or pressure, reciprocating pumps are common. These pumps operate with good efficiency in this region, but also can produce pressure pulsations. This pump type selection graph can be used as an indicator of the most efficient pump type for a specific set of conditions.

8.1.7 Pump characteristics

Head

The head of the pump may be expressed in following ways:

• Static head: It is sum of suction head ( it is the vertical height of the centre line of the pump shaft above the liquid surface in the sump from which liquid is being raised) and delivery head ( It is vertical height of the liquid surface in the tank )
• Manometric head: It is the head against which pump has to work. It is the head measured across the pump inlet and outlet flanges.
• Total, gross or effective head: It is equal to static head plus all the head losses occurring in flow before, through and after the impeller.

Change in head (H) between inlet and exit is

H = [ p/ρg + V^{2 /}2g + Z]₂ – [ p/ρg + V^{2 /}2g + Z]₁ = h₅ – h_f

Where h_s is pump head supplied and hf is losses (losses of head in the impeller and casing)

Efficiency of the pump

The work performed by a pump is a function of the total head and of the weight of the liquid pumped in a given time period. Pump shaft power (Ps) is the actual horsepower delivered to the pump shaft, and can be calculated as follows:

Pump efficiency = Hydraulic power / Pump shaft power

Pump output, water horsepower or hydraulic horsepower (hp) is the liquid horsepower delivered by the pump, and can be calculated as follows:

Hydraulic power = Q (m3/s) x (hd- hs) (m) x ρ (kg/m3) x g (m/s2) / 1000

Where:
Q = flow rate
hd= discharge head
hs = suction head
ρ = density of the fluid
g = acceleration due to gravity

Pump alignment with motor

The shafts of the pump and its driver will rotate on a common axis. If the shafts are not coaxial, the resulting moments will increase the forces on the pump shaft and bearings, causing accelerated wear and premature bearing failure and unreliable operation.

Alignment occurs when two lines that are superimposed on each other form a single line. Misalignment is a measure of how far apart the two lines are away from forming that single line. The two lines we’re concerned with here are the centerlines of the pump shaft and the driver shaft. In one condition, the two lines can be parallel with each other, but at a constant distance apart. This is referred to as offset or parallel misalignment. In the other, one line will be at an angle to the other. This is referred to as angular misalignment.

Bringing the motor shaft into alignment with the pump shaft usually involves moving the front and rear feet of the motor, vertically and horizontally, until the shafts are aligned within acceptable tolerances. In addition to their dependency on data such as speed of rotation, horsepower, spacer length, shaft size, etc., acceptable alignment tolerances also depend, to a large extent, on the level of reliability the pump user expects.
While dial gauges are still a viable method of establishing shaft alignment, laser alignment systems are now providing increased accuracy that reduces maintenance costs while improving reliability. These systems reduce the time it takes to achieve a high level of accuracy—and do so without the need for mathematical graphing and calculating expertise.

8.1.8 The pitfalls of pump piping

Piping design is one area where the basic principles involved are frequently ignored, resulting in problems such as hydraulic instabilities in the impeller, which translate into additional shaft loading, higher vibration levels and premature failure of the seal or bearings. As there are many other reasons why pumps could vibrate, and why seals and bearings fail, the trouble is rarely traced to incorrect piping.
It has been argued that because many pumps are piped incorrectly, yet are operating quite satisfactorily, piping procedure is not important. That doesn’t make questionable piping practice correct, it merely makes it lucky. Any piping mistakes that are made on the discharge side of a pump frequently can be accommodated by increasing the performance of that pump. Problems on the suction side however, can be the source of repetitive failures, which may never be traced back to that area and could continue undetected.

These things can be avoided by following a few straightforward rules.

