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. 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. The classical threedimensional hertz contact problem is reexamined in the present work within the context of couple stress elasticity. Cylinder and cylindrical cavity with parallel axes part i. In this case, we can consider a small area of the contact region da, fig. A clearly laidout window allows you to enter material properties, dimensions and loads. This results in a nominal variation of the hertz stress life exponent. The application performs all calculations automatically. This theory introduces characteristic material length. In addition, the problem is analyzed under dynamic conditions in abaqusstandard to illustrate the use of. Applicability of the hertz contact theory to rolling. It also serves as an excellent illustration of the use of substructuring in abaqusstandard for locally nonlinear cases local surface contact. Over a century ago hertz established a theory of contact mechanics that is still used today by engineers working in tribology to make his theory accessible for engineering applications the program calculates a fast and accurate solution this demonstration presents the hertzian contact stress distribution and elastic deformations it uses a color.
An understanding of the hertz theory of contact pressure. Numerical analysis for development of hertz contact. Jacob etter, tutorial report on hertzian contact stress theory, opti 521. The master surface is the top surface of the block and the slave face is the bottom surface of the cylinder. 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. Useful solutions for standard problems dartmouth college. When this happens, complex stresses are induced under the surface at the contact.
Hertzian contact stress, localized stresses that develop as two curved surfaces come in contact and deform slightly under imposed loads. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of. Contact mechanics in gears chalmers publication library. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. This results in a nominal variation of the hertz stresslife exponent. These stresses were first studied by the german physicist heinrich hertz in 1881. To study the influence of interacting wheel and rail profile topology of standard rail uic60, the. Further reading useful solutions for standard problems mike ashby engineering department trumpington street, cambridge cb2 1pz, uk. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The hertz contact problem massachusetts institute of.
And the bending stresses in the tooth root are examined by using 3d fem model. Hertz contact stress calculations and graphs with hertzwin. Hertzian theory when two curved bodies are brought into contact they initially contact at a single point. Therefore, it is also important to analyze the stress condition below a contact surface and the depths where the shear stress is the maximum. Pdf hertz contact stress analysis and validation using finite. It applies to normal contact between two elastic solids that are smooth and can be described locally with orthogonal radii of.
For linearly graded materials such as casehardened bearing steels, three more design parameters, surface elastic modulus e surface. Patil3 1 2 3head of the department of mechanical engineering, sgdcoe, jalgaon, india. In 1882, heinrich hertz published a theory concerning circular contact areas and elastic deformations in the case of contact between two spheres1. Hertz theory is concerned with the behaviour of two linear elastic bodies, whose curvatures near the point of contact may be adequately represented by parabolas, when pressed together. It causes serious problems if not take it into account in some cases. As per hertz theory, these parameters are principal curvatures of two bodies, their material properties, and the normal load acting on the contact. Extended hertz theory of contact mechanics for case. Contact stress causes deformation, plastic or elastic.
Pure hertzian model only describes normal deformation of spheres. 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. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20. Based on these models, the applicability of the hertz contact theory hct to railwheel contact problems is veri. Contact between two continuous, nonconforming solids is initially a point or line. 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. Applicability of the hertz contact theory to railwheel contact problems w. Table 6 comparison of peak values of the contact stresses by considering different modules. Comparing the results with the hertz contactstress theory made it possible to establish criterion for suspensionclamp design. In analyzing the spiral bevel gear, it is assumed that the contact between the gear and its pinion follows hertz theory of elastic contact. 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. 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. For 9th and 8thpower hertz stress life exponents for ball and roller bearings, respectively, the lundbergpalmgren model best predicts life. High contact stress may lead to failures such as cracks, pits and flaking in the surface material.
Pdf the classical threedimensional hertz contact problem is. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. This page focuses mainly on the normal direction, i. You could divide the hertz stresses by the same factors before comparing them to your allowables.
It can be used to calculate mechanical point and line contact dimensions and material stresses. 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 classical threedimensional hertz contact problem is reexamined in the present work within the context of couplestress elasticity. Introduction contact stress is a description of the stress within mating parts. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. Pdf hertz contact stress analysis and validation using. Tutorial on hertz contact stress university of arizona. The theory of contact stress based on this concept is known as the hertz contact theory.
Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. The conventional method of calculating gear contact stress using hertz s theory for verification by 2d fem analyzer using ansys, in later investigation the. For example, butterflies are often associated with high contact stress 2000 to 4000 mpa, as discussed in more detail in the article contact fatigue of hardened steel in this vol ume. The contact area will change depending on the magnitude of the contact stress. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. Download limit exceeded you have exceeded your daily download allowance.
Hertz contact stress mechanical engineering general. 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. Hence, in the present work, a complete numerical analysis is carried out for the calculation of subsurface stresses. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Relation between hertz stresslife exponent, ballrace. Hertzian cone, the cone produced when an object passes through a solid, such as a bullet through glass. 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. Contact in a spiral bevel gear occurs in 3d following a path along the tooth surface, starting from the fillet of the toe to the top of the heel. Hertzian contact holds as long as the significant dimensions.
Since the area in contact between two bodies is sufficiently small compared to the surface of the bodies, the problems can be analyzed by superposing the basic solutions. An experimental study of interstrand contact stresses existing in a stranded cable while it rests in its supporting clamp has been made using the stressfreezing photoelastic technique. If a lubricant film is present, and the sphere slides over the flat, the pressure distribution and surface deformations predicted by hertzs equations must be modified. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. Hertz 1882 contact model is both elastic and quasistatic in nature. This provides an additional increase in contact stress as the oring deforms to a d shape see figure 3 and the contact area of sealing under pressure increases to almost. The subject investigated of this paper is a kind of large. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. 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. Hertz contact stress is normally defined as pressurep0sqrt1xa2, where p02ppia, 2a is the contact width, p is load per length that is, units are force per length. After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies.
Under the action of a load the solids deform and a contact area is formed as shown in figure 1. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. Hertzian contact stress wolfram demonstrations project. The stress field under the surface is termed hertzian contact stress reference hertz 1881 has done the hard work to derive the equations we need to calculate the stress when there is contact between two bodies that are conformal or nonconformal. Hertzian contact stress hertzian contact theory is a classical theory of contact. Using hertz contact formula i calculated contact stress for cylinder in contact with cylinderical socket but i dont know to which stress to compare this contact stress. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified. In this paper comparison between the results of hertz theory and ansys. Hertz contact theory is derived from the analytical solution of elasticity. In mechanical engineering and tribology, hertzian contact stress is a description. 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. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. The contact stresses are examined by using 2d fem model. The hertz contact problem see timoshenko and goodier, 1951 provides a classic example for verifying the contact capabilities in abaqus.
Assessment of the applicability of hertzian contact theory. Spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. Pdf the hertz contact problem in couplestress elasticity. Tribology and contact mechanics books tribology experts downloads. 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. Fischer summary railwheel contact problems have been analyzed by applying threedimensional. Contact analysis on large negative clearance fourpoint. Hertzwin is a free hertzian contact stress calculator. Theory%20of %20elasticity%20by%20timoshenko%20and%20goodier. Other important limitations are that the dimensions of the contact patch must remain. Rolling bearing life prediction, theory, and application. 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. Hertz contact theory hct is a study of contact stress and deformation which is widely used in many engineering fields.
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