Fundamentals

Stress: Stress is a measure of the internal force an object is experiencing per unit cross sectional area. Hence, the formula for calculating stress is the same as the formula for calculatingDefinition: Stress is defined as the force per unit area of a material.I.e. Stress = force / cross sectional area:

Where,σ = stress,F = force applied, andA= cross sectional area of the object.Units of s: Nm-2 or Pa.

Ultimate Tensile Strength:If the material is stretched until it breaks, the tensile stress has reached the absolute limit and this stress level is called Ultimate Tensile Strength

Yield Stress:This is also known as yield strength.On a stress strain graph beyond the yield point(or elastic limit)the material will no longer return to its original length. This means it has become permanently deformed. Therefore the yield stress is the level of stress at which a material will deform permanently. This is also known as yield strength.

Strain:Strain is defined as extension per unit length.Stresses cause strain. Putting pressure on an object causes it to stretch. Strain is a measure of how much an object is being stretched. The formula for strain is:

, OR Where e = extension = (l-lo)

where is the original length of a bar being stretched, L is its length after it has been stretched.(stretched length) Δl is the extension of the bar, the difference between these two lengths.

Strain has no units because it is a ratio of lengths.We can use the above definitions of stress and strain for forces causing tension or compression.If we apply tensile force we have tensile stress and tensile strainIf we apply compressive force we have compressive stress and compressive strain.A useful tip: In calculations stress expressed in Pa is usually a very large number and strain is usually a very small number. If it comes out much different then, you've done it wrong!

Young Modulus:Def: Young's Modulus is a measure of the stiffness of a material. It states how much a material will stretch (i.e., how much strain it will undergo) as a result of a given amount of stress.

Instead of drawing a force - extension graph, if you plot stress against strain for an object showing (linear) elastic behaviour, you get a straight line.

This is because stress is proportional to strain. The gradient of the straight-line graph is the Young's modulus, E

E is constant and does not change for a given material. It in fact represents 'stiffness' property of the material. Values of the young modulus of different materials are often listed in the form of a table in reference books so scientists and engineers can look them up.

Units of the Young modulus E: Nm-2 or Pa.Note: The values for stress and strain must be taken at as low a stress level as possible, provided a difference in the length of the sample can be measured. Strain is unitless so Young's Modulus has the same units as stress, i.e. N/m² or Pa.(The value of E in Pa can turn out to be a very large number. Therefore some times the value of E may be given MNm-2.)

Yield point : The yield strength or yield point of a material is stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible.

The point in the stress-strain curve at which the curve levels off and plastic deformation begins to occur.

The yield strength  (or elastic limit ), (units: MPa or MN/m2)

Shear Stress: If the applied load consists of two equal and opposite parallel forces which do not share the same line of action, then there will be a tendency for one part of the body to slide over, or shear from the other part:Stress parallel to the plane is usually denoted "shear stress" and can be expressed asτ = R / A      

where

τ = shear stress ((Pa) N/m2, psi)

R = Shear Resistance (N, lbf)A = Shear area (m2, in2)Note: The Shear Stress is tangential to the area over which it acts, and is expressed in the same units as Direct Stress, i.e. Load per unit Area.

Tensile stress – When two equal and opposite forces are applied to a body and the body tends to increase in length is known as tensile stress.σtensile = P/A

Compressive stress – When two equal and opposite forces are applied to a body and the body tends to decrease in length is known as compressive stress.σcompressive = P/A

Shear Stress or Tangential stress: Shear stress is similar to the direct except that the forces are applied tangentially and the body sheared or twisted. Shear Stress, ζ = Shear stress/Shear area = P/A

Torsional Stress: Shear stress produced when we apply the twisting moment to the end of a shaft about its axis is known as Torsional stress.

*Bending Stress: It is a compressive or/and tensile stress due to the non-axial forces acting on a beam. It tends to bend or deflect the beam.

*Thermal Stress: Due to the change in the material temperature, the dimensions of the material also changes. But some of the parts are not free to expand. The stress set up when the parts are not free is expand due to the change in body temperature is known as thermal stress.

Stress-strain Diagram1. Proportional limit. We see from the diagram that from point O to A is a straight line, which represents that the stress is proportional to strain. Beyond point A, the curve slightly deviates from the straight line. It is thus obvious, that Hooke's law holds good up to point A and it is known as proportional limit. It is defined as that stress at which the stress-strain curve begins to deviate from the straight line.2. Elastic limit. It may be noted that even if the load is increased beyond point A upto the point B, the material will regain its shape and size when the load is removed. This means that the material has elastic properties up to the point B. This point is known as elastic limit. It is defined as the stress developed in the material without any permanent set.

Note: Since the above two limits are very close to each other, therefore, for all practical purposes these are taken to be equal.3. Yield point. If the material is stressed beyond point B, the plastic stage will reach i.e. on the removal of the load, the material will not be able to recover its original size and shape. A little consideration will show that beyond point B, the strain increases at a faster rate with any increase in the stress until the point C is reached. At this point, the material yields before the load and there is an appreciable strain without any increase in stress. In case of mild steel, it will be seen that a small load drops to D, immediately after yielding commences. Hence there are two yield points C and D. The points C and D are called the upper and lower yield points respectively. The stress corresponding to yield point is known as yield point stress.4. Ultimate stress. At D, the specimen regains some strength and higher values of stresses are required for higher strains, than those between A and D. The stress (or load) goes on increasing till the point E is reached. The gradual increase in the strain (or length) of the specimen is followed with the uniform reduction of its cross-sectional area. The work done, during stretching the specimen, is transformed largely into heat and the specimen becomes hot. At E, the stress, which attains its maximum value is known as ultimate stress. It is defined as the largest stress obtained by dividing the largest value of the load reached in a test to the original cross-sectional area of the test piece.5. Breaking stress. After the specimen has reached the ultimate stress, a neck is formed, which decreases the cross-sectional area of the specimen. A little consideration will show that the stress (or load) necessary to break away the specimen, is less than the maximum stress. The stress is, therefore, reduced until the specimen breaks away at point F. The stress corresponding to point F is known as breaking stress.Note : The breaking stress (i.e. stress at F which is less than at E) appears to be somewhat misleading. As the formation of a neck takes place at E which reduces the cross-sectional area, it causes the specimen suddenly to fail at F. If for each value of the strain between E and F, the tensile load is divided by the reduced cross sectional area at the narrowest part of the neck, then the true stress-strain curve will follow the dotted line EG. However, it is an established practice, to calculate strains on the basis of original cross-sectional area of the specimen.

6. Percentage reduction in area. It is the difference between the original cross-sectional area and cross-sectional area at the neck (i.e. where the fracture takes place). This difference is expressed as percentage of the original cross sectional area.

Let A = Original cross-sectional area, anda = Cross-sectional area at the neck.Then reduction in area = A – a

7. Percentage elongation. It is the percentage increase in the standard gauge length (i.e. original length) obtained by measuring the fractured specimen after bringing the broken parts together.

Let l = Gauge length or original length, andL = Length of specimen after fracture or final length.

Elongation = ∴ L – l

Note: The percentage elongation gives a measure of ductility of the metal under test. The amount of local extensions depends upon the material and also on the transverse dimensions of the test piece. Since the specimens are to be made from bars, strips, sheets, wires, forgings, castings, etc., therefore it is not possible to make all specimens of one standard size. Since the dimensions of the specimen influence the result, therefore some standard means of comparison of results are necessary.

Working Stress, Allowable Stress, and Factor of Safetyworking stress is defined as the actual stress of a material under a given loading. The maximum safe stress that a material can carry is termed as the allowable stress. The allowable stress should be limited to values not exceeding the proportional limit. However, since proportional limit is difficult to determine accurately, the allowable tress is taken as either the yield point or ultimate strength divided by a factor of safety. The ratio of this strength (ultimate or yield strength) to allowable strength is called the factor of safety.

Moment of Inertia (Mass Moment of Inertia) -  is a measure of an object's resistance to changes in rotation direction Or a quantity expressing a body's tendency to resist angular accelerationthe Moment of Inertia is the mass times the square of perpendicular distance to the rotation reference axis and can be expressed asI = k m r2  wherek = inertial constant - depending on the shape of the body

Polar moment of inertia is a measure of a circular beam's ability to resist torsion. The polar moment of inertia must not be confused with the moment of inertia, which characterizes an object's angular acceleration due to a torque.polar moment of inertia has units of length4 (SI m4)

Bending moment: A bending moment is a measure of the average internal stress induced in a structural element when an external force or moment is applied to the element causing the

element to bend. The internal stresses in a cross-section of a structural element can be resolved into a resultant force and a resultant couple.

Bending strength (Flexural strength, also known as modulus of rupture, bend strength, or fracture strength): A mechanical parameter for brittle material, is defined as a material's ability to resist deformation under load.

Poisson's ratio named after Siméon Poisson, is the negative ratio of transverse to axial strain. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular or parallel to the direction of flow.ORPoisson's ratio is the ratio of the relative contraction strain, or transverse strain normal to the applied load, to the relative extension strain, or axial strain in the direction of the applied load.

Poisson's Ratio can be expressed asυ = - εt / εl     where υ = Poisson's ratioεt = transverse strain  εl = longitudinal or axial strain

Modulus of Rigidity (or Shear Modulus) is the coefficient of elasticity for a shearing force. It is defined as the ratio of shear stress to the displacement per unit sample length (shear strain).ORShear modulus or Modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain.

Density:The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ .Mathematically, density is defined as mass divided by volume.

Failure theories:

There are four important failure theories: maximum shear stress theory, maximum normal stress theory, maximum strain energy theory, and maximum distortion energy theory. Out of these four theories of failure, the maximum normal stress theory is only applicable for brittle materials, and the remaining three theories are applicable for ductile materials. Of the latter three, the distortion energy theory provides most accurate results in majority of the stress conditions. The strain energy theory needs the value of Poisson’s ratio of the part material, which is often not readily available. The maximum shear stress theory is conservative. For simple unidirectional normal stresses all theories are equivalent, which means all theories will give the same result.

Maximum Shear stress Theory- This theory postulates that failure will occur if the magnitude of the maximum shear stress in the part exceeds the shear strength of the material determined from uniaxial testing.

Maximum normal stress theory - This theory postulates that failure will occur if the maximum normal stress in the part exceeds the ultimate tensile stress of the material as determined from uniaxial testing. This theory deals with brittle materials only. The maximum tensile stress should be less than or equal to ultimate tensile stress divided by factor of safety. The magnitude of the maximum compressive stress should be less than ultimate compressive stress divided by factor of safety.

Maximum strain energy theory - This theory postulates that failure will occur when the strain energy per unit volume due to the applied stresses in a part equals the strain energy per unit volume at the yield point in uniaxial testing.

Maximum distortion energy theory - This theory is also known as shear energy theory or von Mises-Hencky theory. This theory postulates that failure will occur when the distortion energy per unit volume due to the applied stresses in a part equals the distortion energy per unit volume at the yield point in uniaxial testing. The total elastic energy due to strain can be divided into two parts: one part causes change in volume, and the other part causes change in shape. Distortion energy is the amount of energy that is needed to change the shape.

Industrial Applications of Failure Theories:Nowadays FEA based solvers are well integrated to use failure theories. User can specify kind of failure criterion in his solution method. Shear strain energy theory is the most commonly used method. These softwares can produce Von-mises stress along material,which is based on Shear strain energy theory. So user can check whether maximum Von-mises stress induced in the body crosses maximum allowable stress value. It is a common practice to introduce Factor of Safety(F.S) while designing, in order to take care of worst loading scenario. So the engineer can say his design is safe if following condition satisfies.

