These stresses can then be analyzed in context of the application. The hertzian contact stress contact stresses lead to octahedral shear stress and orthogonal shearstresses under the surface at the contact. Hertzian impact model and to quantitatively evaluate its limits. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. But yes, in static cases you can often allow for higher stress.
Hertzian static contact stress acceptance criteria. Pdf contact stress distribution of deep groove ball. Relation between hertz stresslife exponent, ballrace. Pdf hertz contact stress analysis and validation using. Hertzwin is a free hertzian contact stress calculator. 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. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. The hertzian contact theory is approximated according to a concept by tanaka 2001, a new calculation method of hertz elliptical contact pressure, asme j. Gear tooth surface wear involves removal or displacement of. If the pressure is integrated over the contact area, it is found that 3f pmax 2nab 3. For example, in mechanical engineering and tribology, hertzian contact stress is a description of the stress within mating parts. Hertzian contact stress theory university of arizona. 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.
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. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. Usually, hertz contact stresses are judged by the shear stress just below the surface. Pdf rigorous treatment of contact problems hertzian contact. When applicable, the hertz theory can be used to accurately model contact dimensions, normal pressures, and stress fields. However, it is nevertheless of interest to examine these predictions either by experiment or by independent computation. Contact stress analysis of spur gear ijert journal. The contact pressure distribution between the ball and the raceway of the bearing 6004 is performed by finite element software. Spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. This provides an accurate value of the contact pressure at low loads. Considering the geometry of the contacting bodies first, the effect of the diameters on the contacting area is given by equation 1.
Stresses formed by the contact of two radii can cause extremely high surface stresses. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance. We report on the elastic contact between a spherical lens and a patterned substrate, composed of an hexagonal lattice of cylindrical. The hertzian contact stress contactstresses lead to octahedral shearstress and orthogonal shearstresses under the surface at the contact. Hertz contact stress mechanical engineering general. Hertzian contact theory applied to edgeloaded ceramicon. Contact pressure and yield stress in the case of point contacts round or elliptical that we may not be justified in using the hertzian contact equations. This stillrelevant classical solution provides a foundation for modern problems in contact mechanics. Useful solutions to standard problems in introduction and synopsis modelling is a key part of design. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified position. For these to be true, it is assumed that the contact is elastic, that the contact zone is flat, that there are no shear stresses in the contact zone and that the contact.
Contact mechanics hertz stress constriction resistance asperities hertzian contact. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. The next issue of technical tidbits will discuss stress relaxation. Tutorial on hertz contact stress university of arizona. References 1 shailendra pipaniya, akhilesh lodwal, contact stress analysis of deep groove bearing 6210 using hertzian contact stress. 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. Contact stress analysis of spur gear for different materials. Figure c1 shows the relationship between the load p and the maximum shear stress that occurs just below the surface. The image to the left schematically illustrates how a cylinder rolling over a flat body in the absence of friction develops subsurface stresses. Indentation depth may be readily compared using standard experimental apparatus. Vicura ab is an engineering company that delivers products which are used in. This kind of stress may not be significant most of the time, but may cause. The software calculates hertzian contact stress and the subsurface stressen of the general contact of two elliptical bodies according to the hertzian theorie. The contactpair topology influences the contact stress magnitude and shape of contact area.
New version of hertzian contact stress calculation mesys ag. The domain in this study was the angular location of the point of contact on the arc of. In 1882, hertz solved the contact problem of two elastic bodies with curved surfaces. Pdf hertz contact stress analysis and validation using finite.
An approximate analysis for hertzian elliptical wheelrail. There the elastohydrodynamic oil film is minimal and the load is less distributed. This paper presents a systematic study of ball impact as a source of stress waves for a number of different material combinations. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Contact stresses and deformations curved surfaces in contact. From contact mechanics2 demonstrating the change in area during conditions of load. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. Conditions are therefore small deformations in regard to the radii of curvature and pure elastic. Using trescas criterion, a minimum yield stress of 422 nmm2 will be required for ductile materials. Nov 15, 2008 an example of hertz contact fem simulation. Some features of this site may not work without it. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. It can be used to calculate mechanical point and line contact dimensions and material stresses.
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. To speed up the process of calculation and accurate the model, fischer et. Contact stress causes deformation, plastic or elastic. This paper examines the contact stress distribution of deep groove ball bearings through analytical and numerical methods.
