Role and Importance of Hertzian Contact Stress - Report Example

Role and Impotance of sub-surfaces Hertizan stresses in the design of marine engineering components Hertzian contact stress pertains to the localized stresses that evolved as two curved surfaces come in contact with each other and mutilate slightly under the heavy intrude loads. This amount of wrenchment is incidental on the elasticity of the the material in contact, i.e., its modulus of elasticity.It describes the contact stress as a application of the normal contact force,the radii of curvature of both bodies and the modulus of elasticity of both bodies.Hertzian contact stress materialize the basis for the equations for load bearing capabilities in bearings, gears, and any other bodies where two surfaces are in contact.These stresses have nothing to do with the unit of measurement of frequency, the hertz (Hz). The Hertzian contact stress theory is based on following fundamentals: At the point of contact both surfaces are ideally smooth; Contact stresses and wrench gratify the differential equations for stress and strain of consistent, isotropic, and elastic bodies in equilibrium; As the distance increases from the contact zone, the stress disappears; Tangential stress components are zero at both surfaces within and outside the contact zone; Normal stress components are zero at both surfaces outside the contact zone; The stress integrated over the contact zone equals the force pushing the two bodies together; The distance between the two bodies is zero within but finite outside the contact zone; Allay of sub-surface impairment in a material is significant to perceive the wrenchment mechanisms in machining and indentation. For rigid and crumbly materials such as ceramics, the modus operandi of cross-section view testing is very much time consuming and arduous to execute. Hertz identifies that the abutment of non-conforming forms was an example of stress accumulation that could be explicated liberated of the geometry and physics of stress field generated in the bodies. According to Heinrich Hertz," we can confine our attention to that part of each body which is very close to the point of contact, since here the stresses are extremely great compared with those occurring elsewhere, and consequently depends only to the smallest extent on the forces applied to other parts of the bodies." By circumscribing concentration to that fragment of the garb padlocked to the areas in contact with each other, the forces and wrench can be observed by evasion the slender cal arch of the surfaces of the two contacted bodies. The hertz theory is stimulated by two factors namely quadratic terms are used to delineate the geometry of general curved surface areas and the area of the body that have a curved surface mutilate as though they have elastic half spaces. From time to time efforts are made to enhance hertz theory by considering higher order terms in the geometric elaboration of cylindrical or spherical profiles and by calculating the deformations of truly cylinder or spherical solids. Considering the hertz theory with respect to Marine engineering components, it has been observed that these components are designed to accommodate a defined life. Considering the case of Roll Bearings, which are used in ships, has approximately life of 65,000 hours and so accordingly this requires its replacement quite frequently during the tenure of the ship. The failure of these bearings is consorted with the inner raceway. The failures, which include the center radial, bearing of thrust bearing pair and radial drive end bearing, are also experienced. A very close examination depicts that the failure is the result of sub-surface fatigue. Once the cracks are instigated then it lead to grows and promulgate sub-surfaces. Following figure shows typical failure morphology of bearings This figure shows that Hertizan stresses plays important role in this failure process. On canvassing and implicating the Hertz theory in above scenario it is serene that shear forces are effectuated sub-surface and repose on plane close to 45 degrees, which is contingent to the raceway surfaces. Hence, the dimension of the normal stresses in the bearing material, originate from the pressure exert as two bodies came in contact with each other and decayed with increasing extent into the material and vacillate between Zero and some compressive value, the shear stresses rotate between malleable and condensed values. Following figure further depicts the detailed microscopic examination of bearings. The stress integrated over the contact zone equals the force pushing the two bodies together. This crack occurs when the material has experienced a significant level of stress developed from a combination of operational and residual origins. These cracks are called butterflies. The wings from which the butterflies got its name are developed by a degree change in the constituent at surrounding temperature and some how under adiabatic situations when mandated to a considerate degree of stress. It is serene from the morphology of wings and through white carved area that the substitutes manifest a matrix structure on a nanometer scale. These characteristics generally prevail at oxide inclusions and also at intricate inclusions comprising of oxides and sulphides. These are the key points where they tend to palpitate mostly at oxide-sulphide edges of the filled cavity. The phenomenon of crack propagation from an inclusion is complex process. The stress field is accountable for driving the crack growth in the purlieu of the crack tip and is normally encompass two sovereign endowments: a malleable component and a shear component. When the flaw has increased to a level where linear elastic condition preponderates, then to a first approach to its increased size will be reigned by the stress intensity relationship. The roughness of the surface plays an important role in these cracks also. The number, type and location on inclusions in a bearing ring are substantial when ruminating the compatibility of a material denomination and regulate the chemical composition of the