Chemical composition

The carbon content in steel can range from 0.1-1.5%, but the most widely used grades of steel contain only 0.1-0.25% carbon. Elements such as manganese, phosphorus and sulphur are found in all grades of steel, but, whereas manganese provides beneficial effects, phosphorus and sulphur are deleterious to steel's strength and durability.

Different types of steel are produced according to the properties required for their application, and various grading systems are used to distinguish steels based on these properties. According to the American Iron and Steel Institute (AISI), steels can be broadly categorized into four groups based on their chemical compositions:

Carbon Steels Alloy Steels Stainless Steels Tool Steels

 1) Carbon Steels:Carbon steels contain trace amounts of alloying elements and account for 90% of total steel production. Carbon steels can be further categorized into three groups depending on their carbon content:Low Carbon Steels/Mild Steels contain up to 0.3% carbonMedium Carbon Steels contain 0.3 – 0.6% carbonHigh Carbon Steels contain more than 0.6% carbon(1.5% max)

2) Alloy Steels:Alloy steels contain alloying elements (e.g. manganese, silicon, nickel, titanium, copper, chromium and aluminum) in varying proportions in order to manipulate the steel's properties, such as its hardenability, corrosion resistance, strength, formability, weldability or ductility. Applications for alloys steel include pipelines, auto parts, transformers, power generators and electric motors.

3) Stainless Steels:Stainless steels generally contain between 10-20% chromium as the main alloying element and are valued for high corrosion resistance. With over 11% chromium, steel is about 200 times more resistant to corrosion than mild steel. These steels can be divided into three groups based on their crystalline structure:

Austenitic: Austenitic steels are non-magnetic and non heat-treatable, and generally contain 18% chromium, 8% nickel and less than 0.8% carbon. Austenitic steels form the largest portion of the global stainless steel market and are often used in food processing equipment, kitchen utensils and piping.Ferritic: Ferritic steels contain trace amounts of nickel, 12-17% chromium, less than 0.1% carbon, along with other alloying elements, such as molybdenum, aluminum or titanium. These magnetic steels cannot be hardened with heat treatment, but can be strengthened by cold works.Martensitic: Martensitic steels contain 11-17% chromium, less than 0.4% nickel and up to 1.2% carbon. These magnetic and heat-treatable steels are used in knives, cutting tools, as well as dental and surgical equipment.

4) Tool Steels: Tool steels contain tungsten, molybdenum, cobalt and vanadium in varying quantities to increase heat resistance and durability, making them ideal for cutting and drilling equipment. Steel products can also be divided by their shapes and related applications:Long/Tubular Products include bars and rods, rails, wires, angles, pipes, and shapes and sections. These products are commonly used in the automotive and construction sectors.Flat Products include plates, sheets, coils and strips. These materials are mainly used in automotive parts, appliances, packaging, shipbuilding, and construction. Other Products include valves, fittings, and flanges and are mainly used as piping materials.

Generally Mild Steel:Carbon 0.16-0.18%Silicon 0.40% maxManganese 0.70-0.90%Sulphur 0.040% MaxPhosphorus 0.040% Max

Microstructure:A material's strength is dependent on its microstructure. The engineering processes to

which a material is subjected can alter this microstructure. The variety of strengthening mechanisms that alter the strength of a material includes work hardening, solid solution

strengthening, precipitation hardening and grain boundary strengthening and can be quantitatively and qualitatively explained. Strengthening mechanisms are accompanied by the caveat that some other mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle.

High carbon steel:

Effects of Alloying Elements in SteelCarbon(C)As I've already stated, the presence of carbon in iron is necessary to make steel. Carbon isessential to the formation of cementite (as well as other carbides), and to the formation ofpearlite, spheroidite, bainite, and iron-carbon martensite, with martensite being thehardest of the micro-structures, and the structure sought after by knifemakers. Thehardness of steel (or more accurately, the hardenability) is increased by the addition ofmore carbon, up to about 0.65 percent. Wear resistance can be increased in amounts up toabout 1.5 percent. Beyond this amount, increases of carbon reduce toughness andincrease brittleness. The steels of interest to knifemakers generally contain between 0.5and 1.5 percent carbon. They are described as follows:• Low Carbon: Under 0.4 percent• Medium Carbon: 0.4 - 0.6 percent• High Carbon: 0.7 - 1.5 percentCarbon is the single most important alloying element in steel.*Manganese(Mn)Manganese slightly increases the strength of ferrite, and also increases the hardnesspenetration of steel in the quench by decreasing the critical quenching speed. This alsomakes the steel more stable in the quench. Steels with manganese can be quenched in oilrather than water, and therefore are less susceptible to cracking because of a reduction inthe shock of quenching. Manganese is present in most commercially made steels.Chromium(Cr)As with manganese, chromium has a tendency to increase hardness penetration. Thiselement has many interesting effects on steel. When 5 percent chromium or more is usedin conjunction with manganese, the critical quenching speed is reduced to the point that

the steel becomes air hardening. Chromium can also increase the toughness of steel, aswell as the wear resistance. Probably one of the most well known effects of chromium onsteel is the tendency to resist staining and corrosion. Steels with 14 percent or morechromium are referred to as stainless steels. A more accurate term would be stainresistant. Stainless tool steels will in fact darken and rust, just not as readily as the nonstainlessvarieties. Steels with chromium also have higher critical temperatures in heattreatment.*Aluminum (Al)As a deoxidizer, up to 0.05% aluminum may be added to steel. For increasing fine grain characteristics or sub-zero impact properties, up to 0·10% may be added. Nitriding steels contain about 1% aluminum for promoting a high surface hardness when heated in ammonia. Still larger additions made to heat resisting steels promote resistance to scaling. Approximately 5% added to chromium steel increases electrical resistivity.*Silicon(Si)Silicon is used as a deoxidizer in the manufacture of steel. It slightly increases thestrength of ferrite, and when used in conjunction with other alloys can help increase thetoughness and hardness penetration of steel.Nickel(Ni)Nickel increases the strength of ferrite, therefore increasing the strength of the steel. It isused in low alloy steels to increase toughness and hardenability. Nickel also tends to helpreduce distortion and cracking during the quenching phase of heat treatment.Molybdenum(Mo)Molybdenum increases the hardness penetration of steel, slows the critical quenchingspeed, and increases high temperature tensile strength.*Sulphur (S)A non-metal, which combines with iron to form iron sulphides, in which form its effect is to make the steel red short but combined with manganese its influence is less injurious. In steel the sulphur content is usually specified as less than 0.05 % but it may be ad*Phosphorus (P)Although it has been used to increase the tensile strength of steel and to improve resistance to atmospheric corrosion, phosphorus is usually regarded as an undesirable impurity because of its embrittling effect. In most British specifications the maximum permitted is 005 %, but in steel for nitriding it may be restricted to a maximum of 0·02 % since during the nitriding treatment phosphorus has a temper embrittling effect.*Vanadium(V)Vanadium helps control grain growth during heat treatment. By inhibiting grain growth ithelps increase the toughness and strength of the steel.Tungsten(W)Used in small amounts, tungsten combines with the free carbides in steel during heattreatment, to produce high wear resistance with little or no loss of toughness. Highamounts combined with chromium gives steel a property known as red hardness. Thismeans that the steel will not lose its working hardness at high temperatures. An example

of this would be tools designed to cut hard materials at high speeds, where the frictionbetween the tool and the material would generate high temperatures.*Copper(Cu)The addition of copper in amounts of 0.2 to 0.5 percent primarily improves steelsresistance to atmospheric corrosion. It should be noted that with respect to knife steels,copper has a detrimental effect to surface quality and to hot-working behavior due tomigration into the grain boundaries of the steel.*Boron(B)Boron can significantly increase the hardenability of steel without loss of ductility. Itseffectiveness is most noticeable at lower carbon levels. The addition of boron is usuallyin very small amounts ranging from 0.0005 to 0.003 percent.*Titanium(Ti)This element, when used in conjunction with Boron, increases the effectiveness of theBoron in the hardenability of steel.

Heat Treatment of Steels:

The Softening Processes:Annealing:Used variously to soften, relieve internal stresses, improve machinability and to develop particular mechanical and physical properties.In special silicon steels used for transformer laminations annealing develops the particular microstructure that confers the unique electrical properties.Annealing requires heating to above the As temperature, holding for sufficient time for temperature equalisation followed by slow cooling. See Curve 2 in Figure 1.

An idealised TTT curve for a plain carbon steel.NormalisingAlso used to soften and relieve internal stresses after cold work and to refine the grain size and metallurgical structure. It may be used to break up the dendritic (as cast) structure of castings to improve their machinability and future heat treatment response or to mitigate banding in rolled steel.This requires heating to above the As temperature, holding for sufficient time to allow

temperature equalisation followed by air cooling. It is therefore similar to annealing but with a faster cooling rate. Curve 3 in Figure I would give a normalised structure.

The Hardening ProcessesHardeningIn this process steels which contain sufficient carbon, and perhaps other alloying elements, are cooled (quenched) sufficiently rapidly from above the transformation temperature to produce Martensite, the hard phase already described, see Curve 1 in Figure 1.There is a range of quenching media of varying severity, water or brine being the most severe, through oil and synthetic products to air which is the least severe.TemperingAfter quenching the steel is hard, brittle and internally stressed. Before use, it is usually necessary to reduce these stresses and increase toughness by 'tempering'. There will also be a reduction in hardness and the selection of tempering temperature dictates the final properties. Tempering curves, which are plots of hardness against tempering temperature. exist for all commercial steels and are used to select the correct tempering temperature. As a rule of thumb, within the tempering range for a particular steel, the higher the tempering temperature the lower the final hardness but the greater the toughness.It should be noted that not all steels will respond to all heat treatment processes, Table 1 summaries the response, or otherwise, to the different processes.

  Anneal Normalise Harden TemperLow Carbon <0.3% yes yes no noMedium Carbon 0.3-0.5% yes yes yes yesHigh Carbon >0.5% yes yes yes yesLow Alloy yes yes yes yesMedium Alloy yes yes yes yesHigh Alloy yes maybe yes yesTool Steels yes no yes yesStainless Steel (Austenitic eg 304, 306) yes no no noStainless Steels (Ferritic eg 405, 430 442) yes no no noStainless Steels (Martensitic eg 410, 440) yes no yes yes

Thermochemical ProcessesThese involve the diffusion, to pre-determined depths into the steel surface, of carbon, nitrogen and, less commonly, boron. These elements may be added individually or in combination and the result is a surface with desirable properties and of radically different composition to the bulk.CarburisingCarbon diffusion (carburising) produces a higher carbon steel composition on the part surface. It is usually necessary to harden both this layer and the substrate after carburising.

NitridingNitrogen diffusion (nitriding) and boron diffusion (boronising or boriding) both produce hard intermetallic compounds at the surface. These layers are intrinsically hard and do not need heat treatment themselves.Nitrogen diffusion (nitriding) is often carried out at or below the tempering temperature of the steels used. Hence they can be hardened prior to nitriding and the nitriding can also be used as a temper.

BoronisingBoronised substrates will often require heat treatment to restore mechanical properties. As borides degrade in atmospheres which contain oxygen, even when combined as CO or C02, they must be heat treated in vacuum, nitrogen or nitrogen/hydrogen atmospheres.

Processing MethodsIn the past the thermochemical processes were carried out by pack cementation or salt bath processes. These are now largely replaced, on product quality and environmental grounds, by gas and plasma techniques. The exception is boronising, for which a safe production scale gaseous route has yet to be developed and pack cementation is likely to remain the only viable route for the for some time to come.The gas processes are usually carried out in the now almost universal seal quench furnace, and any subsequent heat treatment is readily carried out immediately without taking the work out of the furnace. This reduced handling is a cost and quality benefit.