• Provide the suction side with a straight run of pipe, in a length equivalent to 5-10 times the diameter of that pipe, between the suction reducer and the first obstruction in the line. This will ensure the delivery of a uniform flow of liquid to the eye of the impeller, which is essential for an optimum suction condition.
• The pipe diameter on both the inlet and the outlet sides of the pump should be at least one size larger than the nozzle itself.
• Eliminate elbows mounted on, or close to, the inlet nozzle of the pump.
• There is always an uneven flow in an elbow, and when one is installed on the suction of any pump, it introduces that uneven flow into the eye of the impeller. This can create turbulence and air entrainment, which can result in impeller damage and vibration.
• Eliminate the potential for vortices or air entrainment in the suction source.
• If a pump is taking its suction from a sump or tank, the formation of vortices can draw air into the suction line. This usually can be prevented by providing sufficient submergence of liquid over the suction opening.
• Arrange the piping in such a way that there is no strain imposed on the pump casing.

8.2.1 Classification of compressors

There are two types of compressors: positive displacement and dynamic.

Positive Displacement Compressors

• Reciprocating
• Screw
• Sliding Vane
• Lobe
• Scroll
• Vane
• Liquid Ring

Dynamic Compressors

• Centrifugal
• Axial Flow

Compressors can be classified as reciprocating, rotary, jet, centrifugal, or axial-flow, depending on the mechanical means used to produce compression of the fluid, or as positive-displacement or dynamic-type, depending on how the mechanical elements act on the fluid to be compressed. Positive-displacement compressors confine successive volumes of fluid within a closed space in which the pressure of the fluid is increased as the volume of the closed space is decreased. Dynamic-type compressors use rotating vanes or impellers to impart velocity and pressure to the fluid.

PD Compressors

Reciprocating Compressors

The rotary-screw compressor uses two meshed rotating helical rotors within a casing to force the gas into a smaller space. Advantages of this type of compressor include smooth, pulse-free gas output with high output volume.

The rotary screw compressor is a positive displacement compressor, made of two intermeshing helical rotors contained in the housing. The driving rotor is usually made of four lobes and the driven rotor usually consists of six lobes. As the helical rotor grooves pass over the suction port they are filled with gas. As the rotors turn, the grooves are closed by the housing walls, forming a compression chamber to provide lubrication, sealing, cooling and avoid any metal to metal contact; lubricant is injected into the compression chamber. As the rotors mesh, the compression chamber volume decreases, compressing the gas/lubricant mixture toward the discharge port where it exits as the chamber passes over the port. Most manufacturers build a slide stop valve into the casing that can be actuated either manually or with an air or hydraulic piston. This variable volume ratio allows the packager to customize the built in compression ratio as closely as possible to the actual field conditions.

Typical Applications

Rotary screw compressors are ideal in large volume/low suction pressure applications and to upgrade existing reciprocating compressor installations. Since they operate with few moving parts, low maintenance and high reliability are inherent in rotary screws.

The most popular type is the reciprocating (or piston-and-cylinder) compressor, which is useful for supplying small amounts of a gas at relatively high pressures. In this type of compressor, a piston is driven within a cylinder; the gas is drawn in through an inlet valve on the suction stroke of the piston and is compressed and driven through another valve on the return stroke.

A sliding (rotary) vane compressor has a solid rotor mounted inside a water jacketed cylinder, similar to that of a jacketed water section of a reciprocating cylinder. The water jacket around the cylinder is used for cooling. The rotor is fitted with blades that are free to move in and out of the longitudinal slots in the rotor. Blade configurations range from 8 to 12 blades, depending upon manufacturer and pressure differentials. The blades are forced out against the cylinder wall by centrifugal force, creating individual cells of gas which are compressed as the rotor turns. As it approaches the discharge port, this area is reduced and the gas discharged.

Typical Applications
Sliding (rotary) vane compressors are designed to be utilized in very harsh environments. When it comes to vapor recovery, landfill gas, and other low ratio and discharge pressure applications, the sliding vane compressor is typically the most commonly used due to the lubrication system.

Features
Unlike other types of compressors where the lube oil is mixed with the gas stream and then re-used, the lubrication system of a sliding vane is once thru lubrication, thus not contaminating or breaking down the oil viscosity. The sliding (rotary) vane design does not have critical tolerances, due to the use of blades. Since a sliding (rotary) vane does not operate at close tolerances, its life expectancy exceeds those compressor designs that depend on close tolerance.

