Although hertzian contact theory has been applied in the case of concentric ceramiconceramic hip contact mak and jin, 2002, its merits and shortcomings have not been assessed in abnormal states and multiple material couples. Hertz law has been used beyond the limits of its validity on the. The consequences for these limitations are small for optics and unless there is an argument that the stress must be known exact as possible, for optical engineers using the hertz contact theory as is can be bene cial. Hertzian contact theory applied to edgeloaded ceramicon. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. Nov 10, 2011 in the ceramic liners, the edge radius was observed to consist of multiple segments.
Pdf contact mechanics amir rostami and xianzhang wang. Hertz contact theory hct is a study of contact stress and deformation which is widely used in many engineering fields. The franckhertz experiment the franckhertz experiment, first undertaken shortly after bohrs theory of the atom was presented, provided one of the early indications that atoms had discrete energy levels. In this model the normal force component is based on hertzian contact theory hertz 1882. On the other hand, a finite element model has been developed and validated in terms of the contact area, maximum contact pressure, pressure distribution, maximum. You could divide the hertz stresses by the same factors before comparing them to your allowables.
In case of two cylinders in contact with radii, as shown in fig. Hertz 1882 contact model is both elastic and quasistatic in nature. Assessment of the applicability of hertzian contact theory. On the compression of a cylinder in contact with a plane surface. The unit of frequency, cycle per second, was named the hertz in his honor. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. Hertzmindlin no slip this contact model is the default model used in edem due to its accurate and efficient force calculation. Assessment of the applicability of hertzian contact theory to. Dem interaction hertz mindlin contact this is a noslip contact model used for modeling contact between particles the hertzmindlin contact model is a variant of the nonlinear springdashpot contact model based on the hertzmindlin contact theory the forces between two particles, a and b, are defined by the following equations. Contact stress causes deformation, plastic or elastic.
These stresses were first studied by the german physicist heinrich hertz in 1881. Another contact force model recently published was due to flores and his coauthors that was developed with the foundation of the hertz contact theory together with a hysteresis damping parameter that accommodates the loss of energy during the contact process. The consequences for these limitations are small for optics and unless there is an argument that the stress must be known exact as possible, for optical engineers using the hertz contact theory as. Applicability of the hertz contact theory to railwheel contact problems w. Nonadhesive, meaning the two surfaces require no force to separate. Applicability of the hertz contact theory to railwheel contact problems article pdf available in archive of applied mechanics 704. Rolling bearing life prediction, theory, and application erwin v. When discussing the rubbing issue of rotor system, the effect of nonlinear rubbing force is needed to be considered. Beside a standard rail, also a crane rail and a switching component are considered in the verification. Fischer summary railwheel contact problems have been analyzed by applying threedimensional. For this purpose, an expression for the hysteresis damping factor was derived by. The hertz contact theory consists of a series of mathematical equations to calculate normal, hoop, radial, and shear stress components on and within a soft flat surface or halfspace, known as the specimen, when pressed by a rigid hemisphere called the indentor appendix figure 1 1. In this example problem, a steel cylinder with a radius of 5 is pressed against a 2 deep aluminum base. Zaretsky national aeronautics and space administration glenn research center cleveland, ohio 445 summary a tutorial is presented outlining the evolution, theory, and application of rollingelement bearing life prediction from that.
Applicability of the hertz contact theory to rolling. Rolling bearing life prediction, theory, and application. Please see below for the options available which we can assist you. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. The hertz contact theory the hertz contact theory consists of a series of mathematical equations to calculate normal, hoop, radial, and shear stress components on and within a soft flat surface or halfspace, known as the specimen, when pressed by a rigid hemisphere called the indentor appendix figure 1 1. After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies. 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. Under these assumptions, only normal pressure acts between two bodies due to hertz contact producing normal displacements of. Compliant contact force models in multibody dynamics. Even though the derivation of the theory is relatively difficult, the final solution is a set of simple analytical equations relating the properties of the system to the developed stress. Elastic compression of spheres and cylinders at point and. It was observed that, though hertz theory applied at large loads, at low loads the area of contact was larger than that predicted by hertz theory, the area of contact had a nonzero value even when the load was removed, and. Area of contact is dependent on the force applied due to elastic deformation.
Theoretical background and applications of dem simon lo. The hertzmindlin contact model is a variant of the nonlinear springdashpot contact model based on the hertzmindlin contact theory the forces between two particles, a and b, are defined by the following equations. This page focuses mainly on the normal direction, i. General theory a general b geometry of the unstressed surface in the region of contact c equations for area of contact, pressure distribution and compression iii. For an electronic copy pdf of the relevant report, click here consider a simple problem that illustrates a comparison between the analytical and numerical results. Toporov published another theory in 1975, which came to be known as the dmt theory in the research community, which also recovered hertz s formulations under the assumption of zero adhesion. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. In this paper, modeling and numerical simulation were carried out by using the nonlinear rubbing force based on hertz contact theory, and researching the dynamic response of fault rotor system in the conditions of the different rubbing stiffness. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings.
