Contact Stress Theory

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Chapter -2 Literature review
High stresses are induced when a load is applied to two elastic solids in contact. This can cause serious issues in the optomechanical design if not considered and addressed properly. Contact between two continuous, non-conforming solids is initially a point or line. Under the action of a load the solids deform and a contact area is formed. Hertz contact stress theory allows for the prediction of the resulting contact area, contact pressure, compression of the bodies, and the induced stress in the bodies.

2.1 Analysis of surface and sub-surface cracks due to fatigue D. Finney Charles, R. Gnanamoorthy (2010) investigated rolling contact fatigue (RCF) …show more content…

Since all fundamentals of rolling contact fatigue are present in a deep groove ball bearing or a spur gear, these applications are used to exemplify the application mechanics.
As we know the mechanics differs between applications it is realised that the rolling contact consists of some common geometric properties. The nominal contacts can be regarded a two dimensional or line contact where Hertz contact conditions exists.

2.3.1 Hertz pressure Hertzian contact stress refers to the localized stresses that develop as two curved surface come in contact and deform slightly under the imposed load. This amount of deformation is dependent of modulus of elasticity of the material in contact. It gives the contact stress as a function of the normal contact force, radii of curvature of both bodies and modulus of elasticity of both bodies .Hertzian contact stress forms the foundation for the equation for load bearing capabilities and fatigue life in bearings , gears and any other bodies where two surfaces are in contact .
Assumption in Hertzian theory :-
• Strains are small and within the elastic limit
• The surfaces as continuous and non-conforming(implying that the area of contact is much smaller than the characteristic dimensions of the contacting …show more content…

Therefore, the material is case hardened, which gives increased surface hardness combined with residual compressive stresses present at the surface. It should be noted that although the hardness and the residual stresses from heat treatment are results of the same process, the material hardness is only dependent on the local material state whereas the residual stress distribution is dependent on the geometry through the equilibrium of expanded and unaffected material. An increasing resistance against surface fatigue with hardness was documented already by Way in 1935. It was also found that the spalls became smaller for a hardened

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