A reciprocating compressor

A reciprocating compressor consists of a crankshaft (driven by a gas engine, electric motor, or turbine) attached to a connecting rod, which transfers the rotary motion of the crankshaft to a crosshead. The crosshead travels back in forth in a crosshead guide. The crosshead converts the rotating motion to a reciprocating motion. The piston rod is attached to the crosshead and the piston (which is contained in a cylinder) is attached to the piston rod. The piston acting within the cylinder then compresses the gas contained within that cylinder. Gas enters the cylinder through a suction valve at suction pressure and is compressed to reach desired discharge pressure. When the gas reaches desired pressure, it is then discharged through a discharge valve. Desired discharge pressure can be reached through utilization of either a single or double acting cylinder. In a double acting cylinder, compression takes place at both the head end and crank end of the cylinder. The cylinder can be designed to accommodate any pressure or capacity, thus making the reciprocating compressor the most popular in the gas industry.

Typical Applications

Reciprocating compressors are ideal where higher discharge pressures are required or where there is a great pressure difference. When it comes to corrosive applications such as landfill gas, the reciprocating compressor will provide the most flexibility, including multiple staging and ability to add or remove staging should conditions warrant. Reciprocating compressors are either single- or double-acting. In single-acting machines the compression takes place on only one side of the piston; double-acting machines use both sides of the cylinder for compression. Multiple cylinder arrangements are common.

Centrifugal Compressors

The compressor shown above is called a centrifugal compressor because the flow through the compressor is turned perpendicular to the axis of rotation. The very first British jet engines used centrifugal compressors, and they are still used on small turbojets and turbo shaft engines.

The centrifugal compressor consists of a rotating impeller mounted in a casing and revolving at high speed. This causes a gas that is continuously admitted near the center of rotation to experience an outward flow and a pressure increase due to centrifugal action. Centrifugal compressors are particularly suited for compressing large volumes of gas to moderate pressures; they produce a smooth discharge of the compressed gas.

In the axial compressor, the air flows parallel to the axis of rotation. The compressor is composed of several rows of airfoil cascades. The stages have rotors, which are connected to the central shaft and rotate at high speed. The other stages, stators, are fixed and do not rotate. The job of the stators is to increase pressure and keep the flow from spiraling around the axis by bringing the flow back parallel to the axis.

In an axial-flow compressor, the gas flows over a set of airfoils spinning on a shaft in a tapered tube. These draw in gas at one end, compress it, and output it at the other end. Axial-flow compressors are used in aviation and in industry, as well as for chemical gas compression in gas turbine engines.

Air is the most frequently compressed gas, although natural gas, oxygen, and nitrogen are also often compressed. Compressed air exerts an expansive force that can be used as a source of power to operate pneumatic tools or to control such devices as air brakes. Air under compression can be stored in closed cylinders to provide continuous or as-needed supply of pressurized air.

8.2.2 Compressor selection

• Capacity
• Pressure ratio
• Power supply characteristics
• Size and weight of compressor
• Type of foundation required
• Type of controls
• Maintenance costs
• Availability and cost of cooling water

8.3.1 Introduction

A turbine is a rotary engine that extracts energy from a fluid flow. The simplest turbines have one moving part, a rotor assembly, which is a shaft with blades attached. Moving fluid acts on the blades, or the blades react to the flow, so that they rotate and impart energy to the rotor. Early turbine examples are windmills and water wheels.

Gas, steam, and water turbines usually have a casing around the blades that focuses and controls the fluid. The casing and blades may have variable geometry that allows efficient operation for a range of fluid-flow conditions.

A device similar to a turbine but operating in reverse is a compressor or pump.

8.3.2 Classification of turbines

A machine that generates rotary mechanical power from the energy of a moving fluid, such as water ( water turbine), steam (steam turbine), hot gas ( gas turbine), or wind (wind turbine). Turbines convert the kinetic energy or pressure of the fluid to mechanical energy through the principles of impulse (impulse turbines) and reaction (reaction turbines), or a combination of the two. They are mainly classified into

• Reaction turbines
• Impulse turbines

Reaction turbine

This is a turbine that develops torque by reacting to the pressure or weight of a fluid; the operation of reaction turbines is described by Newton’s third law of motion (action and reaction are equal and opposite).

