Assessment of the applicability of hertzian contact theory to. Design considerations for cushion form bearings in artificial hip joints. On the compression of a cylinder in contact with a plane. However, in the late 1960s, several contradictions were observed when the hertz theory was compared with experiments involving contact between rubber and glass spheres.
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. For example, the hct is applied in 2, 3 to investigate the growth of shelltype defects in the head of a railroad rail. Zaretsky national aeronautics and space administration lewis research center cleveland, ohio 445 summary bearing technology, as well as the bearing industry, began to develop with the invention of the bicycle in. 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. Simplified computation of edgeloaded contact stresses could. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. Me 383s bryant february 17, 2006 1 contact mechanical interaction of bodies via surfaces surfaces must touch forces press bodies together size area of contact dependent on forces, materials, geometry, temperature, etc. We can also do wear analysis due to frictional rubbing between the contact.
A theoretical background to the hertz contact theory can be found here. Maximum stress stress occurs at 45 degree to the normal stress, and it can cause deformation by movement of dislocation. E lr a, where r is the radius of curvature of the probing sfm tip, and e is the modulus of the sample only, if the sample material stiffness is much smaller than the modulus of the cantilever material. Experimental study of the force pulse and resulting stress waves gregory c. Assessment of the applicability of the hertzian contact. Hertz contact stress of deep groove ball bearing sciencedirect. 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. Theoretical background and applications of dem simon lo.
Hertzian definition of hertzian by the free dictionary. Hertz is well known for his contributions to the field of electrodynamics see below. Bryant mechanical engineering the university of texas at austin austin, texas 787121063 dedicated to the late dr. 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. Examples are a railway wheel and rail, or a pair of gear wheel teeth. Although hertzian contact theory has been applied in the case of concentric ceramiconceramic hip contact. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. Contact stresses and deformations university of utah. Pure hertzian model only describes normal deformation of spheres.
To understand the effects of adhesion we first have to see what happens when theres no adhesion, which is the hertz case. Spherical contact is a special case of the hertz contact, which is between two spheres, or between a sphere and the surface of a half space. The smaller difference between simulated results obtained by edm and theoretical results calculated by hertzian point contact theory validates the reliability of explicit dynamic model established in this paper. The hertzian contact apparatus is a selfcontained and easytouse unit that shows the nature of contact between two surfaces. When applicable, the hertz theory can be used to accurately model contact dimensions, normal pressures, and stress fields. The displacement of the points on the surface in the contact area between an originally even surface and a rigid sphere of radius r is equal to uz d. Pdf rigorous treatment of contact problems hertzian contact. Hertzian contact practical adhesion science prof steven. When any two curved bodies of different radii of curvature are brought into contact they will initially touch at either a point or along a line. As a preparatory step, we will summarize a few results of the theory of elasticity that have a direct application to contact mechanics. This paper presents to determine the contact stress of large diameter ball bearings using analytical and numerical methods. Stresses surface tractions and sliding contact cylinder.
Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Cone cracks and the auerbach relationship in diamond. Indian telegraph act, 1885 where telegraph is defined as any appliance, instrument, material or apparatus used or capable of use for transmission or reception of signs, signals, writing, images, and sounds or intelligence of any nature by wire, visual or other electromagnetic emissions, radio waves or hertzian waves, galvanic, electric or magnetic means, the civil procedure code 1908. This helps engineers to predict contact areas between common machined surfaces and materials, for example different types of bearings. Tutorial report on hertzian contact stress theory, opti 521. This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. Relation between hertz stresslife exponent, ballrace conformity, and ball bearing life. Dowson, d fisher, j jin, z m auger, d d and jobbins, b 1991.
He became concerned about the effect of contact pressure between the two lenses and set out to analyze the effects. When adhesion between the two bodies in contact is considered, several modifications from the hertz theory have been proposed. Hertzian contact equations for elliptical, spherical and. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a.
Nov 10, 2011 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. The finite element analysis also performed to predict contact pressure in ball and raceway. Pdf assessment of the applicability of the hertzian contact. After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies. Lecture 28 antennas and radiation and the hertzian dipole. Therefore, it is very imporant to calculate the actual stress at the point of contact, the socalled contact stress. Cooper abstract formulations are given for the coefficients x, u, u defined by h. Hertzian contact pressure is applied in a fatigue life model to describe the damage of wheels in 4. 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. Stress concentration in periodically rough hertzian contact. Palmgren revisited a basis for bearing life prediction. With the application of the smallest load, elastic deformation enlarges these into contact areas across which the loads are distributed as.
Assessment of the applicability of the hertzian contact theory to edgeloaded prosthetic hip bearings. 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. Lawn, hertzian fracture experiments on abraded glass surfaces as definitive evidence for an energy balance explanation of auerbachs law, j. The mathematical theory for the general threedimensional contact problem was first developed by hertz in 1881. E lr a, where r is the radius of curvature of the probing sfm tip, and e is the modulus of the sample only, if the sample material stiffness is much smaller than the. A track structure and wheel set connected by means of a hertzian spring is used to describe high frequency. Based on these models, the applicability of the hertz contact theory hct to railwheel contact problems is veri. Hertzian contact stress theory university of arizona. The second missing element was a comprehensive life theory that would fit the observations of palmgren. Ai palmgren revisited a basis for bearing life prediction erwin v. The result was the first satisfactory theory for contact mechanics and is still in use today.
