Analysis of Contact Stress on Coating Based upon Hertz Theory
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Abstract:
It is necessary to study the mechanics performance of thin coating, which composite the prerequisite of coating’s application. The contact stresses are important factors for the design of hard coating/substrate because the failure of the hard coating is usually caused by these stresses. The finite element method is applied to simulate the stress of coating with contact load based on Hertz contact theory. The accuracy of model was initially tested in systems without a film. The contact stresses have been calculated based on various coating/substrate modulus ratios and the coating thickness. Results show that coating thickness changes from 1.5um to 3um, the effects of coating/substrate combination is perfect. The research has important guiding significance for the application of coating.Keywords:
Contact Mechanics
Hertz
Contact Theory
Hertz
Contact Theory
Contact Mechanics
Contact analysis
Contact area
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Hertz
Contact Mechanics
Contact Theory
Contact force
Coulomb friction
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Hertz contact theory was first derived 133 years ago which prescribes the contact behavior of normal contact between elastics. Furthermore, many studies and applications are based on it. However, Hertz contact theory still exists many uncertainties. This study first focused on the contact of a rigid sphere and an elastic half-space, and found that Hertz theory predicts well at large indentation. Besides, the critical contact central angle is 47.8° with maximum von Mises strain of 0.51. This large indentation result is independent of Young's modulus of the elastic half-space and the radius of the sphere, and it could be explained by the conformation of the pressure distribution at contact surface. Results were yielded by finite element method (FEM) and nanoindentation of polydimethylsiloxane (PDMS).
Hertz
Indentation
Contact Mechanics
Contact Theory
Contact area
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In this paper a study of the stresses in the contact zone among a couple of spur gears is realized using the finite elements method. The analysis is done by using a plane model involving the contact between two teeth. The geometry is defined according to the standards of the American Gear Manufacturers Association (AGMA). The results obtained are compared with the value given by two others approaches. The first is the theory of Hertz when it is applied to two curved segments in contact. The second approach is the AGMA procedure for calculating contact stresses in spur gear. The results obtained are very similar either using FEM and Hertz's theory. The contact pressure obtained by FEM is lower than the one obtained by means of Hertz's theory, this fact reflects the influence of the geometry profile which allows the occurrence of contact zones with greater area, and therefore lower pressures.
Spur
Hertz
Contact Mechanics
Contact Theory
Spur Gear
Contact analysis
Contact area
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Hertz
Contact Mechanics
Contact Theory
Contact region
Contact force
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A theoretical approach is presented to the plane theory of rolling contact with friction. In the present paper, the existence of the stick area is considered, then the boundary conditions of this problem are derived and the analyses of elastic contact of two cylinders are given. When the contact area is constituted by the stick area alone, the boundary value problem results in the Hilbert problem in the theory of functions. If two cylinders have the same material properties, the stress field coincides with one of Hertz contact. If they have not the same material properties, the contact width becomes shorter and the maximum contact pressure becomes higher than those of Hertz contact. Then, the tangential force is not transmitted. In addition, the stress field is discussed on the assumption that two cylinders, having the same matertial properties, constitute the stick and slip areas. In this case, the contact pressure and the contact width coincide with those of Hertz contact. Then, the stick area can exist in the neighborhood of the leading edge and the length of the stick area is determined uniquely by the values of the normal force, the tangential force and the coefficient of friction in the slip area.
Hertz
Contact area
Contact Mechanics
Contact Theory
Stress field
Contact patch
Contact force
Contact region
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A theoretical approach is presented to the plane theory of rolling contact with friction. An analysis is given of elastic contact of two cylinders. A comparison is discussed between the elastic stress fields from this analysis and from the theory of Hertz contact problem. If two cylinders have the same material properties, the pressure distribution and the width of contact agree with those of Hertz contact. If they have not the same material properties, the pressure distribution, the width and the location of the contact region differ from those of Hertz contact, however, for practical purposes the latter can be used. On the other hand, because of friction the stress fields in elastic medium shift to the direction of the frictional stress. Accordingly the location, where the material may initially yield, shifts to the same direction and approaches closer to the surface than that of Hertz contact.
Hertz
Contact Theory
Contact Mechanics
Contact area
Stress field
Contact region
Contact analysis
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Hertz
Contact Theory
Contact Mechanics
Contact area
Contact analysis
Ball (mathematics)
Ball bearing
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Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.
Hertz
Contact Mechanics
Contact Theory
Contact area
Contact force
Limiting
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The aim of this work is to evaluate the Hertz contact stiffness or Linear contact stiffness of Helical Gears in dynamic conditions. The Hertz contact occurs when two solids come in contact like sphere on sphere, cylinder on cylinder, cylinder in a groove and many other curved general contacts. In gears the contact is usually cylinder on cylinder. The Hertz model considered for the study consists of two cylinders with a spring that establishes the contact. Also the Helical Gear is modelled using Adams Gear AT. The gear is simulated for required dynamic conditions to evaluate the linear contact stiffness by establishing the relation between the Contact forces, Contact stiffness and Penetration.
Hertz
Contact Theory
Contact Mechanics
Contact force
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