The mechanics of surfaces in contact is called contact mechanics johnson, 1985. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. The common approach to the study of contact mechanics is either. Assessment of the applicability of hertzian contact theory to. Thwaite summary the purpose of this paper is primarily to present in a convenient form the formulae and data for the calculation of the compression effects which occur in the measurement and use of spheres and cylinders in dimensional metrology.
Contact mechanics was first studied by hertz in the 1880s with reference to optical lenses hertz, 1896. W, new algorithms for calculating hertzian stresses, deformations, and contact zone parameters, amp journal of technology, 1992. Another contact case entails friction that causes shear stresses on the contact zone. The material at the contact plane wants to expand outward due the compressive contact force and poissons effect. The magnitude of the load carried by an individual ball depends on the internal geometry of the bear. Cooper abstract formulations are given for the coefficients x, u, u defined by h. It is therefore certainly desirable to model the effect of thermal 31. Contact mechanics in general contact is the study of deformable bodies that touch each other at least one point in the space. Lecture 28 antennas and radiation and the hertzian dipole in this lecture you will learn. Ciavarellab,1 adepartment of mechanical engineering and applied mechanics, university of michigan, ann arbor, mi 481092125, usa bdepartment of engineering science, university of oxford, parks road, oxford, ox1 3pj, uk. The stress distribution for the hertzian contact is given in fig. Hertz contact stress mechanical engineering general. Detailed finite element contact mechanics of the actual cracked body are used to show that the contact pressure is singular at the edge of contact once the.
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. 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. Solid mechanics part i kelly 32 illustrated in fig. A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between the normal force and the radius of contact for soft fingers by considering general softfinger materials, including linearly and nonlinearly elastic materials. Tutorial on hertz contact stress university of arizona. Ciavarellab,1 adepartment of mechanical engineering and applied mechanics, university of michigan, ann arbor, mi 481092125, usa bdepartment of engineering science, university of oxford, parks road, oxford, ox1 3pj, uk abstract contact problems are central to solid mechanics, because contact is the principal method of applying loads to a. Cambridge core solid mechanics and materials contact mechanics by k. It can be used to calculate mechanical point and line contact dimensions and material stresses. Hertzian theory of nonadhesive elastic contact in hertz s classical theory of contact, he focused primarily on nonadhesive contact where no tension force is allowed to occur within the contact area. The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20. Contact mechanics an overview sciencedirect topics. Effect of grain size on hertzian contact damage in alumina.
Normal contact of elastic solids hertz theory chapter 4. This page focuses mainly on the normal direction, i. A general method for the numerical analysis of frictionless nonconformable non hertzian contact of bodies of arbitrary shape is developed. As a preparatory step, we will summarize a few results of the theory of elasticity that have a direct application to contact mechanics. The contact area will change depending on the magnitude of the contact stress.
Introduction when there are two nonconforming surfaces that come into contact the point or line of contact can be a location of very high stress values. One of the methods that adams uses is extrapolated from hertzian contact theory. We investigate the normal contact stiffness in a contact of a rough sphere with an elastic halfspace using 3d boundary element calculations. Pdf assessment of the applicability of the hertzian. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. Contact mechanics, developed based on the continuum mechanics and mechanics of materials, is a theory to describe. Hertzian theory of nonadhesive elastic contact in hertzs classical theory of contact, he focused primarily on nonadhesive contact where no tension force is allowed to occur within the contact area. Dobrynin polymer program, institute of materials science, and department of physics, university of connecticut, storrs, connecticut 06268, united states abstract. This second edition maintains the introductory character of the first with a focus on materials science as distinct from straight solid mechanics. 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.
Stress concentration in periodically rough hertzian contact. Assessment of the applicability of the hertzian contact theory to edgeloaded prosthetic hip bearings. Journal of the mechanics and physics of solids, vol. Contact mechanics has been analyzed in industry for a long time. Bearing l 10 life, defined as number of revolutions for which 90% of bearings survive at a given load, is a strong function of peak hertzian contact pressure and the peak orthogonal subsurface shear stress. A theoretical background to the hertz contact theory can be found here. Frontiers how thermal fluctuations affect hardwall. Pdf how thermal fluctuations affect hardwall repulsion and. Numerical modeling of accretionary wedge mechanics. Jan 21, 2014 2014w engr380 lecture18 spur gear design lewis equation for tooth bending stress, part i duration. The contact radius a is considered significantly smaller than the radius of curvature r, and the two contacting surfaces, as depicted in figure 1, assumed to be nonconformal. Having determined how a bearing carries load, we can determine. Generation of radiation by oscillating charges and currents hertzian dipole antenna ece 303 fall 2005 farhan rana cornell university maxwells equations and radiation maxwells equation predict outgoing radiation from sinusoidally.
Boussinesq made a classical approach to finding the elastic stresses and their spatial distributions. Original article kl johnson and contact mechanics da hills1, d nowell1 and jr barber2 abstract in 2008, the journal of mechanical engineering science was approaching its 50th anniversary and the editorial board arranged some personal contributions from those who had been material in. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. The following assumptions are made in determining the solutions of hertzian contact problems. Introduction to contact mechanics, second edition is a gentle introduction to the mechanics of solid bodies in contact for graduate students, post doctoral individuals, and the beginning researcher. A new theory in contact mechanics for modeling of soft fingers is proposed to define the relationship between the normal force and the radius of contact for soft fingers by considering general soft. Contact stress causes deformation, plastic or elastic. Contact mechanics of nanoparticles university of akron. This interaction or contact can occur on many different scales, ranging from nanoscale asperities up to tires on roads and even contact. Knowing the deformation at the center of tne contact and.
