Useful solutions for standard problems dartmouth college. Me en 7960 precision machine design contact stresses and deformations 720 center displacement depending on material combination 0 1020 30 40 506070 80 90 100 0 1. A numerical study of the contact mechanics and sub. The effect of hertzian stresses resulting from loads acting at the points of contact of beryllia spheres was determined.
Hertzian stress cracks in beryllia and glass turner 1967. The increase in life of the gear or bearing assembly is expressed as l1 chh1n. Nonhertzian contact stresses in a smoothly cradled heavy. The present study extends the previous study to cases with nonhertzian contact. Cylinder and cylindrical cavity with parallel axes part i. Hertzian contact stress, localized stresses that develop as two curved surfaces come in contact and deform slightly under imposed loads.
Contact stresses between curved bodies in compression are often termed hertzian contact stresses after the work on the subject by hertz 1 in germany in 1881. I am unable to find any literature that might give me the method to calculate the contact stresses using hertzian stress criteria. Evaluation of stresses around inclusions in hertzian contacts. Vicura ab is an engineering company that delivers products which are used in.
Lundberg and palmgren do not reference the work of thomas and hoersch in their papers. A clearly laidout window allows you to enter material properties, dimensions and loads. Contact mechanics fully elastic models hertz analyzed the stresses at the contact of two elastic solids, and thereby assumed small strains within the elastic limit. Asme j n this paper a rocket motor turbinepump reduction gear system is analyzed in regard to hertzian gear tooth contact stresses and times of contact. In most situations, contact problems are outside the validity of the hertz theory. Rocket motor gear tooth analysis hertzian contract stresses.
A new version of the software for calculation of hertzian contact stress is available. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. The present study extends the previous study to cases with non hertzian contact. The results from the analysis show that contact stresses.
The description of functionality of rolling bearing calculation for slewing rings. Stresses formed by the contact of two radii can cause extremely high surface stresses. Hertzian stress cracks in beryllia and glass turner. Hertzian contact 5 rigorous treatment of contact problems. However, non hertzian contact often appears in moderately used contact elements. 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. Nonhertzian contacts the deflection can only be presented relative to some datum. Rocket motor gear tooth analysis hertzian contract. Hertzian contact stress hertzian contact theory is a classical theory of. A general method of numerical solution in the non hertzian elastic contact problem is developed using rectangular subdivisions. 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. Pdf hertz contact stress analysis and validation using finite. These elevated stresses are beyond the hertzian field. Over a century ago hertz established a theory of contact mechanics that is still used today by engineers working in tribology.
In the solution for contact stresses, an expression for the distance between corresponding points on the surfaces near the point of contact is required. The software calculates hertzian contact stress and the subsurface stressen of the general contact of two elliptical bodies according to the hertzian theorie. The details and applications of these equations will be explained. This kind of stress may not be significant most of the time, but may cause. Eccentricity of contact ellipse e b a r r b a 2 2 4 3 11. On the theory of hertzian fracture proceedings of the. Stresses within hard coatings for ratios below stresses within hard coatings for ratios below 0.
The hertzian contact stress contact stresses lead to octahedral shearstress and orthogonal shear stresses under the surface at the contact. But yes, in static cases you can often allow for higher stress. Other examples would be seawater pressurising a gas cylinder in deep water and the stress exerted by a train wheel on a train track. Hertzian synonyms, hertzian pronunciation, hertzian translation, english dictionary definition of hertzian. They arise when materials meet at a common surface. On the theory of hertzian fracture proceedings of the royal. Reduction in hertzian and bending stresses in gears and in bearing assemblies is achieved by new configurations of gears and bearing assemblies employing combinations of materials in selected areas of the gears or bearing assemblies or cutting narrow slots into selected areas of the gear teeth or bearing assemblies. Closure to discussions of rocket motor gear tooth analysis hertzian contact stresses and times 1960, asme j. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified position.
Shaffer, battelle laboratories contact fatigue is a surfacepittingtype failure commonly found in ball or roller bearings. It can be used to calculate mechanical point and line contact dimensions and material stresses. Contact stresses in a heavy circular cylinder resting in a smooth rigid cradle of general profile are analyzed for contact zones outside the validity of hertz theory. 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. Approximate analytical model for hertzian elliptical. Hertz contact stress calculations and graphs with hertzwin.