In a reaction turbine the nozzles that discharge the working fluid are attached to the rotor. The acceleration of the fluid leaving the nozzles produces a reaction force on the pipes, causing the rotor to move in the opposite direction to that of the fluid. The pressure of the fluid changes as it passes through the rotor blades. In most cases, a pressure casement is needed to contain the working fluid as it acts on the turbine; where a casing is absent, the turbine must be fully immersed in the fluid flow as in the case of wind turbines. Francis turbines and most steam turbines use the reaction turbine concept.

These turbines are again sub classified according to direction of flow of fluid in the runner

• Radial flow: In this type turbine fluid flows radially.
• Axial flow: In this type turbine fluid flows parallel to the axis of the turbine shaft. Kaplan turbine is an example. In this turbine the runner blades are adjustable and can be rotated about pivots fixed to the boss of the runner. If the runner blades of the axial flow turbines are fixed these are called propeller turbines. This is for medium head and medium rate of flow.
• Mixed flow: In mixed flow turbines the fluid enters the blades radially and comes out axially, parallel to the turbine shaft. Francis turbines have mixed flow runners, which are used for low heads and large quantities of flow.

Impulse turbine

A turbine that is driven by high velocity jets of water or steam from a nozzle directed on to vanes or buckets attached to a wheel. The resulting impulse (as described by Newton’s second law of motion) spins the turbine and removes kinetic energy from the fluid flow.

Before reaching the turbine the fluid’s pressure head is changed to velocity head by accelerating the fluid through a nozzle. This preparation of the fluid jet means that no pressure casement is needed around impulse turbine. Most types of turbine exploit the principles of both impulse turbines and reaction turbines. However, a few, such as the Pelton turbine, use the impulse concept exclusively.

A Pelton turbine has one or more free jets discharging water into an aerated space and impinging on the buckets of a runner. Draft tubes are not required for impulse turbine since the runner must be located above the maximum tail water to permit operation at atmospheric pressure.

A Turgo turbine is a variation on the Pelton. The Turgo runner is a cast wheel whose shape generally resembles a fan blade that is closed on the outer edges. The water stream is applied on one side, goes across the blades and exits on the other side.

(a) Side view of wheel and jet
(b) Top view of bucket
(c) Typical velocity diagram

A Pelton wheel consists of rotor, at the periphery of which is mounted equally spaced double hemispherical buckets. Fluid is transferred from a high head source through penstock which is fitted with a nozzle through which the fluid flows out at a high speed jet. A needle spear moving inside the nozzle controls the fluid flow through the nozzle and the same time provides a smooth flow.

All the available potential energy is thus converted into kinetic energy before the jet strikes the buckets. The pressure all over the wheel is constant and equal to atmosphere so that energy transfer occurs due to purely impulse action.

Velocity triangles can be used to calculate the basic performance of a turbine stage. Gas exits the stationary turbine nozzle guide vanes at absolute velocity Va1. The rotor rotates at velocity U. Relative to the rotor, the velocity of the gas as it impinges on the rotor entrance is Vr1. The gas is turned by the rotor and exits, relative to the rotor, at velocity Vr2. However, in absolute terms the rotor exit velocity is Va2. The velocity triangles are constructed using these various velocity vectors. Velocity triangles can be constructed at any section through the blading (for example: hub, tip, midsection and so on) but are usually shown at the mean stage radius. Mean performance for the stage can be calculated from the velocity triangles, at this radius, using the Euler equation:

Typical velocity triangles for a single turbine stage
ΔH = U * ΔV ω/g

8.3.3 Comparison between turbines

8.3.4 Advantages

• Very high power-to-weight ratio, compared to reciprocating engines
• Smaller than most reciprocating engines of the same power rating
• Moves in one direction only, and doesn’t vibrate, so very reliable;
• Simpler design.

8.3.5 Disadvantages

• Cost is much greater than for a similar-sized reciprocating engine (very high-performance, strong, heat-resistant materials needed);
• Uses more fuel when idling compared to reciprocating engines – not so good unless in continual operation.