Table 2 (Part A). Characteristics of the thermochemical heat treatment processes.Process Temp

(°C)DiffusingElements

Methods ProcessingCharacteristics

Carburising

900-1000

Carbon Gas.Pack.

Salt Bath.Fluidised

Bed.

Care needed as high temperature may cause distortion

Carbo-nitriding

800-880

CarbonNitrogenmainly C

Gas.Fluidised

Bed.Salt Bath.

Lower temperature means less distortion than carburising.

Nitriding 500-800

Nitrogen Gas.Plasma.

Fluidised Bed.

Very low distortion.Long process times, but reduced by plasma and other new techniques.

Nitro-carburising

560-570

NitrogenCarbon

mainly N

Gas.Fluidised

Bed.

Very low distortion.Impossible to machine after processing.

Salt Bath.Boronising 800-

1050Boron Pack. Coat under argon shield.

All post coating heat treatment must be in an oxygen free atmosphere even CO

and CO2 are harmful.No post coating machining.

Table 2 (Part B). Characteristics of the thermochemical heat treatment processes.Process Case

Characteristics

SuitableSteels

Applications

Carburising

Medium to deep case.

Oil quench to harden case.

Surface hardness 675-820 HV (57-

62 HRC) after tempering.

Mild, low carbon and low alloy steels.

High  surface stress conditions.

Mild steels small sections <12mm.

Alloy steels large sections.

Carbo-nitriding

Shallow to medium to deep case.

Oil quench to harden case.

Surface hardness 675-820 HV (57-

62 HRC) after tempering.

Low carbon steels. High surface stress conditions.

Mild steels large sections >12mm.

Nitriding Shallow to medium to deep case.No quench.

Surface hardness 675-1150 HV (57-

70 HRC).

Alloy and tool steels which contain sufficient nitride

forming elements eg chromium, aluminium and vanadium. Molybdenum is usually present to aid core

properties.

Severe surface stress conditions.

May cinfer corrosion resistance.

Maximum hard ness and temperature stability up to

200°C.

Nitro-carburising

10-20 micron compound layer at the

surface.Further

Many steels from low carbon to tool steels.

Low to medium surface stress conditions.

Good wear resistance.Post coating oxidation and impregnation gives good

nitrogen diffusion

zone.Hardness

depends on steel type

carbon & low alloy 350-540

HV (36-50 HRC) high alloy & toll up to 1000

HV (66 HRC).

corrosion resistance.

Boronising Thickness inversely

proportional to alloy

content >300 microns on

mild steel 20 microns on high alloy.

Do not exceed 30 microns if part is to be heat treated.

Hardness >1500 HV

typical.

Most steels from mild to tool steels except austenitic

stainless grades.

Low to high surface stress conditions depending on

substrate steel.Excellent wear resistance.

Techniques and PracticeAs we have already seen this requires heating to above the As temperature, holding to equalise the temperature and then slow cooling. If this is done in air there is a real risk of damage to the part by decarburisation and of course oxidation. It is increasingly common to avoid this by ‘bright’ or ‘close’ annealing using protective atmospheres. The particular atmosphere chosen will depend upon the type of steel.NormalisingIn common with annealing there is a risk of surface degradation but as air cooling is common practice this process is most often used as an intermediate stage to be followed by machining, acid pickling or cold working to restore surface integrity.

HardeningWith many components, hardening is virtually the final process and great care must taken to protect the surface from degradation and decarburisation. The ‘seal quench’ furnace is now an industry standard tool for carbon, low and medium alloy steels. The work is protected at each stage by a specially generated atmosphere.Some tool steels benefit from vacuum hardening and tempering, salt baths were widely used but are now losing favour on environmental grounds.TemperingTempering is essential after most hardening operations to restore some toughness to the structure. It is frequently performed as an integral part of the cycle in a seal quench furnace, with the parts fully protected against oxidation and decarburisation throughout the process. Generally tempering is conducted in the temperature range 150 to 700°C, depending on the type of steel and is time dependent as the microstructural changes occur relatively slowly.Caution : Tempering can, in some circumstances, make the steel brittle which is the opposite of what it is intended to achieve.There are two forms of this brittlenessTemper Brittleness which affects both carbon and low alloy steels when either, they are cooled too slowly from above 575°C, or are held for excessive times in the range 375 to 575°C. The embrittlement can be reversed by heating to above 575°C and rapidly cooling.Blue Brittleness affects carbon and some alloy steels after tempering in the range 230 to 370°C The effect is not reversible and susceptible steels should not be employed in applications in which they sustain shock loads.If there is any doubt consult with the heat treater or in house metallurgical department about the suitability of the steel type and the necessary heat treatment for any application.Martempering and AustemperingIt will be readily appreciated that the quenching operation used in hardening introduces internal stresses into the steel. These can be sufficiently large to distort or even crack the steel.Martempering is applied to steels of sufficient hardenability and involves an isothermal hold in the quenching operation. This allows temperature equalisation across the section of the part and more uniform cooling and  structure, hence lower stresses. The steel can then be tempered in the usual way.Austempering also involves an isothermal hold in the quenching operation, but the structure formed, whilst hard and tough, does not require further tempering. The process is mostly applied to high carbon steels in relatively thin sections for springs or similar parts. These processes are shown schematically in the TTT Curves, (figures 2a and 3b).

Temperature vs. time profiles for (a) austempering and (b) martempering.Localised hardening sometimes as flame hardening, laser hardening, RF or induction hardening and electron beam hardening depending upon the heat source used. These processes are used where only a small section of the component surface needs to be hard, eg a bearing journal. In many cases there is sufficient heat sink in the part and an external quench is not needed. There is a much lower risk of distortion associated with this practice, and it can be highly automated and it is very reproducible.

Isothermal transformation diagrams (also known as time-temperature-transformation (TTT) diagrams) are plots of temperature versus time (usually on a logarithmic scale). They are generated from percentage transformation-vs logarithm of time measurements, and are useful for understanding the transformations of an alloy steel that is cooled isothermally. An isothermal transformation diagram is only valid for one specific composition of material, and only if the temperature is held constant during the transformation, and strictly with rapid cooling to that temperature. Though usually used to represent transformation kinetics for steels, they also can be used to describe the kinetics of crystallization in ceramic or other materials. Time-temperature-precipitation diagrams and time-temperature-embrittlement diagrams have also been used to represent kinetic changes in steels.

Isothermal transformation (IT) diagram or the C-curve is associated with mechanical properties, microconstituents/microstructures, and heat treatments in carbon steels. Diffusional transformations like austenite transforming to a cementite and ferrite mixture can be explained using the sigmoidal curve; For example the beginning of pearlitic transformation is represented by the pearlite start (Ps) curve. This transformation is complete at Pf curve. Nucleation requires an incubation time. The rate of nucleation increases and the rate of microconstituent growth decreases as the temperature decreases from the liquidus temperature reaching a maximum at the bay or nose of the curve. Thereafter, the decrease in diffusion rate due to low temperature offsets the effect of increased driving force due to greater difference in free energy. As a result of the transformation, the microconstituents, Pearlite and Bainite, form; Pearlite forms at higher temperatures and bainite at lower.

Austenite is slightly undercooled when quenched below Eutectoid temperature. When given more time, stable microconstituents can form: ferrite and cementite. Coarse pearlite is produced when atoms diffuse rapidly after phases that form pearlite nucleate. This transformation is complete at the pearlite finish time (Pf).

However, greater undercooling by rapid quenching results in formation of martensite or bainite instead of pearlite. This is possible provided the cooling rate is such that the cooling curve intersects the martensite start temperature or the bainite start curve before intersecting the Ps curve. The martensite transformation being a diffusionless shear transformation is represented by a straight line to signify the martensite start temperature.

Material Knowledge300-Series Stainless Steel

The 300 series has 18-percent chromium and 8-percent nickel added to the steel. Stainless steel with this mix uses 18-8 as its name as well as the 300-series number. These steels aren't attracted to magnets. This is an austenitic stainless steel, so it is easier to weld than some other stainless steels. It can be made magnetic. The 304 grade is the most commonly used stainless steel, and the 316 grade is the second most common. Both have the same general characteristics of the 300 series. Tableware, cooking utensils, food processing equipment, food preparation and mild chemical applications use this stainless steel.400-Series Stainless Steel

This group of stainless steels has an addition of 11 percent chromium and 1-percent manganese. The 400 series is susceptible to rust and corrosion under some conditions. Heat-treating will harden the 400 series. The 400 series of stainless steels have a martensitic crystalline structure that has higher carbon content. This provides high strength and high wear resistance. The welds will deteriorate as the carbon content increases. Martensitic stainless steels aren't as corrosion resistant as the austenitic types.

Can stainless steel be magnetic?Yes to varying degrees. The magnetism of stainless steel is affected by its alloying elements, atomic grain structure, and the amount of cold-working during fabrication.

What are 18-8, 300-Series and 400-Series stainless steels?The American Iron and Steel Institute (AISI) has created widely accepted grades for

stainless steels. These grades are identified by series numbers 100 through 600 where each series is organized by alloy and grain structure properties.

Most common to the electronics fastener industry are 300-series and 400-series stainless steels. The 300-series steels have an “austenitic” metallic grain structure while 400-series have “ferritic” or “martensitic” structures.

Among other alloying elements, several 300-series stainless steels contain approximately 18% chromium and 8% nickel. Thus “18-8” is a loose characterization of stainless steel grades

302-305, 316, 321 and 347. Even more general is the acronym “CRES” which typifies any corrosion-resistant steel.What grades of stainless steel are magnetic?One of the alloying metals, chromium, causes stainless steel to have a magnetic grain structure. Another of the possible alloying elements, nickel, reduces or inhibits magnetic properties. The 300-series stainless steels have varying degrees of nickel making them mostly non-magnetic. Devoid of nickel and with a grain structure similar to carbon steel, the 400-series stainless steels are slightly magnetic.

What causes non-magnetic grades of stainless steel to become magnetic?In their basic forms stainless steels have a ferritic grain structure, similar to carbon steel, and are magnetic. The addition of nickel in the 300-series stainless steels modifies the crystal grain structure to austenitic. The austenitic grades are mostly non-magnetic in the unworked state due to their nickel content. When 300-series stainless steels are cold-worked, straining of the atomic lattice structure in the areas of cold-working forms the magnetic grain structure martensite.Generally speaking, the higher the nickel content the more stable the austenitic structure and less magnetic response from cold-working. Consequently 316 stainless steel, with higher amounts of nickel, exhibits virtually no magnetism after cold-working in most cases. While 304, with lower nickel content, may become mildly magnetic.

Are there any means of reducing or eliminating the magnetic properties of stainless steel?Austenitic (300-series) stainless steels that have become magnetic due to work hardening can be returned to a non- magnetic state through annealing or stress-relieving. Brief heating at elevated temperatures reverts the affected grain structure from the martensitic state to the austenitic. Since 400-series stainless steels are entirely ferritic or martensitic, their magnetic properties cannot be reduced through annealing.There are no plating or finishing processes, such as passiva- tion, that can reduce or eliminate work hardening induced magnetism. They are merely superficial and do not change the affected grain structure.

Is magnetism related to corrosion resistance?Stainless steel, like carbon steel, can rust when exposed to air. However, the chromium in stainless steel forms a protective chromium oxide layer (also known as passivation) which prevents the development of iron oxide rust. The chromium oxide layer is so thin that it is imperceptible and thus the metal retains its attractive finish.

