When this happens, complex stresses are induced under the surface at the contact. 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. 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 groove ball bearing. The stresses and deflections arising from the contact between two elastic. This page focuses mainly on the normal direction, i. Normal contact of elastic solids hertzian contact by. Contact mechanics has been analyzed in industry for a long time. You could divide the hertz stresses by the same factors before comparing them to your allowables. These stresses were first studied by the german physicist heinrich hertz in 1881. These equations combine to create a continuous prediction of ein the range of. For the derivation of the subsurface stresses for line and point hertzian contact, please refer to refs. Hertz contact stress calculations and graphs with hertzwin.
A mechanism for rolling contact fatigue based on tensile stresses from axi symmetric. Maximum contact pressure hertz stress approach of centres. 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. 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. 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. 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.
Analysis of contact stress on coating based upon hertz theory. Spur gears, solids mechanics, contact stresses, hertz theory. The contact area is small compared to the size of the bodies. Hertz contact stress of deep groove ball bearing sciencedirect. Assessment of the applicability of hertzian contact theory. 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. 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. The theory governing the wheelrail contact is hertz theory. Contact of bodies occurs in all interfaces transmitting force or motion, or both. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. From contact mechanics2 demonstrating the change in area during conditions of load.
Contact stress causes deformation, plastic or elastic. The term failure from pitting fatigue is subjective and a source of considerable disagreement. In 1882, heinrich hertz published a theory concerning circular contact areas and elastic deformations in the case of contact between two spheres1. 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. Exact constraint, repeatability, fixture, kinematic coupling, exact constraint, hard coating, hertz contact, stress 1.
Bearing pressure is a particular case of contact mechanics often occurring in cases where a convex surface male cylinder or sphere contacts a concave surface female cylinder or sphere. Then onwards researchers have used this theory for the analysis of the. Introduction a theory of contact is required to predict the shape of this area of contact and how it grows in size with. This type of failure can also be found in gears, cams, valves, rails, and gear couplings. A mechanism for rolling contact fatigue based on tensile stresses from axisymmetric. The hertz contact problem studied consists of two identical, infinitely long cylinders pressed into each other. The accuracy of model was initially tested in systems without a film. The hertz contact problem see timoshenko and goodier, 1951 provides a classic example for verifying the contact capabilities in abaqus. In this paper its make a application of hertz theory used the math cad program for the contact of two cylinders. 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 application performs all calculations automatically. Computers did not exist but he looked at a way to develop his theory and make it workable for engineers. 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 of nanometer repeatability is desired.
Exploitation of hertzs contact pressures in friction drives. As the pressure increases, the oring is forced to the low pressure side of the gland. Nov 10, 2011 in the ceramic liners, the edge radius was observed to consist of multiple segments. International journal for research in applied science. To study the influence of interacting wheel and rail profile topology of standard rail uic60, the standard wheel profile as per. This paper presents the results of a study carried out using the finite element method, on the contact stresses between two bodies. Contact, hertz, nonconforming, math cad, stress, deformations. Hertzwin is a free hertzian contact stress calculator. A proper material selection is a most important in ball. Pdf hertz contact stress analysis and validation using. Contact fatigue has been identified in metal alloys both. It also serves as an excellent illustration of the use of substructuring in abaqusstandard for locally nonlinear cases local surface contact. Tutorial on hertz contact stress university of arizona.
These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. Hertz developed a numerical method with mathematical tools known. For a12 it represents the hertz contact situation see. The hertz theory for contact of two parallel elastic cylinders is used to derive the contact pres. Hertz contact stress mechanical engineering general. 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. This problem is also referred to as bearing resistance. Later he extended it to general case of two elastic bodies in contact. Hertz contact stress calculations hertzwin is a free hertzian contact stress calculator. Unusually high stresses may occur when a load is applied over a small area of contact. High contact stress may lead to failures such as cracks, pits and flaking in the surface material. This type of contact is also called the point contact because theoretically the contact spot is a point before load application. Shaffer, battelle laboratories contact fatigue is a surfacepittingtype failure commonly found in ball or roller bearings.