8.3.6 Selection of turbines

The following points should be considered while selecting right type of the turbine

• Specific speed: High speed is essential where head is low and output is large
• Rotational speed: This depends upon specific speed.
• Efficiency: Turbine should give highest overall efficiency for various operating conditions.
• Disposition of turbine shaft: The vertical shaft arrangement is better for large sized reaction turbine therefore it is almost universally adopted. In case of large size impulse turbines, horizontal shaft arrangement is mostly employed.
• Head

Example

The following data relates to a Pelton wheel:

Solution
H = 72 m; N = 240 r.p.m; P = 115 kW; Cv =0.98 ή = 85%
Design of the Pelton wheel means to find diameter of the wheel D and depth of buckets and number of buckets.

8.4.1 Types of flows

In the case of Newtonian fluid, the flows can be classified depending on characteristic Reynolds numbers, such as:

• Laminar or viscous flow
• Transition flow
• Turbulent flow

Laminar or viscous flow

A laminar flow is one in which paths taken by the individual particles do not cross one another and move along well defined paths, this type of flow is also called stream-line or viscous flow. Examples are the flow through a capillary tube, flow of blood in veins and arteries, ground water flow.

Characteristics of Laminar flow:

• ‘No slip’ at the boundary.
• Due to viscosity, there is a shear between fluid layers
• The flow is rotational.
• Due to viscous shear, there is continuous dissipation of energy and for maintaining the flow energy must be supplied externally.
• Loss of energy is proportional to first power of velocity and first power of viscosity
• The flow remains laminar as long as pVl/µ is less than critical value of Reynolds number.

Turbulent flow

A turbulent flow is that in which fluid particles move in a zig zag way. The fluid motion is irregular and chaotic and there is complete mixing of fluid due to collision of fluid masses with one another. The fluid masses are interchanged between adjacent layers. The shear in this flow is mainly due to momentum transfer.

Example: High velocity flow in a conduit of large size. Nearly all fluid problems encountered in engineering practice have a turbulent character.

Characteristic of turbulent flow:

• The velocity distribution is more uniform than in laminar flow.
• The velocity gradients near the boundary shall be quite large resulting in more shears.
• Random orientation of fluid particles in a turbulent flow gives rise to additional stresses called the Reynolds stresses.
• Formation of eddies, mixing and curving of path lines in turbulent flow results in much greater frictional losses for the same rate of discharge, viscosity and pipe size.

8.4.2 Reynolds number

The flow of real fluid in pipes – real meaning a fluid that possesses viscosity hence looses energy due to friction as fluid particles interact with one another and the pipe wall. The shear stress induced in a fluid flowing near a boundary is given by Newton’s law of viscosity:

τ < du / dy

This tells us that the shear stress, τ, in a fluid is proportional to the velocity gradient – the rate of change of velocity across the fluid path. For a “Newtonian” fluid we can write:

τ = μ (du / dy)

Where the constant of proportionality, μ, is known as the coefficient of viscosity. It is important to determine the flow type as this governs how the amount of energy lost to friction relates to the velocity of the flow. And hence how much energy must be used to move the fluid.

Osborne Reynolds in 1883 with the help of simple experiment demonstrated the existence of different types of flows. The water was made to flow from the tank through the glass tube into the atmosphere and the velocity of flow was varied by an adjusting valve. The liquid dye was introduced into the flow through a small tube.

The following observations were made

1. When the velocity of flow was low the dye remained in the form of straight and stable filament passing through the glass tube. This is Laminar flow where the loss of head is directly proportional to velocity.

2. With the increase of velocity a critical state is reached at which the dye filament showed irregularities and began to wave means the flow is no longer laminar but was a transitional state.

3. With further increase in velocity of flow the fluctuations in the filament of dye became more intense and the dye diffused over the entire cross section of the tube, due to the intermingling of the particles of the flowing fluid which is Turbulent flow. The loss of head is approximately proportional to square of velocity.