The 300-series stainless steels have a higher chromium content than the 400-series stainless steels, as well as, nickel as an alloying element. Nickel enhances chromium’s ability to form a passive surface layer. Consequently, 300-series stainless steels exhibit better corrosion resis- tance. Corrosion resistance is a function of the chromium and nickel content and not the metallic grain structure which causes magnetism.

Is stainless steel heat treatable?

Carbon can be added to stainless steel creating a marten- sitic crystal grain structure. These stainless steels, such as 410 and 416, respond well to heat-treating. Although not heat-treatable, 301 stainless steel work hardens easily making it useful in applications requiring high tensile strength.

How do I know which stainless steel to specify in my application?The table below highlights the general usage and property characteristics of stainless steels commonly used in the electronics fastener industry.

400 Series Martensitic - Typical grade: 410Straight chromium (12-18%), magnetic and can be hardened by heat treatment. Typical use: Fasteners, pump shafts 400 Series Ferritic - Typical grade: 430Straight chromium (12-18%), "low" carbon, magnetic, but not heat treatable. Typical use: Appliance trim, cooking utensils.

300 Series300 Series stainless steels are the most widely used products produced by Allegheny Ludlum Corporation. They are classified as austenitic, and are hardenable only by cold working methods. These grades of stainless have chromium (approx. 18 to 30%) and nickel (approx. 6 to 20%) as their major alloying additions. Type 304 (also known as 18-8) is the most widely used alloy of all stainless steels.

Their nickel content changes their fundamental structure and nature, lowers their thermal conductivity, doubles their coefficient of expansion and makes them non-magnetic as compared to straight chromium 400 Series alloys. They provide high resistance to corrosion and possess great strength and oxidation resistance at elevated temperature, yet retain good ductility at extremely cold temperatures. In the annealed state, 300 Series stainless steels possess unusual ductility and formability, high impact strength and high tensile strength compared to mild carbon steels. The 300 Series alloys have excellent fabrication characteristics, including good weldability.

The 300 Series stainless steels can meet a wide variety of physical and mechanical requirements making them excellent materials for applications including auto molding and trim,

wheel covers, kitchen equipment, hose clamps, springs, truck bodies, exhaust manifolds, stainless flatware, storage tanks, pressure vessels, and piping.AL 304DA™, a clad carbon steel, is used in the cookware industry.

Alloys in the 300 Series include :Stabilized Types 321, 347, 348High strength Types AM 362™, AM 363™

Ferritic Stainless Steels, 400 Series Straight Chromium, Non-HardenableThese grades of stainless have 11 to 30% chromium as the major alloy addition and are

low carbon. Ductility and formability are less than that of the austenitic grades. The corrosion resistance competes with the austenitic grades for certain applications. Thermal conductivity is about half that of carbon steels. Ferritic stainless steels are magnetic, and resistance to high-temperature corrosion is better than that of martensitic types. They generally have good ductility and can be welded or fabricated without difficulty. These grades can be processed to develop an aesthetically pleasing, bright finish and, hence, are often used for automotive trim and appliance molding. They also find use in functional applications where cost is a major factor, e.g., automotive exhaust systems, catalytic converters, radiator caps, and chimney liners. These grades can also be hardened by cold rolling, but cannot be hardened as much as the austenitic alloys.

End uses for ferritic types include appliances, hot water tanks, automotive applications, and deep drawn parts such as cookware. Type 409, developed by Allegheny Ludlum in 1962, is the second most widely used stainless steel behind Type 304, and its primary use is in automotive exhaust systems. Alloys in this series include : 400 series

Martensitic Stainless Steels, 400 Series, Straight Chromium, HardenableThese grades of stainless steel have chromium in the range of 11 to 17% as the major alloying addition, but the carbon levels are in amounts from .10 to .65%. This radically changes the behavior of the martensitic alloys relative to the ferritic 400 Series alloys. The high carbon enables the material to be hardened by heating to a high temperature, followed by rapid cooling (quenching). Martensitic types offer the ideal combination of corrosion resistance and superior mechanical properties, as produced by heat treatment to develop maximum hardness, strength and resistance to abrasion and erosion.

The 400 Series martensitic grades that Allegheny Ludlum makes are AL 403™, AL 410™, AL 410HC™, AL 420™, 420HC, AL 425™ Modified, and AL 440A™. (Note: HC stands for high carbon.) The martensitic grades are usually sold in the soft state. This allows the customers to cut or form the parts before they are thermally hardened. End uses include cutlery, scissors, surgical instruments, wear plates, garbage disposal shredder lugs, and industrial knives. The AL 403™ alloy is used to make vanes for steam turbines.AL 412™ is a dual phase, ferritic-martensitic stainless steel which provides a corrosion resistant alternative to carbon steels.

Alloys in this series also include AL 418™ Special, and AL 440C™, a higher carbon version of 440A.

Machine design

Fit: When two parts are to be assembled, the relation resulting from the difference between their sizes before assembly is called a fit. A fit may be defined as the degree of tightness and looseness between two mating parts.

Why do we use Tolerance: It is used because you can count on parts to not be perfect. So if you want them all to fit and need some room for lubrication(Grease etc)

Types of Fits

1. Clearance fit. In this type of fit, the size limits for mating parts are so selected that clearance between them always occur. It may be noted that in a clearance fit, the tolerance zone of the hole is entirely above the tolerance zone of the shaft. In a clearance fit, the difference between the minimum size of the hole and the maximum size of the shaft is known as minimum clearance whereas the difference between the maximum size of the hole and minimum size of the shaft is called maximum clearance. The clearance fits may be slide fit, easy sliding fit, running fit, slack running fit and loose running fit.

2. Interference fit. In this type of fit, the size limits for the mating parts are so selected that interference between them always occur. It may be noted that in an interference fit, the tolerance

zone of the hole is entirely below the tolerance zone of the shaft. In an interference fit, the difference between the maximum size of the hole and the minimum size of the shaft is known as minimum interference, whereas the difference between the minimum size of the hole and the maximum size of the shaft is called maximum interference. The interference fits may be shrink fit, heavy drive fit and light drive fit.

3. Transition fit. In this type of fit, the size limits for the mating parts are so selected that either a clearance or interference may occur depending upon the actual size of the mating parts. It may be noted that in a transition fit, the tolerance zones of hole and shaft overlap. The transition fits may be force fit, tight fit and push fit.

Clearance Fit Clearance fit can be sub-classified as follows : Loose Fit

It is used between those mating parts where no precision is required. It provides minimum allowance and is used on loose pulleys, agricultural machineries etc. Running Fit

For a running fit, the dimension of shaft should be smaller enough to maintain a film of oil for lubrication. It is used in bearing pair etc. An allowance 0.025 mm per 25 mm of diameter of boaring may be used.Fit and Tolerances Slide Fit or Medium Fit

It is used on those mating parts where great precision is required. It provides medium allowance and is used in tool slides, slide valve, automobile parts, etc.

Interference Fit:A negative difference between diameter of the hole and the shaft is called interference. In

such cases, the diameter of the shaft is always larger than the hole diameter. Interference fit has a negative allowance, i.e. interference exists between the high limit of hole and low limit of the shaft.

In such a fit, the tolerance zone of the hole is always below that of the shaft. The shaft is assembled by pressure or heat expansion. The interference fit can be sub-classified as follows : Shrink Fit (or Heavy Force Fit)

It refers to maximum negative allowance. In assembly of the hole and the shaft, the hole is expanded by heating and then rapidly cooled in its position. It is used in fitting of rims, wheel belts, tires, coupling under certain conditions etc.

Force Fit (Medium)These fits have medium negative allowance. Considerable pressure is required to

assemble the hole and the shaft. It is used in car wheels, armature of dynamos etc.

Tight Fit or Press Fit One part can be assembled into the other with a hand hammer or by light pressure. A

slight negative allowance exists between two mating parts (more than wringing fit). It gives a semi-permanent fit and is used on a keyed pulley and shaft, rocker arm, etc.

Transition Fit :Transition fit can be sub-classified as follows : Push Fit It refers to zero allowance and a light pressure (10 cating dowels, pins, etc.) is required in assembling the hole and the shaft. The moving parts show least vibration with this type of fit. It is also known as snug fit.

Force Fit or Shrink Fit A force fit is used when the two mating parts are to be rigidly fixed so that one cannot move without the other. It either requires high pressure to force the shaft into the hole or the hole to be expanded by heating. It is used in railway wheels, etc.

Wringing Fit A slight negative allowance exists between two mating parts in wringing fit. It requires pressure to force the shaft into the hole and gives a light assembly. It is used in fixing keys, pins, etc.

ORThe lower RC numbers are the tighter fits, the higher numbers are the looser fits.RC1: Close Sliding FitsThis kind of fits are intended for the accurate location of parts which must assemble without noticeable play.RC2: Sliding FitsThis kind of fits are intended for the accurate location but with greater maximum clearance than class RC1. Parts made to this fit turn and move easily. This type is not designed for free run. Sliding fits in larger sizes may seize with small temperature changes.RC3: Precision Running FitsThis kind of fits are about the closest fits which can be expected to run freely. Precision running fits are intended for precision work at low speed, low bearing pressures, and light journal pressures. RC3 is not suitable where noticeable temperature differences occur.RC4: Close Running FitsThis kind of fits are mostly for running fits on accurate machinery with moderate surface speed, bearing pressures, and journal pressures where accurate location and minimum play are desired. This kind of fits also can be described as smaller clearances with higher requirements for precision fit.

RC5 and R6: Medium Running FitsThis kind of fits are designed for machines running at higher running speeds, considerable bearing pressures, and heavy journal pressure. This kind of fits also can be described with greater clearances with common requirements for fit precision.RC7: Free Running FitsThis kind of fits are intended to use where accuracy is not essential. It is suitable for great temperature variations. This fits are suitable to use without any special requirements for precise guiding of shafts.RC8 and RC9: Loose Running FitsThis kind of fits are intended for use where wide commercial tolerances may be required on the shaft. With this fits, The parts with great clearances with having great tolerances. Loose running fits exposed to effects of corrosion, contamination by dust and thermal or mechanical deformations.

SYSTEMS OF FIT:A fit system is the systems of standard allowance to suit specific range of basic size. If

these standard allowances are selected properly and assigned in mating parts ensures specific classes of fit. There are two systems of fit for obtaining clearance, interference or transition fit. These are : (i) Hole basis system (ii) Shaft basis system

Hole Basis system: If the system of assembly of shaft and hole is consisting of basic hole, then that type of system is known as Hole Basis System. It means for the system of assembly of shaft and hole, the zero line will be lying on the minimum diameter of the hole as shown figure. For this system the lower limit size of hole is equal to basic size.

Hole basis system

Shaft Basis system: If the system of assembly of shaft and hole consisting of basic shaft, then that type of system is known as Shaft Basis System. It means for the assembly of shaft and hole, the zero line will be lying on the maximum size of the shaft as shown. For this system the Upper Limit Size of shaft is equal to the Basic Size.

Shaft Basis SystemLocation Fits: Location fits are intended to determine only the location of the mating parts; they may provide rigid or accurate location, as with interference fits, or provide some freedom of location, as with clearance fits.

