Engineering Mechanics II

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EngineeringMechanics II

EngineeringMechanics II

Question5: Autofrettage and its influence on the strength of the thick walledcylinder

Autofrettagerefer to a technique that involves subjecting a given vessel to ahigh pressure with the objective of making its internal portions givein to plasticity. This process of subjecting internal parts of avessel to a high pressure is expected to result in residual stresseswhen that pressure is released. The main purpose of performing anautofrettage is to enhance the durability of the vessel andresistance to corrosion cracking.

Autofrettageenhances a walled cylinder by forcing its internal layers to stretchbeyond their respective elastic limits. This is accomplished bysubjecting the cylinder to a pressure of a given magnitude in orderto increase its bore. When the bore is enlarged, the inner layers ofthe cylinder stretch to a point in which the material used to makethe walls of the cylinder cannot return to their normal shape whenthe high pressure is released (Kumar, 2015, p. 190). The outer layersdo not stretch beyond their respective elastic point. This is becausestress is distributed in the wall of the cylinder in a non-uniformway, where maximum value is obtained in portions that are close tothe source of the high pressure. This means that the outer layers areable to return to their normal shape, but they are prevented by innerlayers, which puts the layers to a compression that is responsiblefor the strength of the walls of a cylinder.

A).Type of stresses discussed in the article

Thearticle discusses about four types of stresses. The first type isresidual stress, which refers to a type of stress that is locked intoa given material. Residual stress tends to remain even when theexternal source of pressure is removed. Residual stress is consideredas a product of material reaching equilibrium after going throughplastic deformation.

Thesecond type of stress considered in the article is von Mises stress(Kumar, 2015, p. 189). This is a type of stress that is often used todetermine whether a given vessel or design has the ability towithstand some loading condition. Von Mises type of stress is aconcept that is founded on the idea of distortion energy. The conceptimplies that the failure of the material used to make the vesseloccurs when the energy in an actual case exceeds energy in the caseof simple tension. The distorting energy is used to deform the shareof a given material.

Thethird type of stress discussed in the article is normal stress or adirect type of stress (Kumar, 2015, p. 189). This is a type of stressthat occurs when stress acts normal to the plane of a given sectionor at a section. The term normal stress combines compressive stressand tensile stress that are also discussed in the article.Compressive stress is a type of stress that acts by reducing thelength or the volume of a given material. The outcome of applyingcompressive stress is a material that is capable of reacting withsome ductile behavior. Tensile stress, on the other hand, is a typeof stress that tends to increase the length or the volume of a givenmaterial. Tensile stress forces the material to elongate or stretch. Other categories of normal stress discussed in the article includehoop stress, radial stress, and axial stress. Hoop stress is a typeof normal stress that acts in a tangential direction. Axial stress,on the other hand, acts in a parallel manner to an axis of a givencylindrical symmetry. Radial stress acts in a direction that iscoplanar with a symmetry axis, but perpendicular to that axis.

B).Discussing the conclusion

Thestudy concluded that it is possible to determine optimum ellipsevolume where stresses can be improved and the material saved. Theauthors illustrated how the ANSYS model can be used to arrive at thisvolume. ANSYS is a model that is used to determine the stressesaffecting elliptical vessels. This model is used instead of themathematical formulas because these formulas are cumbersome andlengthy. To arrive at this conclusion, the authors had to develop amodel of elliptical vessel in PTC-Creo and convert the model intoIGES for importation to ANSYS. The model was then discretized inANSYS with the help of SOLID 186 element, after which pressure wasimposed into the inner surface. This helped the authors find thesolution using ANSYS Sparse solver.

Thesimulation conducted using the solver helped the authors come up withthree results, including radial stress, hoop stress, and von-Misesstress distribution (Kumar, 2015, p. 189). The authors determined thedistribution of the three types of stress with and withoutautofrettage conditions. The authors managed to determine that theHoop stress’s maximum value is usually less under autofrettagecondition. In addition, the distribution of Hoop stress in the wholevolume of an elliptical vessel changes more than the distribution ofHoop stress that is derived without autofrettage condition.

Similarly,the authors identified that the distribution of radical stress in thewhole volume of an elliptical vessel can change more than thedistribution that is derived in the absence of autofrettagecondition. This means that the maximum value of radical stress thatis developed in a vessel is less when an autofrettage is performed(Kumar, 2015, p. 197).

