First, a hertz stress value can be realized by different combinations of contact force and contact geometry, each producing different values of connector contact resistance. Pdf contact stress distribution of deep groove ball. 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. This paper discusses the hertz contact theory validation using finite element analysis. Initiation of plastic flow starts at a lower pressure and occurs when the max shear stress reaches the shear yield stress k for the material.
Contact mechanics in 1881 1882, hertz published two articles on what was to become known as the field of contact mechanics. Pdf hertz contact stress analysis and validation using. Contact stress reduction mechanisms for the cambased. Any time there is a radius in contact with another radius or flat, contact stresses will occur. Hertz stress refers to the stress and deformation generated on bodies in contact under applied load. 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. This kind of stress may not be significant most of the time, but may cause serious problems if not take it into account in some cases. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. Stress concentration in periodically rough hertzian contact.
Contact between two continuous, nonconforming solids is initially a point or line. 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. Tutorial on hertz contact stress university of arizona. The scope of the present study includes the contact stress. In mechanical engineering and tribology, hertzian contact stress is a description. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Introduction gear is a rotating cylindrical wheel having teeth cut on it. The shear stress limit is generally half the allowable stress intensity limit. Tables of hertzian contactstress coefficients duane h.
Calculating maximum contact pressure on a heavily loaded journal bearing fea calculation using the ansys staticstructural package, fea calculations were made to calculate the contact stress. Contact pressure and yield stress phoenix tribology. The application performs all calculations automatically. Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of hertzian contact stress equations can estimate. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. Assessment of the applicability of hertzian contact theory. Elastic compression of spheres and cylinders at point and. 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. A frictionless, augmented lagrange method was used to control the contact between the shaft and bushing.
Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. Patterned substrate, surface fraction, stress concentration, real contact area, hertz to softflatpunch. To determine the contact stress 5, 6, 7 between a pair of teeth while transmitting power by treating the pair of teeth in contact as cylinders of radii equal to the radii of curvature of the mating involutes at the pitch point. The term failure from pitting fatigue is subjective and. Typical bearing contact widths are of the order of 200 m. On the compression of a cylinder in contact with a plane. The equations simplify when the contact area is circular such as with spheres in contact. These stresses were first studied by the german physicist heinrich hertz in 1881.
For 9th and 8thpower hertz stress life exponents for ball and roller bearings, respectively, the lundbergpalmgren model best predicts life. Hertz stress ii connector and cable assembly supplier. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Unusually high stresses may occur when a load is applied over a small area of contact. In many cases, the resultant stresses are not of design significance, but in some cases failure can. In 1882, heinrich hertz published a theory concerning circular contact areas and elastic deformations in the case of contact between two spheres1. In contact mechanics there are multiple models for predicting contact forces and geometrical deformations. This paper examines the contact stress distribution of deep groove ball bearings through analytical and numerical methods. Contact mechanics is the study of the deformation of solids that touch each other at one or more.
Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. Rolling bearing life prediction, theory, and application. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. In the first hertz stress article, i cited two limitations of hertz stress as a connector design parameter. The application of hertzian contact stress equations can estimate maximum stresses produced. 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. It applies to normal contact between two elastic solids that are smooth and can be described locally with orthogonal radii of. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. 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 hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. 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. Hertz is well known for his contributions to the field of electrodynamics see below. This page focuses mainly on the normal direction, i. 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.
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. Contact stress analysis of spur gear ijert journal. Hlim also allowable contact number this is the limit of rolling contact stress that the camsteel can sustain for ncycles, with a reliability of 99%, without failure by pitting. With these tools, distribution of contact zones, contact stress and contact pressure for different configuration of the wheel and rail profiles are obtained. But yes, in static cases you can often allow for higher stress. Heinrich hertz introduced the idea on contact mechanics in 1982. However, more sophisticated problems require that the action of forces be described in terms of stress, that is, force divided by area. Pdf contact stress analysis in wheelrail by hertzian. Hertzian contact stress forms the foundation for the equations for load bearing. By theory of elasticity, developed by hertz, in 1881. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of. Higher hertz stress is associated with the contact force being distributed across a smaller apparent contact area, where a smaller number.