Accordingly, they are divided into three groups:Location Clearance fits (LC): Location Clearance fits are intended for parts which are normally stationary, but which can be freely assembled or disassembled. They range from snug fits for parts requiring accuracy of location, through the medium clearance fits for parts such as spigots, to looser fastener fits where freedom of assembly is a prime importance.Location Transition fits(LT): Location Transition fits are compromise between clearance and interference fits, for application where accuracy of location is important, but either a small amount of clearance or interference is permissible.Location interference fits (LN): Location interference fits are used where accuracy of location is of prime importance and for parts requiring rigidity and alignment with no special requirements for bore pressure. Such fits are not intended for parts designed to transmit frictional load from one part to another by virtue of the tightness of fit, as these conditions are covered by force fits.

Force Fits(FN): Force or shrink fits constitute a special type of interference fit, normally characterized by maintenance of constant bore pressures throughout the range of sizes. The interference therefore varies almost directly with diameter, and the difference between its minimum and maximum value is small, to maintain the resulting pressure within reasonable limits.

These fits are described as Light drive fits(FN1): Light drive fits are those requiring light assembly pressures, and produce more or less permanent assemblies. They are suitable for thin sections or long fits, or in cast-iron external members.

Medium drive fits (FN2): Medium drive fits are suitable for ordinary steel parts , or for shrink fits on light sections. They are about the tightest fits that can be used with high grade cast iron external members.Heavy drive fits (FN3): Heavy drive fits are suitable for heavier steel parts or for shrink fits in medium sectionsForce fits (FN4&5): Force fits are suitable for parts which can be highly stressed or for shrink fits where the heavy pressing forces required are impractical.

Shaft Design:General Considerations1. To minimize both deflections and stresses, the shaft length should be kept as short as possible

and overhangs minimized.2. A cantilever beam will have a larger deflection than a simply supported (straddle mounted)

one for the same length, load, and cross section, so straddle mounting should be used unless a cantilever shaft is dictated by design constraints. (Figure 9-2 shows a situation in which an overhung section is required for serviceability.)

3. A hollow shaft has a better stiffness/mass ratio (specific stiffness) and higher natural frequencies than a comparably stiff or strong solid shaft, but will be more expensive and larger in diameter.

4. Try to locate stress-raisers away from regions of large bending moment if possible and minimize their effects with generous radii and relief.

5. General low carbon steel is just as good as higher strength steels (since deflection is typical the design limiting issue).

6. Deflections at gears carried on the shaft should not exceed about 0.005 inches and the relative slope between the gears axes should be less than about 0.03 degrees.

7. If plain (sleeve) bearings are to be used, the shaft deflection across the bearing length should be less than the oil-film thickness in the bearing.

8. If non-self-aligning rolling element bearings are used, the shaft’s slope at the bearings should be kept to less than about 0.04 degrees.

9. If axial thrust loads are present, they should be taken to ground through a single thrust bearing per load direction. Do not split axial loads between thrust bearings as thermal expansion of the shaft can overload the bearings.

10. The first natural frequency of the shaft should be at least three times the highest forcing frequency expected in service, and preferably much more. (A factor of ten times or more is preferred, but this is often difficult to achieve).

Material Used for ShaftsThe material used for shafts should have the following properties :

1. It should have high strength.2. It should have good machinability.3. It should have low notch sensitivity factor.4. It should have good heat treatment properties.5. It should have high wear resistant properties.

The material used for ordinary shafts is carbon steel of grades 40C8, 45C8, 50 C 4 and 50 C 12.When a shaft of high strength is required, then an alloy steel such as nickel, nickel-chromium orChrome-vanadium steel is used.

Manufacturing of ShaftsShafts are generally manufactured by hot rolling and finished to size by cold drawing or turningand grinding. The cold rolled shafts are stronger than hot rolled shafts but with higher residual stresses. The residual stresses may cause distortion of the shaft when it is machined, especially when slots or keyways are cut. Shafts of larger diameter are usually forged and turned to size in a lathe.

Shaft Power: Power is the time rate of change of energy (work).work = Force * distance or Torque * angle,

So Power = Torque * angular velocityP = Torq ∗ ω

Types of Shafts:The following two types of shafts are important from the subject point of view :

1. Transmission shafts: These shafts transmit power between the source and the machinesabsorbing power. The counter shafts, line shafts, over head shafts and all factory shafts are transmission shafts. Since these shafts carry machine parts such as pulleys, gears etc., therefore they are subjected to bending in addition to twisting.

2. Machine shafts: These shafts form an integral part of the machine itself. The crank shaft isan example of machine shaft.Standard Sizes of Transmission Shafts

The standard sizes of transmission shafts are :25 mm to 60 mm with 5 mm steps; 60 mm to 110 mm with 10 mm steps ; 110 mm to 140 mmwith 15 mm steps ; and 140 mm to 500 mm with 20 mm steps.The standard length of the shafts are 5 m, 6 m and 7 m.

Stresses in Shafts:The following stresses are induced in the shafts :1. Shear stresses due to the transmission of torque (i.e. due to torsional load).2. Bending stresses (tensile or compressive) due to the forces acting upon machine elementslike gears, pulleys etc. as well as due to the weight of the shaft itself.3. Stresses due to combined torsional and bending loads.Maximum Permissible Working Stresses for Transmission Shafts:

According to American Society of Mechanical Engineers (ASME) code for the design of transmission shafts, the maximum permissible working stresses in tension or compression may be taken as(a) 112 MPa for shafts without allowance for keyways.(b) 84 MPa for shafts with allowance for keyways.

For shafts purchased under definite physical specifications, the permissible tensile stress (σt)may be taken as 60 per cent of the elastic limit in tension (σel), but not more than 36 per cent of the ultimate tensile strength (σu). In other words, the permissible tensile stress,

σt = 0.6 σel or 0.36 σu, whichever is less.

The maximum permissible shear stress may be taken as(a) 56 MPa for shafts without allowance for key ways.(b) 42 MPa for shafts with allowance for keyways.

For shafts purchased under definite physical specifications, the permissible shear stress (τ) maybe taken as 30 per cent of the elastic limit in tension (σel) but not more than 18 per cent of the ultimate tensile strength (σu). In other words, the permissible shear stress,

τ = 0.3 σel or 0.18 σu, whichever is less.Design of Shafts:The shafts may be designed on the basis of1. Strength, and 2. Rigidity and stiffness.

In designing shafts on the basis of strength, the following cases may be considered :(a) Shafts subjected to twisting moment or torque only,(b) Shafts subjected to bending moment only,(c) Shafts subjected to combined twisting and bending moments, and(d) Shafts subjected to axial loads in addition to combined torsional and bending loads.

Permissible stress design (in USA construction more commonly called allowable stress design) is a design philosophy used by civil engineers. The designer ensures that the stresses developed in a structure due to service loads do not exceed the elastic limit. This limit is usually determined by ensuring that stresses remain within the limits through the use of factors of safety.

Factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry load must be determined to a reasonable accuracy.

OR

ORShafts Subjected to Twisting Moment OnlyWhen the shaft is subjected to a twisting moment (or torque) only, then the diameter of the shaftmay be obtained by using the torsion equation. We know that

where T = Twisting moment (or torque) acting upon the shaft,

J = Polar moment of inertia of the shaft about the axis of rotation.

τ = Torsional shear stress, and r = d / 2; where d is the diameter of the shaft.

1. The hollow shafts are usually used in marine work. These shafts are stronger per kg ofmaterial and they may be forged on a mandrel, thus making the material more homogeneous thanwould be possible for a solid shaft.When a hollow shaft is to be made equal in strength to a solid shaft, the twisting moment of boththe shafts must be same. In other words, for the same material of both the shafts,

2. The twisting moment (T) may be obtained by using the following relation :We know that the power transmitted (in watts) by the shaft,

where T = Twisting moment in N-m, and N = Speed of the shaft in r.p.m.

3. In case of belt drives, the twisting moment ( T ) is given by

Where T1 and T2 = Tensions in the tight side and slack side of the belt respectively, andR = Radius of the pulley.

Shafts Subjected to Bending Moment OnlyWhen the shaft is subjected to a bending moment only, then the maximum stress (tensile orcompressive) is given by the bending equation. We know that

where M = Bending moment, I = Moment of inertia of cross-sectional area of the shaft about the axis of rotation, σb = Bending stress, and y = Distance from neutral axis to the outer-most fibre.

For Solid Shaft:

For Hollow Shaft:

Note:We have already discussed in Art. 14.1 that the axles are used to transmit bending moment only. Thus,axles are designed on the basis of bending moment only.

Shafts Subjected to Combined Twisting Moment and Bending MomentWhen the shaft is subjected to combined twisting moment and bending moment, then the

shaft must be designed on the basis of the two moments simultaneously. Various theories have been suggested to account for the elastic failure of the materials when they are subjected to various types of combined stresses. The following two theories are important from the subject point of view :1. Maximum shear stress theory or Guest's theory. It is used for ductile materials such as mildsteel.2. Maximum normal stress theory or Rankine’s theory. It is used for brittle materials such ascast iron.Let τ = Shear stress induced due to twisting moment, andσb = Bending stress (tensile or compressive) induced due to bendingmoment.According to maximum shear stress theory, the maximum shear stress in the shaft,

The expression is known as equivalent twisting moment and is denoted by Te. Theequivalent twisting moment may be defined as that twisting moment, which when acting alone, produces the same shear stress (τ) as the actual twisting moment. By limiting the maximum shear stress (τmax) equal to the allowable shear stress (τ) for the material, the may be written as

The expression is known as equivalent bending moment and is denotedby Me. The equivalent bending moment may be defined as that moment which when acting alone produces the same tensile or compressive stress (σb) as the actual bending moment. By limiting the maximum normal stress [σb(max)] equal to the allowable bending stress (σb), then the equation may be written as

For hollow shaft,

It is suggested that diameter of the shaft may be obtained by using both the theories and the larger of the two values is adopted.

High Speed Tool SteelsThese steels are used for cutting metals at a much higher cutting speed than ordinary carbon tool steels. The carbon steel cutting tools do not retain their sharp cutting edges under heavier loads and higher speeds. This is due to the fact that at high speeds, sufficient heat may be developed during the cutting operation and causes the temperature of the cutting edge of the tool to reach a red heat. This temperature would soften the carbon tool steel and thus the tool will not work efficiently for a longer period. The high speed steels have the valuable property of retaining their hardness even when heated to red heat. Most of the high speed steels contain tungsten as the chief alloying element, but other elements like cobalt, chromium, vanadium, etc. may be present in some proportion. Following are the different types of high speed steels:

1.High speed steel. This steel, on an average, contains 18 per cent tungsten, 4 per centchromium and 1 per cent vanadium. It is considered to be one of the best of all purpose tool steels. It is widely used for drills, lathe, planer and shaper tools, milling cutters, reamers, broaches, threading dies, punches, etc.

2. Molybdenum high speed steel. This steel, on an average, contains 6 per cent tungsten, 6 percent molybdenum, 4 per cent chromium and 2 per cent vanadium. It has excellent toughness andcutting ability. The molybdenum high speed steels are better and cheaper than other types of steels. It is particularly used for drilling and tapping operations.

3. Super high speed steel. This steel is also called cobalt high speed steel because cobalt isadded from 2 to 15 per cent, in order to increase the cutting efficiency especially at high temperatures.

This steel, on an average, contains 20 per cent tungsten, 4 per cent chromium, 2 per cent vanadium and 12 per cent cobalt. Since the cost of this steel is more, therefore, it is principally used for heavy cutting operations which impose high pressure and temperatures on the tool.

Stresses in screw fastenings :It is necessary to determine the stresses in screw fastening due to both static and dynamic

loading in order to determine their dimensions. In order to design for static loading both initial tightening and external loadings need be known. Initial tightening load When a nut is tightened over a screw following stresses are induced:

(a) Tensile stresses due to stretching of the bolt (b) Torsional shear stress due to frictional resistance at the threads. (c) Shear stress across threads (d) Compressive or crushing stress on the threads

(e) Bending stress if the surfaces under the bolt head or nut are not perfectly normal to the bolt axis.