In this model the normal force component is based on hertzian contact theory hertz 1882. 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. Normal contact of elastic solids hertz theory chapter 4. 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. Hertz contact stress involutes gear tooth contact stress analysis one of the main gear tooth failure is pitting which is a surface fatigue failure due to many repetition of high contact stresses occurring in the gear tooth. Such as the hertzian theory, the jkr solution is also restricted to elastic sphere contacts. Present study utilizes the application of hertz contact theory to the wheelrail contact problem to study the effect of variation of wheel. 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. In the jkrtheory the contact is considered to be adhesive. In a static contact, the interface is the principal plane no shear stress. Jan 21, 2014 2014w engr380 lecture18 spur gear design lewis equation for tooth bending stress, part i duration. An approximate analysis for hertzian elliptical wheelrail. If determined to be applicable to edgeloaded bearings, the hertz theory would offer the benefit of an analytical solution to a complicated problem. It compares experiment results with predictions based on hertzs original theories.
Hertzian contact theory applied to edgeloaded ceramicon. Hertzian contact stress hertzian contact theory is a classical theory of. When the load was applied there is some elastic deformation that takes place to provide a larger area so that the stresses are not in nite. 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 company was founded in 2011 and is majority owned by fouriertransform ab. Contact mechanics in 1881 1882, hertz published two articles on what was to become known as the field of contact mechanics. Lecture 28 antennas and radiation and the hertzian dipole in this lecture you will learn. In 1882, hertz solved the contact problem of two elastic bodies with curved surfaces. In analytical method the contact stress is found out using the hertzian elliptical contact theory. Hertzian contact models hertz contact model is nonlinear model which takes in account elastic deformation of spherical solids and changing contact radius. An improvement over the hertzian theory was provided by johnson et al.
If determined to be applicable to edgeloaded bearings, the hertz. You could divide the hertz stresses by the same factors before comparing them to your allowables. Contact stresses and deformations me en 7960 precision machine design topic 7 me en 7960 precision machine design contact stresses and deformations 72 curved surfaces in contact the theoretical contact area of two spheres is a point 0dimensional the theoretical contact area of two parallel cylinders is a line 1. Hertz 1882 contact model is both elastic and quasistatic in nature. Contact of bodies occurs in all interfaces transmitting force or motion, or both. Hertzian contact stress refers to the localized stresses that develop as two curved. Oct 16, 2019 the smaller difference between simulated results obtained by edm and theoretical results calculated by hertzian point contact theory validates the reliability of explicit dynamic model established in this paper. Photoelasticity analysis of hertz contact problem shear stresses. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. These elevated stresses are beyond the hertzian field.
The theory of contact between elastic bodies can be used to find contact areas and. To engineer a contact condition like that the cylinder needs a profile with end reliefs. This paper discusses the hertz contact theory validation using finite element analysis. It was observed that, though hertz theory applied at. Assessment of the applicability of hertzian contact theory. The contact area will change depending on the magnitude of the contact stress. Another contact case entails friction that causes shear stresses on the contact zone. Assessment of the applicability of hertzian contact theory to edgeloaded prosthetic hip bearings. Archive of applied mechanics 70 2000 255268 o springer. Elastic compression of spheres and cylinders at point and. Ball bearing thrust bearing roller bearing contact stress causes deformation, plastic or elastic.
Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller. In dynamic wheelrail models, the hertzian contact stiffness is an important parameter. Hertzian loaddisplacement relation holds for spherical. Hertz contact stress mechanical engineering general. Pdf hertz contact stress analysis and validation using finite.
Relation between hertz stresslife exponent, ballrace. Glaser department of civil and environmental engineering, university of california, berkeley, 621a sutardja dai. Contact mechanics is the study of the deformation of solids that touch each other at one or more. 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. The finite element analysis also performed to predict contact pressure in.
The hertzian contact hertz 1881, 1882 is referred to the frictionless contact between two bodies. Tutorial on hertz contact stress university of arizona. Palmgren, as will be discussed, distrusted hertz theory 12 and depended on a loadlife relation. Failure analysis of rolling bearings based on explicit. 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.
Later extensions of the model add viscosity, shear response including friction and adhesion. The following assumptions are made in determining the solutions of hertzian contact problems. Tables of hertzian contact stress coefficients duane h. In 1880 heinrich hertz developed his theory for contact stress after studying newtons rings with two glass lenses. Morning coffee jazz relaxing instrumental bossa nova jazz playlist have a nice day.
Below contacting surface, sigma x, sigma z, and shear stress varies with depth. 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. The simplest modification is to crown the cylinder that the contact is of double radius type, just as hertzian theory handles. 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. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. Next he discusses the influence of friction and the topographical roughness of surfaces, and this is incorporated into the theory of contact mechanics.
The hertzian theory has previously been used to describe the contact mechanics of the congruent hip couple 4, but not the edgeloaded couple. Pdf hertz contact stress analysis and validation using. The limits normally adopted for hertz s contact stresses are 4 times the allowable stress for linear contact and 5. Applicability of the hertz contact theory to railwheel contact problems w. Hertzian theory has previously been used to describe the contact mechanics of the congruent hip couple 4, but not the edgeloaded couple. The unit of frequency, cycle per second, was named the hertz in his honor. This is true for tires, needle bearings and other roller type of devices.
In mechanical engineering and tribology, hertzian contact stress is a description. Roller bearing contact stress causes deformation, plastic or elastic. This paper presents a study by the finite element method fem of the contact tensions between two bodies and the results obtained are compared with the calculations obtained on basis of the relations of the theory of h. Dem interaction hertz mindlin contact this is a noslip contact model used for modeling contact between particles the hertz mindlin contact model is a variant of the nonlinear springdashpot contact model based on the hertz mindlin contact theory the forces. The tangential force model is based on mindlinderesiewicz work mindlin 1949 mindlin and deresiewicz 1953. Hertz mindlin no slip this contact model is the default model used in edem due to its accurate and efficient force calculation. Jkr adhesion theory starts with measurements of little rubber balls being pressed into contact with a flat surface.
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