In this case, we can consider a small area of the contact region da, fig. 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 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. Cooper abstract formulations are given for the coefficients x, u, u defined by h. A practical and accurate formulation is still in demand 2. 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. The crucial requirement of effective power transmission in various machines, automobiles, elevators, generators, etc has created an increasing demand for more accurate analysis of the characteristics of gear systems. A clearly laidout window allows you to enter material properties, dimensions and loads. Indentation depth may be readily compared using standard experimental. The application performs all calculations automatically.
We can also do wear analysis due to frictional rubbing between the contact surfaces. You could divide the hertz stresses by the same factors before comparing them to your allowables. The description of functionality of rolling bearing calculation for slewing rings. Hertzian contact stress allowable hertzian contact stress transverse pressure angle operating pressure angle base helix angle angular velocity. We consider the deformations in an elastic halfspace, which are caused by a given stress acting upon its surface. In case of two cylinders in contact with radii, as shown in fig. In many cases, the resultant stresses are not of design significance, but in some cases failure can. Hertz contact stress calculations and graphs with hertzwin. 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. Tables of hertzian contactstress coefficients welcome to the ideals repository.
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. A theoretical background to the hertz contact theory can be found here. In another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface. The contact area will change depending on the magnitude of the contact stress. Pdf contact stress analysis in wheelrail by hertzian. From fea modeling, materion developed an empirical calculator to approximate the maximum contact stress for a. Contact between two continuous, nonconforming solids is initially a point or line. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. This page focuses mainly on the normal direction, i. Another contact case entails friction that causes shear stresses on the contact zone. Hertzian contact equations for elliptical, spherical and. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. Assessment of the applicability of hertzian contact theory. Eccentricity of contact ellipse e b a r r b a 2 2 4 3 11.
Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of hertzian contact stress equations can estimate. However, as the load increases, the hertzian model becomes inaccurate as well. Contact stress analysis of spur gear for different. The hertzian theory has previously been used to describe the contact. In this case, we can consider a small area of the contact region. Impactgenerated vibrations were recorded with an array of pm sensitive high. Contact fatigue has been identified in metal alloys both ferrous and nonferrous and in ceramics and cer mets. Hertz contact stress of deep groove ball bearing sciencedirect. Contact mechanics is the study of the deformation of solids that touch each other at one or more. Me en 7960 precision machine design contact stresses and deformations. This tutorial addresses the basics of hertzian contact stress. The contact pair topology influences the contact stress magnitude and shape of contact area. 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. 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.
Contact stress reduction mechanisms for the cambased. Assessment of the applicability of hertzian contact theory to. Pdf hertzian contact stress calculator ames dennyza. 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. The hypothesis of this work is that the contact mechanics of edgeloaded hip bearings can be accurately described using hertzian contact theory. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue. A brief discussion of what affects hertz stress, and why in connector design even if hertz stress. Hertzian stress between the two cylindrical contact surfaces. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The tensile stress at the major radius sa is maximum. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20. The term failure from pitting fatigue is subjective and a source of considerable disagreement.
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. This condition is modeled as a pair of cylinders in line contact, and a hertzian contact stress. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. Contact pressure and yield stress phoenix tribology. Contact stress has been expressed clearly in this work by finite element model. 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.
Nicholas lecain, tutorial of hertzian contact stress analysis, opti 521, college of optical sciences, university of arizona, tucson, az. The ellipticity parameter k can be written in terms of. Tables of hertzian contactstress coefficients duane h. We consider the deformations in an elastic halfspace, which are caused by a given stress acting upon its. A new version of the software for calculation of hertzian contact stress is available. A brief discussion of what affects hertz stress, and why in connector design even if hertz stress itself is not. For these to be true, it is assumed that the contact is elastic, that the contact zone is flat, that there are no shear stresses in. The contact pressure is intensified near the pitch circle, where the contact is pure rolling with zero sliding velocity. The domain in this study was the angular location of the point of contact on the arc of action from the beginning to the end of contact between this pair of teeth. Apr 22, 20 step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained.
305 1027 68 1306 989 483 1147 332 368 305 800 274 170 1351 83 759 824 1408 1214 215 1311 1050 343 692 1409 1193 942 43 1316 15 1042 989 159 141 1488 1281 902 419 657