(a) Tensile stress Since none of the above mentioned stresses can be accurately determined bolts are usually designed on the basis of direct tensile stress with a large factor of safety. The initial tension in the bolt may be estimated by an empirical relation P1=284 d kN, where the nominal bolt diameter d is given in mm. The relation is used for making the joint leak proof. If leak proofing is not required half of the above estimated load may be used. However, since initial stress is

inversely proportional to square of the diameter bolts of smaller diameter such as M16 or M8 may fail during initial tightening. In such cases torque wrenches must be used to apply known load. The torque in wrenches is given by T= C P1d where, C is a constant depending on coefficient of friction at the mating surfaces, P is tightening up load and d is the bolt diameter.

(b) Torsional shear stress

This is given by where T is the torque and d the core diameter. We may relate torque T to the tightening load P1 in a power screw configuration and taking collar friction into account we may write

where dm and dcm are the mean thread diameter and mean collar diameter respectively, and are the coefficients of thread and collar friction respectively and mcmμcμα is the semi thread angle. If we consider that

then we may write T= C P1 dm where C is a constant for a given arrangement. As discussed earlier similar equations are used to find the torque in a wrench.

A typical power screw configuration

(c) Shear stress across the threads:

This is given by where dc is the core diameter and b is the base width of the thread and n is the number of threads sharing the load.

(d) Crushing stress on threads

This is given by where d0 and dc are the outside and core diameters.

(e) Bending stress If the underside of the bolt and the bolted part are not parallel , the bolt may be subjected to

bending and the bending stress may be given by where x is the difference in height between the extreme corners of the nut or bolt head, L is length of the bolt head shank and E is the young’s modulus.

Development of bending stress in a bolt

Stresses due to an external load If we consider an eye hook bolt . where the complete machinery weight is supported by

threaded portion of the bolt, then the bolt is subjected to an axial load and the weakest section will be at the root of the thread. On this basis we may write

where for fine threads dc =0.88d and for coarse threads dc =0.84d, d being the nominal diameter.Bolts are occasionally subjected to shear loads also, for example bolts in a flange coupling . It should be remembered in design that shear stress on the bolts must be avoided as much as possible. However if this cannot be avoided the shear plane should be on the shank of the bolt and not the threaded portion. Bolt diameter in such cases may be found from the relation

where n is the number of bolts sharing the load, τ is the shear yield stress of the bolt material. If the bolt is subjected to both tensile and shear loads, the shank should be designed for shear and the threaded portion for tension. A diameter slightly larger than that required for both the cases should be used and it should be checked for failure using a suitable failure theory.

A typical rigid flange coupling

Classification of Pressure VesselsThe pressure vessels may be classified as follows:1. According to the dimensions. The pressure vessels, according to their dimensions, may be classified as thin shell or thick shell. If the wall thickness of the shell (t) is less than 1/10 of the diameter of the shell (d), then it is called a thin shell. On the other hand, if the wall thickness of the shell is greater than 1/10 of the diameter of the shell, then it is said to be a thick shell. Thin shells are used in boilers, tanks and pipes, whereas thick shells are used in high pressure cylinders, tanks, gun barrels etc.Note: Another criterion to classify the pressure vessels as thin shell or thick shell is the internal fluid pressure (p) and the allowable stress (σt). If the internal fluid pressure (p) is less than 1/6 of the allowable stress, then it is called a thin shell. On the other hand, if the internal fluid pressure is greater than 1/6 of the allowable stress, then it is said to be a thick shell.2. According to the end construction. The pressure vessels, according to the end construction, may be classified as open end or closed end. A simple cylinder with a piston, such as cylinder of a press is an example of an open end vessel, whereas a tank is an example of a closed end vessel. In case of vessels having open ends, the circumferential or hoop stresses are induced by the fluid pressure, whereas in case of closed ends, longitudinal stresses in addition to circumferential stresses are induced.

Stresses in a Thin Cylindrical Shell due to an Internal PressureThe analysis of stresses induced in a thin cylindrical shell are made on the followingassumptions:1. The effect of curvature of the cylinder wall is neglected.2. The tensile stresses are uniformly distributed over the section of the walls.3. The effect of the restraining action of the heads at the end of the pressure vessel is neglected.

When a thin cylindrical shell is subjected to an internal pressure, it is likely to fail in the following two ways:1. It may fail along the longitudinal section (i.e. circumferentially) splitting the cylinder into two troughs, as shown in Fig. 7.1 (a).2. It may fail across the transverse section (i.e. longitudinally) splitting the cylinder into two cylindrical shells, as shown in Fig. 7.1 (b).

Thus the wall of a cylindrical shell subjected to an internal pressure has to withstand tensile stresses of the following two types: (a) Circumferential or hoop stress, and (b) Longitudinal stress.These stresses are discussed, in detail, in the following articles.

Circumferential or Hoop StressConsider a thin cylindrical shell subjected to an internal pressure as shown in Fig. 7.2 (a)

and (b). A tensile stress acting in a direction tangential to the circumference is called circumferential or hoop stress. In other words, it is a tensile stress on *longitudinal section (or on the cylindrical walls).

Let p = Intensity of internal pressure,d = Internal diameter of the cylindrical shell,l = Length of the cylindrical shell,t = Thickness of the cylindrical shell, andσt1 = Circumferential or hoop stress for the material of the cylindrical shell.

We know that the total force acting on a longitudinal section (i.e. along the diameter X-X) of the shell = Intensity of pressure × Projected area = p × d × l ...(i)and the total resisting force acting on the cylinder walls

= σt1 × 2t × l ...( therefore of two sections) ...(ii)From equations (i) and (ii), we have

The following points may be noted:1. In the design of engine cylinders, a value of 6 mm to 12 mm is added in equation (iii) to permit reboring after wear has taken place. Therefore

2. In constructing large pressure vessels like steam boilers, riveted joints or welded joints are used in joining together the ends of steel plates. In case of riveted joints, the wall thickness of the cylinder,

where ηl = Efficiency of the longitudinal riveted joint.

3. In case of cylinders of ductile material, the value of circumferential stress (σt1) may be taken 0.8 times the yield point stress (σy) and for brittle materials, σt1 may be taken as 0.125 times the ultimate tensile stress (σu).4. In designing steam boilers, the wall thickness calculated by the above equation may be compared with the minimum plate thickness as provided in boiler code as given in the following table.

Note: If the calculated value of t is less than the code requirement, then the latter should be taken, otherwise the calculated value may be used.

The boiler code also provides that the factor of safety shall be at least 5 and the steel of theplates and rivets shall have as a minimum the following ultimate stresses.

Tensile stress, σt = 385 MPaCompressive stress, σc = 665 MPaShear stress, τ = 308 MPa

Longitudinal StressConsider a closed thin cylindrical shell subjected to an internal pressure as shown in Fig. 7.3 (a) and (b). A tensile stress acting in the direction of the axis is called longitudinal stress. In other words, it is a tensile stress acting on the *transverse or circumferential section Y-Y (or on the ends of the vessel).

Let σt2 = Longitudinal stress.In this case, the total force acting on the transverse section (i.e. along Y-Y)

= Intensity of pressure × Cross-sectional area

...(i)and total resisting force = σt2 × π d.t ...(ii)From equations (i) and (ii), we have

If ηc is the efficiency of the circumferential joint, then

From above we see that the longitudinal stress is half of the circumferential or hoop stress.Therefore, the design of a pressure vessel must be based on the maximum stress i.e. hoop stress.

Simple Confusing Concepts

Acceleration Due to Gravity: The acceleration due to gravity is the acceleration of a body due to the influence of the pull of gravity alone, usually denoted by ‘g’. This value varies from one celestial body to another. For example, the acceleration due to gravity would be different on the Moon as compared to the one here on Earth. Similarly, you would have different values for both Jupiter and Pluto. Exactly 9.80665 m/s2

Center of Gravity: The center of gravity of a collection of masses is the point where all the weight of the object can be considered to be concentrated.

Specific gravity is the ratio of the density of a substance to the density (mass of the same unit volume) of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance.

Centroid or geometric center of a two-dimensional region is, informally, the point at which a cardboard cut-out of the region could be perfectly balanced on the tip of a pencil, assuming uniform density and a uniform gravitational field. Formally, the centroid of a plane figure or two-dimensional shape is the arithmetic mean ("average") position of all the points in the shape.

Moment of inertia, also called mass moment of inertia or the angular mass, (SI units kg m2, Imperial Unit slug ft 2) is a measure of an object's resistance to changes in its rotation rate. It is the rotational analog of mass. That is, it is the inertia of a rigid rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational dynamics as mass does in basic dynamics, determining the relationship between angular momentum and angular velocity, torque and angular acceleration, and several other quantities. While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment allows the analysis of such complicated systems as spinning tops and gyroscopic motion.

Polar moment of inertia of an area is a quantity used to predict an object's ability to resist torsion, in objects (or segments of objects) with an invariant circular cross-section and no significant warping or out-of-plane deformation. It is used to calculate the angular displacement of an object subjected to a torque. It is analogous to the area moment of inertia, which characterizes an object's ability to resist bending and is required to calculate displacement. The larger the polar moment of inertia, the less the beam will twist, when subjected to a given torque. Polar moment of inertia should not be confused with moment of inertia, which characterizes an object's angular acceleration due to a torque.

How to find center of gravity:1Q)Calculate the weight of the object. When you're calculating the center of gravity, the first thing you should do is to find the weight of the object. Let's say that you're calculating the weight of a see-saw that weighs 30 lbs. Since it's a symmetrical object, its center of gravity will be

exactly in its center if it's empty. But if the see-saw has people of different weights sitting on it, then the problem is a bit more complicated.

2Q)Calculate the additional weights. To find the center of gravity of the see-saw with two children on it, you'll need to individually find the weight of the children on it. The first child weighs 40 lbs. and the second child weights 60 lbs.Steps:

1)Choose a datum. The datum is an arbitrary starting point placed on one end of the see-saw. You can place the datum on one end of the see-saw or the other. Let's say the see-saw is 16 feet long. Let's place the datum on the left side of the see-saw, close to the first child.

2)Measure the datum's distance from the center of the main object as well as from the two additional weights. Let's say the children are each sitting 1 foot away from each end of the see-saw. The center of the see-saw is the midpoint of the see-saw, or at 8 feet, since 16 feet divided by 2 is 8. Here are the distances from the center of the main object and the two additional weights form the datum:

Center of see-saw = 8 feet away from datum. Child 1 = 1 foot away from datum

Child 2 = 15 feet away from datum

3)Multiply each object's distance from the datum by its weight to find its moment. This gives you the moment for each object. Here's how to multiply each object's distance from the datum by its weight:

The see-saw: 30 lb. * 8 ft. = 240 ft. x lb. Child 1 = 40 lb. x 1 ft. = 40 ft. x lb.

Child 2 = 60 lb. x 15 ft. = 900 ft. x lb.4)Add up the three moments. Simply do the math: 240 ft. x lb. + 40 ft. x lb. + 900 ft. x lb = 1180 ft. x lb. The total moment is 1180 ft. x lb.5)Add the weights of all the objects. Find the sum of the weights of the seesaw, the first child, and the second child. To do this, add up the weights: 30 lbs. + 40 lbs. + 60 lbs. = 130 lbs.6)Divide the total moment by the total weight. This will give you the distance from the datum to the center of gravity of the object. To do this, simply divide 1180 ft. x lb. by 130 lbs.