However, it is nevertheless of interest to examine these predictions either by experiment or by independent computation. As with the block, the force will actually be distributed over a contact region. Extended hertz theory of contact mechanics for casehardened. Pdf contact mechanics amir rostami and xianzhang wang. Hertz contact stress calculations and graphs with hertzwin. Introduction to contact mechanics nanohubtechtalks. However, real surfaces are not smooth and the contact mechanics of two real bodies can bitterly deviate from the hertzian predictions since only. The theoretical contact area of two spheres is a point 0dimensional the theoretical contact area of two parallel cylinders is a line 1dimensional as a result, the pressure between two curved surfaces should be infinite the infinite pressure at the contact should cause immediate yielding of both surfaces.
However, material further away has lower compressive stress along the zaxis and does not want to expand outward as much so it constrains the material below it pushing inward. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. The application performs all calculations automatically. The limits normally adopted for hertz s contact stresses are 4 times the allowable stress for linear contact and 5. Frictional and mechanical properties of fe5si3particledispersed si3n4 fabricated by solutioninfiltration method. Tables of hertzian contact stress coefficients duane h. Stress concentration in periodically rough hertzian.
A detailed description of the impact function will follow in chapter 2. 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. It will be shown in part ii that the ball and the large object will deform and. In the end of the 19th century hertz presented a formula for calculating the contact stresses in two infinite elastic half spaces magi and melkersson, 2009, which became the general. Ball bearing mechanics the loads carried by ball bearings are transmitted through the balls from one ring to the other.
You could divide the hertz stresses by the same factors before comparing them to your allowables. For small normal forces, it is found that the stiffness behaves according to the law of pohrtpopov for nominally flat selfaffine surfaces, while for higher normal forces, there is a transition to hertzian behavior. Kita, hideki hirai, takene iizuka, tateoki and osumi, kazuo 2003. Indentation depth may be readily compared using standard experimental. There are no real life applications in which this type of contact occurs. Contact mechanics of hertzian cone cracking sciencedirect. This interaction or contact can occur on many different scales, ranging from. Numerical difficulties arise because the solution is extremely sensitive to the manner in which one discretizes the governing integral equation. For the great majority of cases, an application of hertz theory requires little more than selecting the correct formula, and this end could be served by a simple handbook compilation. The output from a contact mechanics study generally includes contact stresses, both at the bearing surfaces also known as the contact pressure and. Modeling of contact mechanics and friction limit surfaces for. Modeling of contact mechanics and friction limit surfaces. Contact mechanics fully elastic models hertz analyzed the stresses at the contact of two elastic solids, and thereby assumed small strains within the elastic limit. Contact mechanics is the study of the deformation of solids that touch each other at one or more points.
We consider the deformations in an elastic halfspace, which are caused by a given stress acting upon its. These elevated stresses are beyond the hertzian field. Traditional hertzian contact solution for determining subsurface elastic stress fields for two bodies in contact is applicable only for homogeneous materials. Next he discusses the influence of friction and the topographical roughness of surfaces, and this is incorporated into the theory of contact mechanics. However, experimental observations suggest that as the contact radius approaches the cone crack radius at the surface, interaction effects lead to a non hertzian pressure distribution. Elastic compression of spheres and cylinders at point and line contact by m. The output from a contact mechanics study generally includes contact stresses, both at the bearing surfaces also known as the contact pressure and within the component, and the contact area. Contact mechanics is a fundamental field of tribology and generally refers to the interaction of solid surfaces. It is tempting to accept the predictions regarding indentation depth and radius of circle of contact between two elastic bodies in contact given by the wellknown hertz equations at face value. Hertzian contact equations for elliptical, spherical and. In essence, many of these tests were invented before we understood either surface chemistry or contact mechanics. Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of hertzian contact stress equations can estimate maximum stresses produced and ways.
The unit of frequency, cycle per second, was named the hertz in his honor. In vivo comparison of hip mechanics for minimally invasive versus traditional total hip arthroplasty. Pdf assessment of the applicability of the hertzian contact. It applies to normal contact between two elastic solids that are smooth and. Contact stresses and deformations university of utah. Lecture 28 antennas and radiation and the hertzian dipole. Hertzwin is a free hertzian contact stress calculator. Elastic compression of spheres and cylinders at point and. Jul 18, 20 we investigate the normal contact stiffness in a contact of a rough sphere with an elastic halfspace using 3d boundary element calculations.
Apr 22, 20 step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. The following video demonstrates steps to mesh the geometry using edge sizing. A 3d object may contact on a or a series of shared points or surfaces. Numerical solution of nonhertzian elastic contact problems. Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact stresses.
How thermal fluctuations affect hardwall repulsion and thereby hertzian contact mechanics article pdf available in frontiers in mechanical engineering 5. Pdf hertz contact stress analysis and validation using. I the principal reference for this chapter is contact mechanics by johnson, 1985. 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. 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. Assessment of the applicability of hertzian contact theory. Progress over the last century in contact mechanics can be seen as the gradual relaxation of the restrictions imposed by the original hertzian treatment. Zhou y, wang a and muser mh 2019 how thermal fluctuations affect hardwall repulsion and thereby hertzian contact mechanics. Pdf contact mechanics is a fundamental field of tribology and generally. Sliding hertzian point contact tests phoenix tribology. Pdf rigorous treatment of contact problems hertzian contact. These contact stresses are called hertz contact stresses. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. We can also do wear analysis due to frictional rubbing between the contact surfaces.