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. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. 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. An approximate analysis for hertzian elliptical wheelrail. After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. The contact elliptical area is small so stresses developed will be higher. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. The results are compared, following the analysis, to the results calculated on basis of the relations in h. With application of the expression for the radii of flanks curvatures and the expression for the equivalent curvatures radius in the contact point, the expression 5. The unit of frequency, cycle per second, was named the hertz in his honor. The contact area will change depending on the magnitude of the contact stress. Hertzian elastic contact and jkr adhesiveelastic contact as function of load.
In this example problem, a steel cylinder with a radius of 5 is pressed against a 2 deep aluminum base. The hertzian contact hertz 1881, 1882 is referred to the frictionless contact between two bodies. 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. Hertzs analysis of contact stress involves the following set of assumptions. Similar to cylindrical or line contact, hertz also solved the case of an axisymmetric. Over a century ago hertz established a theory of contact mechanics that is still used today by engineers working in tribology. If the equations for the calculation of the active stresses on meshing tooth flanks, which are developed from the hertz s solution for contact stresses while two cylinders are in contact, are applied, then this ratio takes the following form.
Hertz contact theory appeared in 1881 to solve the problem of pressure distribution between two elastic spherical bodies in contact. Hx and active stress for contact in the pitch point. 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. Elastic contact stress formulae newcastle university. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. The contact stresses are important factors for the design of hard coatingsubstrate because the failure of the hard coating is usually caused by these stresses. The nature of hertzian contact interfaces and the need for geometric stability discontinuous interfaces are essential and troublesome components of precision hardware. Contact stress analysis in wheelrail by hertzian method. The solution quantities of most interest are the pressure distribution on the contacting area, the size of the contact area, and the stresses near the contact area. This tutorial provides a brief introduction to the hertzian. Spherical contact is a special case of the hertz contact, which is between two spheres, or between a.
A clearly laidout window allows you to enter material properties, dimensions and loads. The limits normally adopted for hertz s contact stresses are 4 times the allowable stress for linear contact and 5. The finite element method is applied to simulate the stress of coating with contact load based on hertz contact theory. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. Hertz stress analysis assumes a cir cular, elliptical, or line contact surface area be tween curved surfaces depending on the geome try of the contacts and a parabolic pressure distribution with the maximum pressure at the center of the contact. Pdf contact mechanics is a fundamental field of tribology and generally refers. Pdf contact mechanics is a fundamental field of tribology and generally refers to the interaction of. 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. Pdf the hertz contact problem in couplestress elasticity. Pure hertzian model only describes normal deformation of spheres. For the simplest model to calculate the stresses, one uses the hertz theory and evaluates the effect of the weight only. The state of stress in nonconformal contacts where rcf occurs is complex and multiaxial and governed by the hertzian contact theory.
Hertz 1882 contact model is both elastic and quasistatic in nature. Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. The analysis of contact stress on meshed teeths flanks along the path contact for a tooth pair 1057 where. 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. An initial estimate of the value of t max for many materials is h6 where h is the material hardness. Lesson 9 hertz contact problem patran 322 exercise workbook 93 model description. Relation between hertz stresslife exponent, ballrace. Contact stresses between two cylindrical bodies cylinder.
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. In addition, the problem is analyzed under dynamic conditions in abaqusstandard to illustrate the use of contact. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. Pdf the classical threedimensional hertz contact problem is reexamined in the present. Hertzian contact stress wolfram demonstrations project. Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to peening. Deformations, contact pressures and elastic subsurface stresses are.
Assessment of the applicability of hertzian contact theory to. In mechanical engineering and tribology, hertzian contact stress is a description. 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. Calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and mesys tool analysis. In addition the solution to a nonhertzian contact problem with a multiply. Tutorial on hertz contact stress tutorial on hertz. The problem is linear except the contact condition at the base which is modeled using the contact pair approach.
1205 619 61 1421 1523 920 72 174 195 715 1536 560 212 35 275 486 133 993 199 291 709 370 1106 1096 1328 1156 1249 1168 790 418 1200 798 307 286 557 677 671 29 548 1193 92 908 994 1426 302 1001