The flow in a closed conduit depends upon the following factors
Width or thickness of pipe (L)
Density of the liquid (ρ)
Viscosity of the liquid (µ)
Velocity of the flow (V)
By combing these variables Reynolds determined a quantity equal to ρVL / µ which is known as Reynolds number (Re)

Re = ρVL / µ

When 0 < Re < 1 → highly viscous laminar “creeping” motion

1 < Re < 10³ → Laminar

10³ < Re < 10⁴ →Transition to turbulence

10⁴ < Re < ∞ Turbulent

8.4.3 Flow in circular pipes

When fluid flows in a pipe, it experiences some resistance to its motion, due to which its velocity and ultimately the head available is reduced. This loss of energy is classified as follows:

• Major energy losses are due to friction
• Minor energy losses are due to sudden enlargement or contraction of pipe, bend of pipe, an obstruction in pipe or pipe fittings etc.

These losses which are due to friction are calculated by Darcy-Weisbach formula

Pressure loss during laminar flow in a pipe

In general the shear stress τ_w is almost impossible to measure. But for laminar flow it is possible to calculate a theoretical value for a given velocity, fluid and pipe dimension. The pressure loss in a pipe with laminar flow is given by the Hagen-Poiseuille equation:

Δp = 32μLu /d²

Or in terms of head

h _{f,lam =} 128μL Q/ πρgd⁴

Where h_f is known as the head-loss due to friction

Pressure loss during turbulent flow in a pipe

In this derivation we will consider a general bounded flow – fluid flowing in a channel – we will then apply this to pipe flow. In general it is most common in engineering to have. Turbulent flow – in both closed (pipes and ducts) and open (rivers and channels). However analytical expressions are not available so empirical relationships are required (those derived from experimental measurements).

h _f = 0.316 (μ/ρVd)^1/4 (L/d) (V²/2g)

So, for a general bounded flow, head loss due to friction can be written

h _f = f (L/d) (V²/2g)

Where f= Darcy coefficient of friction
L = Length of the pipe between sections 1 and 2
D = Diameter of the pipe
V= Average flow velocity
This equation is known as Darcy-Weisbach equation and it holds good for all types of flows provided a proper value of f is chosen
This equation is equivalent to the Hagen-Poiseuille equation for laminar flow with the exception of the empirical friction factor f introduced.

Selection of pipe size

The selection of the best size for a pipe to carry a given flow rate, which is a very common design exercise, is made easier if the relationship between the head loss and pipe diameter is known for the specific case of constant flow rate
For a given flow rate, the mean velocity in the pipe is given by:

1) Q = (πD²/4) V hence V = 4Q/πD²

a) Substituting for V into Poiseuille’s equation for laminar flow

i = h _f /L = 32 μV / ρgD² = 32 μ4Q/ρgπD² hence, i ά 1/ D⁴

b) And using the Darcy-Weisbach equation for turbulent flow

i = h _f /L = 4fV²/D2g = (4f /D2g) [4q/π²]² hence, i ά 1/ D⁵

The head loss is therefore inversely proportional to the diameter of the pipe raised to the fourth power for laminar flow and inversely proportional to the diameter raised to the fifth power for turbulent flow.

Colebrook-White equation for f

Colebrook and White did a large number of experiments on commercial pipes and they also brought together some important theoretical work by von Karman and Prandtl. This work resulted in an equation attributed to them as the Colebrook-White equation:

1/ √f = – 4log₁₀ [k₅/3.71d + 1.26/Re√f ]
Or
1/ f ^{1/2 =} -2.0 log [(έ/d) /3.7 + 2.51/Re_d f ^½]

It is applicable to the whole of the turbulent region for commercial pipes and uses an effective roughness value (k_s) obtained experimentally for all commercial pipes.

Note a particular difficulty with this equation. f appears on both sides in a square root term and so cannot be calculated easily. Trial and error methods must be used to get f once k_s, Re and d are known.

Moody made a useful contribution to help, he plotted f against Re for commercial pipes – see Figure 8.22.

8.4.4 Moody Chart

Figure 8.22 shows the Moody Diagram. [Note that this figure uses λ (= 4f) for friction factor rather than f. The shape of the diagram will not change if f were used instead.]

He also developed an equation based on the Colebrook-White equation that made it simpler to calculate f:

f = 0.001375 [ 1+ (200k₅/d + 10⁶/Re)^1/3

This equation of Moody gives f correct to +/- 5% for 4 × 103 < Re < 1 × 107 and for ks/d < 0.01.