Assume that two elastic solids are brought into contact at a point 0 as in figure if collinear forces are applied so as to press the two solids together, deformation occurs, and we expect a small contact area to replace the. Hertz contact stress calculations and graphs with hertzwin. High contact stress may lead to failures such as cracks, pits and flaking in the surface material. Contact stresses between curved bodies in compression are often termed hertzian contact stresses after the work on the subject by hertz1 in germany in 1881. As the pressure increases, the oring is forced to the low pressure side of the gland. This work was concerned primarily with the evaluation of the maximum compressive stresses set up at the mating surfaces for various geometries of contacting body but it formed the basis. This paper has been written to discuss the hertz contact stress and examples of fea. 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. The mesh density in contact region is found to have a direct influence on the accuracy of the solution 1. In another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface.
Using trescas criterion, a minimum yield stress of 422 nmm2 will be required for ductile materials. Spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. Hertzian contact stress theory university of arizona. 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. Other important limitations are that the dimensions of the contact patch must remain. In this case, we can consider a small area of the contact region da, fig. The calculation procedure consists of calculation of maximum contact pressure at different loads using analytical formulas and comparison of results with mesys tool to predict the contact pressure between inner race and ball of single row deep.
Contact stress and bending stress analysis of spur gear by. Hertz contact stress mechanical engineering general. Contact stress calculations using hertz equation to determine the contact stress5, 6, 7 between a pair of teeth while transmitting power by treating the pair of teeth in contact as cylinders of radii equal to the radii of curvature of the mating involutes at the pitch point. The mean pressure for full plastic contact analogous to a hardness test is about 3y where y is the uniaxial yield stress. Cooper abstract formulations are given for the coefficients x, u, u defined by h. The hertzian contact theory is approximated according to a concept by tanaka 2001, a new calculation method of hertz elliptical contact pressure, asme j. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. 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. You could divide the hertz stresses by the same factors before comparing them to your allowables. The contact pressure distribution between the ball and the raceway of the bearing 6004 is performed by finite element software. Relation between hertz stresslife exponent, ballrace. The first three sections present the hertz equations for these distinct cases. A brief discussion of what affects hertz stress, and why in connector design even if hertz stress itself is not. Usually, hertz contact stresses are judged by the shear stress just below the surface.
After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies. Pdf hertz contact stress analysis and validation using finite. This results in a nominal variation of the hertz stresslife exponent. In reality, a small contact area is being created through elastic deformation, thereby limiting the stresses considerably. Essentially youre comparing stress intensity with the material yield stress and so it is irrelevant whether or not the principal stress is compressive or tensile. The phenomenon of rcf occurs in a very small volume of stressed material, because the contact stress. Hertz 1882 contact model is both elastic and quasistatic in nature. Keywords hertz contact stress, contact fe analysis, stresses within rollers, roller contact analysis and. Under the action of a load the solids deform and a contact area is formed as shown in figure 1. 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 crossed at right angles 25 26 26 33 37 38 38 39.
Hertz stress ii achieving the right degree of resistance. The maximum shear stress in a hertz contact is buried at 0. Contact stresses and deformations curved surfaces in contact. Design of hard coated hertzian contacts for precision equipment submitted to precision engineering as the repeatability of kinematic couplings is coupled with surface finish, it is still necessary to preserve the finish of the contact patches if tens. Hertzwin is a free hertzian contact stress calculator. Hertzian static contact stress acceptance criteria. Contact stress and shear stress analysis of spur gear. In this thesis, an attempt is made to analyze contact stress using hertz theory. It can be used to calculate mechanical point and line contact dimensions and material stresses. Surface and contact stress the concept of the force is fundamental to mechanics and many important problems can be cast in terms of forces only, for example the problems considered in chapter 2. Calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and mesys tool analysis.
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