Thedistribution of von Mises stress also changed more than thedistribution derived without autofrettage condition. However, themaximum value of reduced when an autofrettage was performed. Usingthe maximum values of distribution of the three types of stress andcircular cross-section, the author managed to determine the volume ofthe elliptical vessel in question. This lead to a conclusion, thatone can determine the optimum ellipse volume at which stresses can beenhanced and material saved.

Question8

A).Vibration control methods

Thereare four major methods of vibration control mentioned in the article.The first method is known as the isolation method, which involves thereduction of response of a system to transmitted vibration byrearranging the energy in a way that allows inertia to oppose theforce (Curadelli, 2004, p. 1087). Vibration reduction is achievedwhen isolators (such as springs and elastomeric) decouple the systemfrom the force inputs causing the isolated system to be out of phasewith inputs of the force that caused the vibration. This technique ismainly used in rotating machines.

Thesecond method is referred to as tuning, which refers to a process ofeliminating some amplification caused by resonance (Curadelli, 2004,p. 1088). This is accomplished by changing the system’s naturalfrequency in order to ensure that it is not concurrent with frequencyof a given force input. Resonance of equipment is expected to amplifythe response of the vibration up to a certain level depending on itsdamping characteristics.

Thethird method of vibration control technique mentioned in the articleis damping. Damping technique controls vibration close to or atresonance by dispersing energy (Curadelli, 2004, p. 1090). Viscousdamping force is usually generated by some masses that move throughthe fluid. The damping force may result from sliding motion thatoccurs between dry surfaces. Structural damping is mainly caused bysome internal friction that is experienced within a given material.

Thefourth type of vibration reduction mentioned in the article is massaddition (Curadelli, 2004, p. 1098). This technique applies thesecond law of Newton, which holds that adding the m ass of the systemwhile holding the force input constant leads to a decrease inacceleration. The mass addition technique is mainly applied inequipments with high vibration and impacting forces.

B).Main conclusion

Thearticle concluded that the use of built-in masses to controlvibration produces the same level of efficiency conventional baseisolation systems when the point of source is far. This implies thatthe replacement of the traditional systems becomes necessary when itsapplication is difficult and there is a possibility of attaching somemasses to the plate. The authors also concluded that an additionalmass of 10 % of the mass of the machine is sufficient to bring asubstantial reduction in the level of vibration. However, thetraditional isolation control technique is highly recommended whenthe vibration is near its source.

Theauthors arrived at this conclusion by conducting a numerical and anexperimental study. The two approaches involved the testing andcomparison of the traditional base isolation (using the helicalspring) and the built-in masses methods in reducing vibration both atthe point near the source and at the point away from the source. Innumerical analysis, the behavior of the system was simulated usingthe finite element software while frame elements were used to modelthe beams (Curadelli, 2004, p. 1095). The authors managed to showthat the numerical model can reproduce the response of the system ata point far from the source of vibration with accuracy in the absenceof the vibration control. However, the numerical model could notreproduce the resonance response of a system with in-built mass forvibration control.

Theexperimental analysis revealed that it could be possible to lower thevibration by about 98 % when using a spring or a built-in mass of 15% (Curadelli, 2004, p. 1097). The authors also proved that the levelsof vibration control are similar when control is conducted at a pointnear the source and built-in masses of 10 and 15 % used.

Acomparative analysis of the two techniques indicated that the use ofa helical spring and the in-built masses of 10 and 15 % could reducevibration by about 84 % and a point far from the source (Curadelli,2004, p. 1098). With these results, the authors were able to concludethat an alternative system produces the same level of efficiency asthe traditional vibration control systems when placed at a point farfrom the exciting machine. This implies that alternative systems ofcontrolling vibration should be applied in scenarios in which theapplication of traditional systems is impossible. This is because theintroduction of alternative systems (built-in masses) at a point farfrom the exciting machine will not make any difference in terms ofefficiency.

Listof references

Curadelli,R. Ambrosini, R. And Danesi, R., 2004. Vibration control by attachingmasses to a plate excited by rotating machinery. Journalof Sound and Vibration,273, p. 1087-1100.

Kumar,M, Kumar, S. and Moulick, K. Comparative stress analysis ofelliptical and cylindrical pressure vessel with and withoutautofrettage consideration using finite element method. InternalJournal of Advanced Engineering Research and Studies,1, p. 189-195.

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