The problem with these formulas still remains that these contain a dependence on ks. What value of ks should be used for any particular pipe? Fortunately pipe manufactures provide values and typical values can often be taken similar to those in Table 8.3.

So the Moody chart is used to solve three types of pipe-flow problems:

• Head-loss problem: Given d, L, and V or Q, ρ, μ, and g, compute the head loss hf
• Flow-rate problem: Given d, L, hf, ρ, μ, and g compute the flow rate Q
• Sizing problem: Given Q, L, hf, ρ, μ, and g, compute the diameter d of the pipe

8.4.5 Example

A crude oil of viscocity 0.9 poise and relative density 0.9 is flowing through a horizontal circular pipe of diameter 120mm and length 12m. Calculate the difference of pressure at two ends of the pipe, if 785 N of the oil is collected in a tank in 25 seconds

Solution:
Viscocity of the crude oil μ           = 0.9 poise = 0.09 Ns/m²
Relative density                             = 0.9
Weight density w                           = 0.9 x 9810 = 8829 N/m³
Diameter of the pipe, D                 = 120mm = 0.12 m
Length of the pipe, L                     = 12m
Weight of the oil collected in 25 s = 785 N

Difference of pressure (p₁-p₂):

The difference of pressure for laminar flow is given by

Δp = 32μLu/ d²

8.5.1 Laws of Thermodynamics

Let’s first understand the basic definitions of Heat, Work and energy.

Heat

Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess ‘heat’.

Work

Work refers to an activity involving a force and movement in the direction of the force.

Internal energy

The appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object – this is more correctly called heating.

Energy

Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle, which is “Energy can neither be created nor destroyed”.

First law of Thermodynamics

“The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to the system and the work done on the system.”

The principle of the conservation of energy states that energy can neither be created nor destroyed. When a system undergoes a complete cycle, the net heat supplied is equal to the net work done.
ΔQ = ΔU + ΔW

The net heat supplied = Change in the internal energy of the system + Work done on the system.

The First Law identifies both heat and work as methods of energy transfer which can bring about a change in the internal energy of a system. When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done by a gas at constant pressure is:

For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is:

Work done by a system decreases the internal energy of the system, as indicated in the First Law of Thermodynamics. System work is a major focus in the discussion of heat engines.

The Second Law of Thermodynamics

“The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.”

dS = dQ/T

The change in entropy can be described as the heat added per unit temperature and has the units of Joules/Kelvin (J/K).

Q > W

If the heat input to a heat engine is Q and the work output of the engine is W, then the heat supplied must be greater than the net work done, i.e. some heat must be rejected.
The second law sets limits on the possible efficiency of the machine and determines the direction of energy flow.

8.5.2 Heat engines

A heat engine is defined as a device that converts heat energy into mechanical energy or more exactly a system which operates continuously and only heat and work may pass across its boundaries.

The mechanical output is called work and the thermal energy input is called heat. Heat engines typically run on a specific thermodynamic cycle. Heat engines are often named after the thermodynamic cycle they are modeled by. They often have alternate names, such as gasoline/petrol, turbine, or steam engines. Heat engines can generate heat inside the engine itself or it can absorb heat from an external source. Heat engines can be open to the atmospheric air or sealed and closed off to the outside (Open or closed cycle).

Common thermodynamic cycles (gas only cycles)
In these cycles and engines the working fluid is always like gases:

• Carnot cycle (Carnot heat engine)
• Ericsson Cycle (Caloric Ship John Ericsson)
• Stirling cycle (Stirling engine, thermoacoustic devices)
• Internal combustion engine (ICE):
• Otto cycle (e.g. Gasoline/Petrol engine, high-speed diesel engine)
• Diesel cycle (e.g. low-speed diesel engine)
• Atkinson Cycle (Atkinson Engine)
• Brayton cycle or Joule cycle originally Ericsson Cycle (gas turbine)
• Lenoir cycle (e.g. pulse jet engine)

A heat engine absorbs heat energy from the high temperature heat source, converting part of it to useful work and delivering the rest to the cold temperature heat sink.

A heat engine performs the conversion of heat energy to mechanical work by exploiting the temperature gradient between a hot “source” and a cold “sink”. Heat is transferred from the source, through the “working body” of the engine, to the sink, and in this process some of the heat is converted into work by exploiting the properties of a working substance (usually a gas or liquid).