Pdf hertz contact stress analysis and validation using. Railwheel contact problems have been analyzed by applying threedimensional finite element models. The mathematical theory for the general threedimensional contact problem was first developed by hertz in 1881. In this experiment, electrons are accelerated and pass through mercury vapor, where they lose energy by. Frictional and mechanical properties of fe5si3particledispersed si3n4 fabricated by solutioninfiltration method. Force modulation sfm and hertzian theory the hertzian theory of elastic circular point contact for a planar surface and an assumed spherically caped tip, fig. It applies to normal contact between two elastic solids that are smooth and can be described locally with orthogonal radii of curvature such as a toroid. In addition, the problem is analyzed under dynamic conditions in abaqusstandard to illustrate the use of contact. Hertz theory assumes that surfaces are continuous and nonconforming, strains are small, each solid can be considered as an elastic halfspace, and surfaces are frictionless. Jul 01, 2012 an analytical approach for stress analysis of gear drives with localized bearing contact based on the hertz theory is proposed. Hertz contact stress mechanical engineering general.
The hertz contact theory the hertz contact theory consists of a series of mathematical equations to calculate normal, hoop, radial, and shear stress components on and within a soft flat surface or halfspace, known as the specimen, when pressed by a. Normal contact of elastic solids hertz theory chapter 4. Similar to this theory, however using different assumptions, b. Contact is a point or line when there are no applied forces or moments. Use the following categories below to email us regarding your questions or comments. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. Oct 23, 2014 5 contact parameters are also tricky, midas nfx is using the penalty method for general contact, so you should keep in mind that the penetration will play a big influence on the results. Lesson 9 hertz contact problem patran 322 exercise workbook 93 model description.
High contact stress may lead to failures such as cracks, pits and flaking in the surface material. Contact mechanics in 1881 1882, hertz published two articles on what was to become known as the field of contact mechanics. Based on these models, the applicability of the hertz contact theory hct to railwheel contact problems is veri. Therefore, it is very imporant to calculate the actual stress at the point of contact, the socalled contact stress by theory of elasticity, developed by hertz, in 1881, when he was 23 years old. Dynamic analysis of rubbing rotor system based on hertz. Pure hertzian model only describes normal deformation of spheres. It also serves as an excellent illustration of the use of substructuring in abaqusstandard for locally nonlinear cases local surface contact. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. In the case of a contact between the standard rail. Kita, hideki hirai, takene iizuka, tateoki and osumi, kazuo 2003. On the compression of a cylinder in contact with a plane.
The tangential force model is based on mindlinderesiewicz work mindlin 1949 mindlin and deresiewicz 1953. The proposed approach provides a complete and effective solution of the contact problem but satisfaction of the hypotheses for application of the hertz theory is its main drawback. The contact area will change depending on the magnitude of the contact stress. Hertzian elastic contact and jkr adhesiveelastic contact as function of load. Toward realtime detection of deep tissue injury risk in. Pdf applicability of the hertz contact theory to railwheel. A theoretical background to the hertz contact theory can be found here. For higher separations, the hertz theory closely predicts the contact mechanics, but further work is needed to evaluate the component geometry and the predictions for lower separations. Based on these models, the applicability of the hertz contact theory hct to railwheel contact problems is verified in the present paper. This interaction or contact can occur on many different scales, ranging from nanoscale asperities up to tires on roads and even contact. Pdf applicability of the hertz contact theory to rail.
From contact mechanics2 demonstrating the change in area during conditions of load. Relation between hertz stresslife exponent, ballrace. A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies surfaces known as the normal direction and frictional stresses acting tangentially between the surfaces. Archive of applied mechanics 70 2000 255268 o springer. Hertz developed a theory to calculate the contact area and pressure between the two surfaces and predict the resulting compression and stress induced in the objects.
Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Special cases a two spheres in contact b sphere in contact with a plane c sphere in contact with an internal sphere d equal cylinders. The problem is linear except the contact condition at the base which is modeled using the contact pair approach. Hertz is committed to providing our customers with the highest level of service. Tutorial on hertz contact stress university of arizona. Hertzian contact equations for elliptical, spherical and. Pdf compliant contact force models in multibody dynamics. Contact hertz stress the contact hertz stresses at the respective races of a bearing are a function of the bearing geometry, the normal load at the contact, and the elastic properties of the bearing materials. If we determine the size and shape of this contact area and the distribution of normal pressure, then the interval stresses and deformation can be calculated. Hertz contact theory maintains both surfaces are frictionless. Hertz is well known for his contributions to the field of electrodynamics see below. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately.
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