Assignment truss is axial tension or compression.

AssignmentStress analysis of a workpiece in any Lathe Process1. Objective:i. To analyze the stresses produced during straight turning on Lathe Machine.

ii. To determine the Modulus of Rigidity.2. Apparatus:i. Work piece of cast ironii. Single point cutting tooliii. Universal Lathe Machineiv. Meter rodv.

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Vernier caliper3. Introduction:One of our principal concerns in this course is material behavior (Strength). But strength models are often intimately related to stress. Thus, we need to be able to compute stresses. Stresses, however, cannot be directly measured, but stain is measurable and can be directly related to stress. The principal force in each element in a truss is axial tension or compression. 3.1 Stress: ‘Stress is defined as the force across a “small” boundary per unit area of that boundary, for all orientations of the boundary.

Being derived from a fundamental physical quantity (force) and a purely geometrical quantity (area), stress is also a fundamental quantity, like velocity, torque or energy, that can be quantified and analyzed without explicit consideration of the nature of the material or of its physical causes.’ 2 Mathematically, Stress=Force/Area ?=F/A Figure No 2: Stress 3 3.1.1 Units: ‘ The dimension of stress is that of pressure, and therefore its coordinates are commonly measured in the same units as pressure: namely, Pascals (Pa, that is, newtons per square meter) in the International System, or Pounds per square inch (psi) in the Imperial system. Because mechanical stresses easily exceed a million Pascals, MPa, which stands for megapascal, is a common unit of stress.

‘ 3.1.2 Classification: Stress is classified as, i. Normal Stressii. Shear Stress iii. Volumetric Stressiv. Torsional Stress 3.

1.2.1 Normal Stress: ‘When the load applied is perpendicular to the stretched surface, the stress produced is called normal stress. It can be compressive or can be tensile.’ 4 Figure No 3: Normal Stress 5 Shear Stress: ‘When the load applied is parallel to the stretched surface, the stress produced is called shear stress.

Usually denoted by “?”.’ 6 Figure no 4: Shear Stress 7 3.1.2.

3 Volumetric Stress: ‘Volumetric stress is a particular stress state in which all three directions are uniformly.’ 8 Figure no 5: Volumetric Stress 9 Torsional Stress: ‘Torsional shear stress or Torsional stress is the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it.

‘ 10 Figure no 6: Torsional Stress 11 3.2 Strain: ‘Strain, represented by the Greek letter ?, is a term used to measure the deformation or extension of a body that is subjected to a force or set of forces. The strain of a body is generally defined as the change in length divided by the initial length.’ 12 Mathematically, Strain=Change in length/Original length ?=&l/l 3.2.1 Units: As it is a ratio, so it has no units. 3.

2.1 Classification: The Strain is classified as,i. Normal strainii.

Shear strainiii. Bulk(volumetric) strain Normal Strain: ‘When a change in length is produced by applying load to the cross section, then it is normal strain.’ 13 Strain=Change in length/Original length ?=&L/L Figure no 7: Normal strain (tensile and compressive) 14 3.

2.1.2 Shear Strain: ‘The engineering shear strain is defined as the tangent of that angle, and is equal to the length of deformation at its maximum divided by the perpendicular length in the plane of force application which sometimes makes it easier to calculate.’ 15Mathematically, Shear strain= Tan(?) Figure no 8: Shear strain 16 Bulk strain: ‘The volumetric strain is the unit change in volume, i.e.

the change in volume divided by the original volume.’ 17Mathematically, Bulk strain=Change in volume/Original volume ?=&V/V Figure no 9: Bulk strain 18 3.3 Hooke’s Law: ‘A law stating that the strain in a solid is proportional to the applied stress within the elastic limit of that solid.

‘ 19 Mathematically, Strain ? Stress ? ? ? ?=E?Where,E= Modulus of elasticity (proportionality constant) Figure no 10: Hooke’s Law 203.3 Modulus of Elasticity: ‘It is defined as a ratio of stress to strain. Usually denoted by “E”. As strain has no units so its units are the same as that of stress which is pascal or pound per inch square.’ 21Mathematically, E=Stress/Strain 3.3.

1 Classification: Modulus of elasticity is classified as,i. Young’s Modulusii. Bulk Modulusiii. Shear Modulus 3.

3.1.1 Young’s Modulus: ‘Young’s modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression. Young’s modulus is equal to the longitudinal stress divided by the strain. Usually denoted by “Y”. ’22Mathematically, Y= P&L/ALWhere,P= Load applied?L= Change in lengthA= Area of cross section L= Original length Figure no 11: Young’s Modulus 23 3.3.

1.2 Bulk Modulus: ‘The relative change in the volume of a body produced by a unit compressive or tensile stress acting uniformly over its surface. Usually denoted by “K”. ’24Mathematically, K= P ;V/AVWhere,P= Load applied;V= Change in VolumeA= Area of cross section V= Original Volume Figure no12: Bulk Modulus 25 Shear Modulus/ Modulus of rigidity: ‘It is defined as the ratio of shear stress to the shear strain. Usually denoted by “G”.