The general surroundings are the heat sink, providing relatively cool gases which, when heated, expand rapidly to drive the mechanical motion of the engine. The first law and second law of thermodynamics constrain the operation of a heat engine. The first law is the application of conservation of energy to the system, and the second sets limits on the possible efficiency of the machine and determines the direction of energy flow.

When we apply the first law of thermodynamics to the heat engine:
Net heat supplied = Net work done
Q1 –Q2 = W

When second law ofthermodynamics is applied:
Q1 > W

Thermal efficiency
Thermal efficiency for heat engine is the ratio of net work done in the cycle by heat supplied. It relates how much useful power is output for a given amount of heat energy input.

In general terms, the larger the difference in temperature between the hot source and the cold sink, the larger is the potential thermal efficiency of the cycle within material limits.
The efficiency of various heat engines proposed or used today ranges from 3 percent (97 percent waste heat) through 25 percent for most automotive engines, to 45 percent for a supercritical coal plant, to about 60 percent for a steam-cooled combined cycle gas turbine. All of these processes gain their efficiency (or lack thereof) due to the temperature drop across them.

The combined cycle gas turbines use natural-gas fired burners to heat air to near 1530 °C, a difference of a nearly 1500°C, and so the efficiency can be high when the steam-cooling cycle is added in.

Heat engine models – Energy reservoir model

One of the general ways to illustrate a heat engine is the energy reservoir model. The engine takes energy from a hot reservoir and uses part of it to do work, but is constrained by the second law of thermodynamics to exhaust part of the energy to a cold reservoir. In the case of the automobile engine, the hot reservoir is the burning fuel and the cold reservoir is the environment to which the combustion products are exhausted.

• PV Diagram

Heat engine processes are shown on a PV diagram. Besides constant pressure, volume and temperature processes, a useful process is the adiabatic one. An adiabatic process is one in which no heat is gained or lost by the system. The first law of thermodynamics with Q=0 shows that all the change in internal energy is in the form of work done. This puts a constraint on the heat engine process leading to the adiabatic condition. This condition can be used to derive the expression for the work done during an adiabatic process.

8.5.3 Heat pumps

A heat pump is a device which extracts heat from one place and transfer it to other place. A heat pump is a device which applies external work to extract an amount of heat Q_C from a cold reservoir and delivers heat Q_H to a hot reservoir. A heat pump is subject to the same limitations from the second law of thermodynamics as any other heat engine and therefore a maximum efficiency can be calculated from the Carnot cycle. All real heat pumps require work to get heat to flow from a cold area to a warmer area. Heat Pumps are usually characterized by a coefficient of performance which is the number of units of energy delivered to the hot reservoir per unit work input.

The coefficient of performance (COP) is a measure of a heat pump’s efficiency. It is determined by dividing the energy output of the heat pump by the electrical energy needed to run the heat pump, at a specific temperature. The higher the COP, the more efficient the heat pump. This number is comparable to the steady steady-state efficiency of oil- and gas-fired furnaces.

Coefficient of Performance = Q / W = Heat input / Net input work

For cooling effect C.O.P. >1

8.5.4 Refrigeration

The heat pump is thermodynamic counterpart of the heat engine. It raises the temperature level of heat by means of work input. In its usual form a compressor takes refrigerant vapor from a low-pressure, low-temperature evaporator and delivers it at high pressure and temperature to a condenser.

Heat pumps transfer heat by circulating a substance called a refrigerant through a cycle of evaporation and condensation. A compressor pumps the refrigerant between two heat exchanger coils. In one coil, the refrigerant is evaporated at low pressure and absorbs heat from its surroundings. The refrigerant is then compressed en route to the other coil, where it condenses at high pressure. At this point, it releases the heat it absorbed earlier in the cycle.

Refrigerators and air conditioners are both examples of heat pumps operating only in the cooling mode. A refrigerator is essentially an insulated box with a heat pump system connected to it. The evaporator coil is located inside the box, usually in the freezer compartment. Heat is absorbed from this location and transferred outside, usually behind or underneath the unit where the condenser coil is located.