oxygen; titanium and sulphur degrees during the manufacturing progression are significant so as to achieve the desired and appropriate material properties and composition In case of marine bearing manufacture the forging activity demands optimization in order to accommodate material of a appropriate quality and quantity for the bearing rings, which will undergo strongly fluctuating loads during their tenure. Normally the bearing rings consist of a baintic matrix and it is observed that the degree of preserved austenite within this matrix should be kept below 4% of large bearings. If the retained austenite level becomes too high then this results in hardness of the material concerned and there is a hazard that the austenite phase may metamorphose, mainly to abandoned marten site which would be extremely brittle and could lead to cracks within the matrix. Increase in material hardness will generally yield an increase in the fatigue life of the material. Therefore several conscious candid methods are adopted to overcome these issues and the bonded interface technique (BIT) is the part of one of those methodologies and has been employed by number of groups to expedite the canvass of sub-surface impairment. The BIT bestows two relatively square and alike shaped samples of the identical material. A garb on each exemplar is burnished and mucilage sane by a cyanoacrylate superglue, as shown in below The mucilage layer in the impressed exemplar will be determined chemically and the sub-surface destruction caused by the groove can then be scrutinize expediently by examining the few parts of the sample. However, this strategy breaks the ax symmetric, perpetual and consistent situations on which the diagnostic hertzian stress. It is postulated that if the layer is thin enough the overhead discrepancies will have a picayune percussion on the groove eventuates. The proceeds of the elastic finite element diagnosis depicts that a peculiar stress is fraternize with the BIT that is sufficiently diligent from the normal Hertzian stress. For the level of mucilage mechanical properties analyzed, it has been observed that the glue has a minimal effect on this basic behavior. It can be depicted that the stress degrees in the mucilage or glue layer are significantly less than those observed in the integral model where the exemplar is a perpetual alumina. The conventional sub-surface Hertzian stress is not prolonged. This depicts that the glue layer not only destroys the persistency of the alumina, but also in effect yields almost free surfaces on the interface planes areas. Since free surface areas enthrall disarticulation by their capability to decrease dislocation energy field, it is gestated that both displacement and splits circulation behavior would be affected, and a difference in sub-surface erosion is visible between groove of integral alumina specimens, and BIT ones. The next important issue with the glue layer is its power to hold the shearing energy that is being used. The percussion and stress resistance of drape cover is remarkably leveraged by the residual strain (or stress) field persuaded during coating accumulation, post-treatment, and in-service loading. Optimization of the residual strain field is therefore meticulous to the vitality and achievements of components. Non destructive measurement of these strain fields in relatively thin thermal spray coatings, however, masquerade a defiance because orthodox approach, such as deep hole drilling, x-ray diffraction, synchrotron diffraction, and changes in beam curvature either make these systems pernicious and/or deliver only a very near-surface strain measurement. This specifically tangled the strain analysis in cermets coatings, deposited by the thermal spraying process, where the low penetration depth of x-ray and synchrotron-diffraction ray can only provide a through thickness measurement of stress or strain profile via the destructive layer removal technique. Recent investigations have therefore concentrated on the use of neutron diffraction technique for such analysis, and since neutrons are not charged, they do not interact with the electron cloud surrounding the atom (unlike x-ray); hence, diffraction results from the interaction with the atomic nucleus. Neutrons therefore have greater penetration depth in most engineering materials, and therefore provide a nondestructive through thickness strain measurement. This significantly influences the contact stress performance by improving both the cohesive and adhesive strength of these coatings. Optimizing design or studying the consequences of differences of fabrication situations on shape, size, deformation, and stress in the contact zone stipulates quite big series of organized or haphazardly differentiated principal radii of curvature of the contacting surfaces. Such series can be distinguished and elaborated by a matrix whose elements are ordered quadruples of the four radii of each individual combination. For monotone series of the principal radii of curvature, the elements are algebraically related and by proper selection of their number the central element of the matrix represents a sphere-on-sphere contact that serves as reference. References Guiberteau, F & Padture, NP & Lawn, BR 1994, 'E!ect of grain size on hertzian contact damage in alumina', Journal of the American Ceramic Society ,vol. 77,31. Lawn, BR & Padture, NP & Guiberteau, F & Cai, H 1994,' A model for the micro-crack initiation and propagation beneath hertzian contacts in polycrystalline ceramics'. Acta Metalurgica Materialia, vol 42,93. Latella, BA & O'Connor, BH & Padture, NI & Lawn, BR 1997, 'Hertzian contact damage in porous alumina', Journal of the American Ceramic Society, vol. 80,31. Johnson, KL 1985, Contact mechanics. Cambridge, Cambridge University Press, UK. Green, DJ 1998, An introduction to the mechanical properties of ceramics, Cambridge University Press,Cambridge, UK Goodman, LE & Keer, LM 1965,'The Contact stress problem for an elastic sphere indenting an elastic cavity',Int. j. Solids & Structures,Vol 1,407. Timoshenko, SP & Goodier, JN 1951,Theory of elasticit ,McGraw-Hill Read More