1180 ft. x lb. ÷ 130 lbs = 9.08 ft.

The center of gravity is 9.08 feet from the datum, or measured 9.08 feet from the end of the left side of the see-saw, which is where the datum was placed.

Coefficient of friction:The coefficient of friction (COF), often symbolized by the Greek letter µ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one.

Coefficient of discharge (Cd) Coefficient of discharge is defined as

Coefficient Of Discharge : In a nozzle or other constriction, the discharge coefficient (also known as coefficient of discharge) is the ratio of the actual discharge to the theoretical discharge,[1] i.e., the ratio of the mass flow rate at the discharge end of the nozzle to that of an ideal nozzle which expands an identical working fluid from the same initial conditions to the same exit pressures.

Mathematically the discharge coefficient may be related to the mass flow rate of a fluid through a straight tube of constant cross-sectional area through the following equation:

Where:= Discharge Coefficient through the constriction (unit-less).

= Cross-sectional area of flow constriction (unit length squared).= Mass flow rate of fluid through constriction (unit mass of fluid per unit time).= Gravitational constant (Dimensionless)

= Density of fluid (unit mass per unit volume).= Pressure drop across constriction (unit force per unit area).

(i) Law of conservation of mass: This law when applied to a control volume statesthat the net mass flow through the volume will equal the mass stored or removed from thevolume. Under conditions of steady flow this will mean that the mass leaving the control volumeshould be equal to the mass entering the volume. The determination of flow velocity for aspecified mass flow rate and flow area is based on the continuity equation derived on the basisof this law.(ii) Newton’s laws of motion: These are basic to any force analysis under variousconditions of flow. The resultant force is calculated using the condition that it equals the rateof change of momentum. The reaction on surfaces are calculated on the basis of these laws.Momentum equation for flow is derived based on these laws.(iii) Law of conservation of energy: Considering a control volume the law can bestated as “the energy flow into the volume will equal the energy flow out of the volume understeady conditions”. This also leads to the situation that the total energy of a fluid element in a

steady flow field is conserved. This is the basis for the derivation of Euler and Bernoulli equations for fluid flow.(iv) Thermodynamic laws: are applied in the study of flow of compressible fluids.

Bernoulli's principle : In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738.

Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers (usually less than 0.3). More advanced forms may in some cases be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.[4]

Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.

Incompressible flow equation:In most flows of liquids, and of gases at low Mach number, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible and these flows are called incompressible flow. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is:

where:is the fluid flow speed at a point on a streamline,is the acceleration due to gravity,is the elevation of the point above a reference plane, with the positive z-direction

pointing upward – so in the direction opposite to the gravitational acceleration,is the pressure at the chosen point, andis the density of the fluid at all points in the fluid.

This form will be used in equations, but as in the case of KE, one should be familiar with

both the forms and choose the suitable form as the situation demands.

Application:In modern everyday life there are many observations that can be successfully explained by

application of Bernoulli's principle, even though no real fluid is entirely inviscid(no viscosity)

and a small viscosity often has a large effect on the flow. Bernoulli's principle can be used to calculate the lift force on an airfoil if the behavior of

the fluid flow in the vicinity of the foil is known. For example, if the air flowing past the top surface of an aircraft wing is moving faster than the air flowing past the bottom surface, then Bernoulli's principle implies that the pressure on the surfaces of the wing will be lower above than below. This pressure difference results in an upwards lifting force. Whenever the distribution of speed past the top and bottom surfaces of a wing is known, the lift forces can be calculated (to a good approximation) using Bernoulli's equations – established by Bernoulli over a century before the first man-made wings were used for the purpose of flight. Bernoulli's principle does not explain why the air flows

faster past the top of the wing and slower past the underside. To understand why, it is helpful to understand circulation, the Kutta condition, and the Kutta–Joukowski theorem.

The carburetor used in many reciprocating engines contains a venturi to create a region of low pressure to draw fuel into the carburetor and mix it thoroughly with the incoming air. The low pressure in the throat of a venturi can be explained by Bernoulli's principle; in the narrow throat, the air is moving at its fastest speed and therefore it is at its lowest pressure.

The Pitot tube and static port on an aircraft are used to determine the airspeed of the aircraft. These two devices are connected to the airspeed indicator, which determines the dynamic pressure of the airflow past the aircraft. Dynamic pressure is the difference between stagnation pressure and static pressure. Bernoulli's principle is used to calibrate the airspeed indicator so that it displays the indicated airspeed appropriate to the dynamic pressure.

The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For a horizontal device, the continuity equation shows that for an incompressible fluid, the reduction in diameter will cause an increase in the fluid flow speed. Subsequently Bernoulli's principle then shows that there must be a decrease in the pressure in the reduced diameter region. This phenomenon is known as the Venturi effect.

The maximum possible drain rate for a tank with a hole or tap at the base can be calculated directly from Bernoulli's equation, and is found to be proportional to the square root of the height of the fluid in the tank. This is Torricelli's law, showing that Torricelli's law is compatible with Bernoulli's principle. Viscosity lowers this drain rate. This is reflected in the discharge coefficient, which is a function of the Reynolds number and the shape of the orifice.

In open-channel hydraulics, a detailed analysis of the Bernoulli theorem and its extension were recently (2009) developed. It was proved that the depth-averaged specific energy reaches a minimum in converging accelerating free-surface flow over weirs and flumes (also). Further, in general, a channel control with minimum specific energy in curvilinear flow is not isolated from water waves, as customary state in open-channel hydraulics.

The Bernoulli grip relies on this principle to create a non-contact adhesive force between a surface and the gripper.

Flutes and fipple flutes

Bernoulli Equation The Bernoulli Equation can be considered to be a statement of the conservation of energy

principle appropriate for flowing fluids. The qualitative behavior that is usually labeled with the term "Bernoulli effect" is the lowering of fluid pressure in regions where the flow velocity is increased. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy.

Bernoulli's Principle This is an important principle involving the movement of a fluid through a pressure difference. Suppose a fluid is moving in a horizontal direction and encounters a pressure difference. This pressure difference will result in a net force, which by Newton's 2nd law will cause an acceleration of the fluid. The fundamental relation,

in this situation can be written as

which furthermore can be expressed as

In other words,

which is known as Bernoulli's principle. This is very similar to the statement we encountered before for a freely falling object, where the gravitational potential energy plus the kinetic energy was constant (i. e., was conserved).

Flow Velocity Profiles Not all fluid particles travel at the same velocity within a pipe.   The shape of the velocity curve (the  velocity  profile  across  any  given  section  of  the  pipe)  depends  upon  whether  the flow  is laminar or turbulent.   If the flow in a pipe is laminar, the velocity distribution at a cross section will be parabolic in shape with the maximum velocity at the center being about twice the average velocity in the pipe.  In turbulent flow, a fairly flat velocity distribution exists across the section of pipe, with the result that the entire fluid flows at a given single value.  Figure 5 helps illustrate the above ideas.   The velocity of the fluid in contact with the pipe wall is essentially zero and increases the further away from the wall.

Laminar and Turbulent Flow Velocity Profiles Note from Figure 5 that the velocity profile depends upon the surface condition of the pipe wall. A smoother wall results in a more uniform velocity profile than a rough pipe wall.

Flow profiles always exist, they can be influenced by Reynolds number, piping configurations and obstructions and pipe wall roughness. The Reynolds number is influenced by temperature, pressure, kind of fluid, velocity and pipe diameter

If there was no viscosity, the velocity of a flowing fluid would be uniform across a pipe section. Unfortunately the presence of even the small absolute viscosity of a gas induces a shearing action between adjacent fluid particles that reduces the velocity to zero at the pipe wall and thus forms a non-uniform velocity profile.Reynolds number:The Reynolds number is the ratio of inertial forces (vsρ) to viscous forces (μ/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. Thus, it is used to identify different flow regimes, such as laminar or turbulent flow.

:

Spring Rate (Stiffness of the spring):

Lead Screw and GearImportant Terms Used in Screw Threads:

1. Major diameter. It is the largest diameter of an external or internal screw thread. Thescrew is specified by this diameter. It is also known as outside or nominal diameter.2. Minor diameter. It is the smallest diameter of an external or internal screw thread. It isalso known as core or root diameter.3. Pitch diameter. It is the diameter of an imaginary cylinder, on a cylindrical screw thread,the surface of which would pass through the thread at such points as to make equal the width of the thread and the width of the spaces between the threads. It is also called an effective diameter. In a nut and bolt assembly, it is the diameter at which the ridges on the bolt are in complete touch with the ridges of the corresponding nut. 4. Pitch. It is the distance from a point on one thread to the corresponding point on the next.This is measured in an axial direction between corresponding points in the same axial plane.

Mathematically,5. Lead. It is the distance between two corresponding points on the same helix. It may alsobe defined as the distance which a screw thread advances axially in one rotation of the nut. Lead is equal to the pitch in case of single start threads, it is twice the pitch in double start, thrice the pitch in triple start and so on.6. Crest. It is the top surface of the thread.7. Root. It is the bottom surface created by the two adjacent flanks of the thread.8. Depth of thread. It is the perpendicular distance between the crest and root.9. Flank. It is the surface joining the crest and root.10. Angle of thread. It is the angle included by the flanks of the thread.11. Slope. It is half the pitch of the thread.

Types of lead screw or power screw:Power screws are classified by the geometry of their thread. V-threads are less suitable for leadscrews than others such as Acme because they have more friction between the threads. Their threads are designed to induce this friction to keep the fastener from loosening. Leadscrews, on

the other hand, are designed to minimize friction. Therefore, in most commercial and industrial use, V-threads are avoided for leadscrew use. Nevertheless, V-threads are sometimes successfully used as leadscrews, for example on microlathes and micromills.

Types of Screw Threads used for Power ScrewsFollowing are the three types of screw threads mostly used for power screws :1. Square thread: A square thread is adapted for the transmission of power in either direction. This thread results in maximum efficiency and minimum radial or bursting pressure on the nut.

It is difficult to cut with taps and dies. It is usually cut on a lathe with a single point tool and it cannot be easily compensated for wear. The square threads are employed in screw jacks, presses and clamping devices. The standard dimensions for square threads according to IS : 4694 – 1968 (Reaffirmed 1996), are shown in Table 17.1 to 17.3.

2. Acme or trapezoidal thread. An acme or trapezoidal thread, as shown in Fig. 17.1 (b), is a modification of square thread. The slight slope given to its sides lowers the efficiency slightly than square thread and it also introduce some bursting pressure on the nut, but increases its area in shear. It is used where a split nut is required and where provision is made to take up wear as in the lead screw of a lathe. Wear may be taken up by means of an adjustable split nut. An acme thread may be cut by means of dies and hence it is more easily manufactured than square thread. The standard dimensions for acme or trapezoidal threads are shown in Table 17.4 (Page 630).

3. Buttress thread. A buttress thread, as shown in Fig.17.1 (c), is used when large forces act along the screw axis in one direction only. This thread combines the higher efficiencyof square thread and the ease of cutting and the adaptability to a split nut of acme thread. It is stronger than other threads because of greater thickness at the base of the thread. The buttress thread has limited use for power transmission. It is employed as the thread for light jack screws and vices.

Torque Required to Raise Load by Square Threaded Screws:Let p = Pitch of the screw,

d = Mean diameter of the screw,α = Helix angle,P = Effort applied at the circumference of the screw to lift the load,W = Load to be lifted, andμ = Coefficient of friction, between the screw and nut= tan φ, where φ is the friction angle.