‘ 26Mathematically, G=P/Axtan(?)Where,P= Load appliedA= Area of cross sectionTan(?)= shear strain Figure 13 shear modulus 273.4 Central Lathe Machine:’A lathe is a machine that rotates the workpiece about an axis of rotation to perform various operations such as cutting, sanding, knurling, drilling, deformation, facing, and turning, with tools that are applied to the workpiece to create an object with symmetry about that axis.’28 Figure no 14: Central Lathe Machine 293.4.1 Uses and Applications:’Lathes are used in woodturning, metalworking, metal spinning, thermal spraying, parts reclamation, and glass-working. Lathes can be used to shape pottery, the best-known design being the potter’s wheel. Most suitably equipped metalworking lathes can also be used to produce most solids of revolution, plane surfaces and screw threads or helices.

Ornamental lathes can produce three-dimensional solids of incredible complexity. The workpiece is usually held in place by either one or two centers, at least one of which can typically be moved horizontally to accommodate varying workpiece lengths. Other work-holding methods include clamping the work about the axis of rotation using a chuck or collet, or to a faceplate, using clamps or dogs.’3.4.2 Components: The lathe consists following parts. 301.

Bed: ‘It is the main body of the machine. All main components are bolted on it. It is usually made by cast iron due to its high compressive strength and high lubrication quality. It is made by casting process and bolted on floor space.’2. Tool post: ‘It is bolted on the carriage. It is used to hold the tool at correct position. Tool holder mounted on it.

‘3. Chuck: ‘Chuck is used to hold the workspace. It is bolted on the spindle which rotates the chuck and work piece. It is four jaw and three jaw according to the requirement of machine.’4. Head stock: ‘Head stock is the main body parts which are placed at left side of bed.

It is served as holding device for the gear chain, spindle, driving pulley etc. It is also made by cast iron.’5. Tail stock: ‘Tail stock situated on bed. It is placed at right hand side of the bed.

The main function of tail stock to support the job when required. It is also used to perform drilling operation.’6. Lead screw: ‘Lead screw is situated at the bottom side of bed which is used to move the carriage automatically during thread cutting.’7. Legs: ‘Legs are used to carry all the loads of the machine. They are bolted on the floor which prevents vibration.

‘8. Carriage: ‘It is situated between the head stock and tail stock. It is used to hold and move the tool post on the bed vertically and horizontally.

It slides on the guide ways. Carriage is made by cast iron.’9. Apron: ‘It is situated on the carriage.

It consists all controlling and moving mechanism of carriage.’10. Chips pan: ‘Chips pan is placed lower side of bed. The main function of it to carries all chips removed by the work piece.’11. Guide ways: ‘Guide ways take care of movement of tail stock and carriage on bed.

’12. Speed controller: ‘Speed controller switch is situated on head stock which controls the speed of spindle.’13. Spindle: ‘It is the main part of lathe which holds and rotates the chuck.’3.4.

3 Operations: ‘To understand the different operations the machinist must know how to give different feeds on the machine. And also, must have a clear idea about the cutting tools. Different types of lathes are available in the industry. So, lets discuss the processes and follow the diagrams for a better understanding.’ 311. Facing: ‘Facing is used to make a flat surface at the end of the work piece. The work part should be rotating and the implied feed should be radial.

‘ Figure no 15: Facing 322. Con tour turning: ‘In this operation of lathe machine, the tool is not fed in a straight path, Instead the tool follows a contour. A contoured form is created in the turned part.

‘ Figure no 16: Con tour turning 333. Form turning: ‘In this method a special shaped tool is used. The tool is inserted radially.’ Figure no 17: Form turning 344. Taper turning: ‘Like contour turning the tool is not fed parallel to the axis of rotation of the work part. The tool is fed at an angle.

This turning operation gives a conical and taper cylindrical shape.’ Figure no 18: Taper turning 35Chamfering: ‘Only the cutting edge is used at the corner of cylindrical shapes which is used for stress relieving of the workpiece.’ Figure no 19: Chamfering 36Cutoff or Parting: ‘In parting operation, the tool is fed radially and the end part of the workpiece is cut off.’ Figure no 19: Parting 37Boring: ‘A single point tool head is fed linearly to the end of the workpiece (on the inside diameter).’ Figure no 20: Boring 38Threading: ‘A pointed tool is used at the outside surface of the workpiece with linear feed.

‘ Figure 21: Threading 39Drilling: ‘Drilling and reaming is done by feeding the lathe tool along the axis of the rotating job part.’ Figure no 22: Drilling 40Knurling: ‘It is a metal forming method which creates a regular cross hatched pattern. It is not a machining process. It does not involve any cutting of the metal.’ Figure no 23: Knurling 414.

Comments:? The work piece is made up of cast iron.? The error in the determination of modulus of rigidity is due toi. Personal errorii. Instrumental error? There is also an effect of friction and rake angle on the shear angle.

i. Friction is inversely proportional to shear angle.ii. Rake angle is directly proportional to shear angle.5. References:1 2 UPAC, Compendium of Chemical Terminology, 2nd ed.

(the “Gold Book”) (1997). Online corrected version: (2006–)3 4 McSkimin, H.J.; Andreatch, P. (1972). “Elastic Moduli of Diamond as a Function of Pressure and Temperature”5 www. Crandall, Dahl, Lardner (1959). An Introduction to the Mechanics of Solids. Boston: McGraw-Hill7 www. Spanos, Pete (2003). “Cure system effect on low temperature dynamic shear modulus of natural rubber”9https://www. 10 Landau LD, Lifshitz EM. Theory of Elasticity, vol. 7. Course of Theoretical Physics. (2nd Ed) Pergamon11 12 verton, W.

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, (1996), Electron Correlation in Molecules and Condensed Phases, Springer16 17 Varshni, Y. (1970).

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