Torque Required to Lower Load by Square Threaded Screws:

Efficiency of Square Threaded Screws:Where P = W tan (α + φ)

W = Load to be lifted,α = Helix angle,φ = Angle of friction, andμ = Coefficient of friction between the screw and nut = tan φ.

Maximum Efficiency of a Square Threaded Screw:

Types Of Gears:Spur Gears: Spur gears are the most common type used. Tooth contact is primarily rolling, with sliding occurring during engagement and disengagement. Some noise is normal, but it may become objectionable at high speeds.

Rack and Pinion. Rack and pinion gears are essentially a linear shaped variation of spur gears The spur rack is a portion of a spur gear with an infinite radius. Internal Ring Gear:Internal gear is a cylindrical shaped gear with the meshing teeth inside or outside a circular ring. Often used with a spur gear. Internal ring gears may be used within a planetary gear arrangement. 

Helical Gear:Helical gear is a cylindrical shaped gear with helicoid teeth. Helical gears operate with less noise and vibration than spur gears. At any time, the load on helical gears is distributed over several teeth, resulting in reduced wear. Due to their angular cut, teeth meshing results in thrust loads along the gear shaft. This action requires thrust bearings to absorb the thrust load and maintain gear alignment. They are widely used in industry. A negative is the axial thrust force the helix form causes.

Helical Rack Gear: Helical rack gears are linear shaped and meshes with a rotating helical gear.  

Double Helical Gear: Double helical gear may have both left-hand and right-hand helical teeth. The double helical form is used to balance the thrust forces and provide additional gear shear area. 

Face Gear:Face gears are a circular disc with a ring of teeth cut on one side. The gear teeth are tapered toward the center of the tooth. These gears typically mate with a spur gear. 

Worm Gear:Worm gears teeth resembles ACME screw thread which mates with a helical gear, except that it is made to envelope the worm as seen along the worm's axis. Operation of worm gears is analogous to a screw. The relative motion between these gears is sliding rather than rolling. The uniform distribution of tooth pressures on these gears enables use of metals with inherently low coefficients of friction such as bronze wheel gears with hardened steel worm gears. These gears rely on full fluid film lubrication and require heavy oil compounded to enhance lubricity and film strength to prevent metal contact.

Double Enveloping Worm Gear:The double enveloping worm gear has a radial changing pitch diameter. This increases the number and amount of tooth shear area. Hypoid Gear:Hypoid gears are typically found within the differential (rear axle) of automobiles. The gear arrangement allows the translation of torque ninety degrees. Hypoid gears are similar to spiral bevel gears except that the shaft center lines do not intersect. Hypoid gears combine the rolling action and high tooth pressure of spiral bevels with the sliding action of

worm gears. This combination and the all-steel construction of the drive and driven gear result in a gear set with special lubrication requirements, including oiliness and anti-weld additives to withstand the high tooth pressures and high rubbing speeds.

Straight Bevel Gear:Straight bevel gears have tapered conical teeth which intersect the same tooth geometry. Bevel gears are used to transmit motion between shafts with intersecting center lines. The intersecting angle is normally 90 deg but may be as high as 180 deg. When the mating gears are equal in size and the shafts are positioned at 90 degrees to each other, they are referred to as miter gears. The teeth of bevel gears can also be cut in a curved manner to produce spiral bevel gears, which produce smoother and quieter operation than straight cut bevels.

Spiral Bevel Gear:Spiral bevel gears have a helical angle spiral teeth.  

Screw Gear (Crossed Helical Gear):

Screw gears are helical gears of opposite helix angle will mesh when their axes are crossed.  

Design Considerations for a Gear Drive:In the design of a gear drive, the following data is usually given :1. The power to be transmitted.2. The speed of the driving gear,3. The speed of the driven gear or the velocity ratio, and4. The centre distance.The following requirements must be met in the design of a gear drive :(a) The gear teeth should have sufficient strength so that they will not fail under static loading or dynamic loading during normal running conditions.(b) The gear teeth should have wear characteristics so that their life is satisfactory.(c) The use of space and material should be economical.(d) The alignment of the gears and deflections of the shafts must be considered because they effect on the performance of the gears.(e) The lubrication of the gears must be satisfactory.

Terms used in Gears:

Design Procedure for Spur GearsIn order to design spur gears, the following procedure may be followed :1. First of all, the design tangential tooth load is obtained from the power transmitted and the pitch line velocity by using the following relation:

N = Speed in r.p.m., andCS = Service factor.

Note : The above values for service factor are for enclosed well lubricated gears. In case of non-enclosed andgrease lubricated gears, the values given in the above table should be divided by 0.65.2. Apply the Lewis equation as follows :

Notes : (i) The Lewis equation is applied only to the weaker of the two wheels (i.e. pinion or gear).(ii) When both the pinion and the gear are made of the same material, then pinion is the weaker.(iii) When the pinion and the gear are made of different materials, then the product of (σw × y) or (σo × y)is the *deciding factor. The Lewis equation is used to that wheel for which (σw × y) or (σo × y) is less.((((* We see from the Lewis equation that for a pair of mating gears, the quantities like WT, b, m and Cv areconstant. Therefore (σw × y) or (σo × y) is the only deciding factor.))))

Welded Joints

A welded joint is a permanent joint which is obtained by the fusion of the edges of the two parts to be joined together, with or without the application of pressure and a filler material.

Advantages and Disadvantages of Welded Joints over Riveted JointsFollowing are the advantages and disadvantages of welded joints over riveted joints.Advantages1. The welded structures are usually lighter than riveted structures. This is due to the reason, that in welding, gussets or other connecting components are not used.2. The welded joints provide maximum efficiency (may be 100%) which is not possible in case of riveted joints.3. Alterations and additions can be easily made in the existing structures.4. As the welded structure is smooth in appearance, therefore it looks pleasing.5. In welded connections, the tension members are not weakened as in the case of riveted joints.6. A welded joint has a great strength. Often a welded joint has the strength of the parent metal itself.7. Sometimes, the members are of such a shape (i.e. circular steel pipes) that they afford difficulty for riveting. But they can be easily welded.8. The welding provides very rigid joints. This is in line with the modern trend of providing rigid frames.9. It is possible to weld any part of a structure at any point. But riveting requires enough clearance.10. The process of welding takes less time than the riveting.Disadvantages1. Since there is an uneven heating and cooling during fabrication, therefore the members may get distorted or additional stresses may develop.2. It requires a highly skilled labour and supervision.3. Since no provision is kept for expansion and contraction in the frame, therefore there is a possibility of cracks developing in it.4. The inspection of welding work is more difficult than riveting work.

Welding ProcessesThe welding processes may be broadly classified into the following two groups:1. Welding processes that use heat alone e.g. fusion welding.2. Welding processes that use a combination of heat and pressure e.g. forge welding.These processes are discussed in detail, in the following pages.Fusion WeldingIn case of fusion welding, the parts to be jointed are held in position while the molten metal is supplied to the joint. The molten metal may come from the parts themselves (i.e. parent metal) or filler metals which normally have the composition of the parent metal. The joint surface becomes plastic or even molten because of the heat from the molten filler metal or other source. Thus, when the molten metal solidifies or fuses, the joint is formed.

The fusion welding, according to the method of heat generated, may be classified as:1. Thermit welding, 2. Gas welding, and 3. Electric arc welding.

Thermit Welding

In thermit welding, a mixture of iron oxide and aluminium called thermit is ignited and the iron oxide is reduced to molten iron. The molten iron is poured into a mould made around the joint and fuses with the parts to be welded. A major advantage of the thermit welding is that all parts of weld section are molten at the same time and the weld cools almost uniformly. This results in a minimum problem with residual stresses. It is fundamentally a melting and casting process.

The thermit welding is often used in joining iron and steel parts that are too large to be manufactured in one piece, such as rails, truck frames, locomotive frames, other large sections used on steam and rail roads, for stern frames, rudder frames etc. In steel mills, thermit electric welding is employed to replace broken gear teeth, to weld new necks on rolls and pinions, and to repair broken shears.

Gas WeldingA gas welding is made by applying the flame of an oxy-acetylene or hydrogen gas from a

welding torch upon the surfaces of the prepared joint. The intense heat at the white cone of the flame heats up the local surfaces to fusion point while the operator manipulates a welding rod to supply the metal for the weld. A flux is being used to remove the slag. Since the heating rate in gas welding is slow, therefore it can be used on thinner materials.

Electric Arc WeldingIn electric arc welding, the work is prepared in the same manner as for gas welding. In

this case the filler metal is supplied by metal welding electrode. The operator, with his eyes and face protected,strikes an arc by touching the work of base metal with the electrode. The base metal in the path of the arc stream is melted, forming a pool of molten metal, which seems to be forced out of the pool by the blast from the arc, as shown in Fig. 10.1. A small depression is formed in the base metal and the molten metal is deposited around the edge of this depression, which is called the arc crater. The slag is brushed off after the joint has cooled. The arc welding does not require the metal to be preheated and since the temperature of the arc is quite high, therefore the fusion of the metal is almost instantaneous. There are two kinds of arc weldings depending upon the type of electrode.

1. Un-shielded arc welding, and2. Shielded arc welding.

When a large electrode or filler rod is used for welding, it is then said to be un-shielded arc welding. In this case, the deposited weld metal while it is hot will absorb oxygen and nitrogen from the atmosphere.This decreases the strength of weld metal and lower its ductility and resistance to corrosion. In shielded arc welding, the welding rods coated with solid material are used, as shown in Fig.10.1. The resulting projection of coating focuses a concentrated arc stream, which protects the globules of metal from the air and prevents the absorption of large amounts of harmful oxygen and nitrogen.

Forge WeldingIn forge welding, the parts to be jointed are first heated to a proper temperature in a furnace or forge and then hammered. This method of welding is rarely used now-a-days. An electric-resistance welding is an example of forge welding. In this case, the parts to be joined are pressed together and an electric current is passed from one part to the other until the metal is heated to the fusion temperature of the joint. The principle of applying heat and pressure, either sequentially or simultaneously, is widely used in the processes known as *spot, seam, projection, upset and flash welding.

Types of Welded JointsFollowing two types of welded joints are important from the subject point of view:1. Lap joint or fillet joint, and 2. Butt joint.

Lap JointThe lap joint or the fillet joint is obtained by overlapping the plates and then welding the edges of the plates. The cross-section of the fillet is approximately triangular. The fillet joints may be1. Single transverse fillet, 2. Double transverse fillet, and 3. Parallel fillet joints.The fillet joints are shown in Fig. 10.2. A single transverse fillet joint has the disadvantage that the edge of the plate which is not welded can buckle or warp out of shape.

Butt JointThe butt joint is obtained by placing the plates edge to edge as shown in Fig. 10.3. In butt welds, the plate edges do not require bevelling if the thickness of plate is less than 5 mm. On the other hand, if the plate thickness is 5 mm to 12.5 mm, the edges should be bevelled to V or U-groove on both sides.

The butt joints may be1. Square butt joint, 2. Single V-butt joint 3. Single U-butt joint,4. Double V-butt joint, 5. Double U-butt joint.

These joints are shown in Above.The other type of welded joints are corner joint, edge joint and T-joint as shown

The main considerations involved in the selection of weld type are:1. The shape of the welded component required,2. The thickness of the plates to be welded, and3. The direction of the forces applied.Basic Weld Symbols

Supplementary Weld Symbols: Finishing symbols after weld,

Elements of a Welding SymbolA welding symbol consists of the following eight elements:1. Reference line, 2. Arrow,3. Basic weld symbols, 4. Dimensions and other data,5. Supplementary symbols, 6. Finish symbols,7. Tail, and 8. Specification, process or other references.