Background 1 contact between two continuous, nonconforming solids is initially a point or line. Definition of hertzian contact stresses and times hertz, the german physicist, derived the equations of elasticity by means of which the contact stresses between elastic bodies could be predicted 1. Oct 23, 2014 general contact with a contact tolerance of 0. 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. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Nonhertzian contact stress analysis for an elastic half. Hertzwin is a free hertzian contact stress calculator. Shape of surfaces near point of contact before loading if two bodies are in contact at a point, there is a common tangent plane to the surfaces at the point of contact. This page focuses mainly on the normal direction, i. Hertzian static contact stress acceptance criteria physics. Contact stress analysis in wheelrail by hertzian method and.
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. Further reading useful solutions for standard problems mike ashby engineering department trumpington street, cambridge cb2 1pz, uk. Xmultiple uses contact mechanics software to determine contact size and dimensions for many of our connector. Pdf hertz contact stress analysis and validation using. The major application of the method given is in the sliding contact of a short rough cylinder with an elastic half space. Contact fatigue has been identified in metal alloys both. Is hertzian stress criteria the right way to approach this problem. Me en 7960 precision machine design contact stresses and deformations 71 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 hertzian contact stress equations come in two forms, spherical and cylindrical. A simple, accurate method for calculation of stresses and deformations in elliptical hertzian contacts a dyson, h p evans, r w snidle, 1992.
Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. Contact stress causes deformation, plastic or elastic. A tutorial for the calculation of multiple cylindrical roller bearings as bearings for a planetary gear. Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. 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. Hertzian contact stress wolfram demonstrations project.
To study the influence of interacting wheel and rail profile topology of standard rail uic60, the standard wheel profile as per. Using approximations of elliptical functions and with a mathematical study of hertzian results, an empirical explicit formulation is proposed in this paper and allows us to obtain the dimensions, the displacement, and the contact stress with at least 0. Useful solutions to standard problems in introduction and synopsis modelling is a key part of design. The image to the left schematically illustrates how a cylinder rolling over a flat body in the absence of friction develops subsurface stresses. 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. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a. Connor j, woodward a and tabor d 1997 the effect of the indenter elasticity on the hertzian fracture of brittle materials, proceedings of the royal society of london. The tensile stress at the major radius sa is maximum. These stresses can then be analyzed in context of the application. The lundbergpalmgren lif e equations have been incorporated into both the international organization for standardiza. In this case the contact region can still be bounded by a plane, although the contact pressure is not hertzian. Hertzian cone, the cone produced when an object passes through a solid, such as a bullet through glass. Also, pairs of these beryllia spheres were pressed together.
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. A tutorial for calculation of a pair of angular contact bearings as introduction into using the calculation software. The shear stresses in the microhertzian contact in each asperity are shown to combine and form, at a greater depth below the surface, shear stresses generally associated with contact stress theory. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20.
This tutorial addresses the basics of hertzian contact stress theory and it relates to certain aspects of optomechanical design. Contact mechanics in gears chalmers publication library. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. Classical mechanics deals solely with bulk material properties contact mechanics deals with bulk properties that consider surface and geometrical constraints. These macrohertzian stresses are compared with the microhertzian stresses in the asperities. We examine, in detail, the classical contact problem of normal contact between a rigid sphere and an elastic halfspace, which is often used to analyze more complex models. The master surface is the top surface of the block and the slave face is the bottom surface of the cylinder. Tutorial on hertz contact stress university of arizona. A simple, accurate method for calculation of stresses and. The bottomleft plot shows the contact zone with a color function. Introduction any time there is a radius in contact with another radius or flat, contact stresses will occur. Shear stresses below asperities in hertzian contact as. Due to the fact that the surface of the bodies cannot be considered quadratic near the contact point, or the presence of friction in the contact area, the hertz solution is not applicable.
In another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface. Relation between hertz stresslife exponent, ballrace. W, new algorithms for calculating hertzian stresses, deformations, and contact zone parameters, amp journal of technology, 1992. 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. However, nonhertzian contact often appears in moderately used contact elements. New version of hertzian contact stress calculation mesys ag. Under the influence of the forces that act on the free surface, the medium is deformed. Closure to discussions of rocket motor gear tooth analysis. Rolling bearing life prediction, theory, and application. Numerical results are presented for various circular cradles having radii different from that of the cylinder and contact angles up to seventyfive degrees. Using trescas criterion, a minimum yield stress of 422 nmm2 will be required for ductile materials. Contact stress analysis in wheelrail by hertzian method and finite element method. Us3636792a hertzian stressreducing means for gears.
The contact area will change depending on the magnitude of the contact stress. In mechanical engineering and tribology, hertzian contact stress is a description. Contact stresses and deformations university of utah. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance. New algorithms for calculating hertzian stresses, deformations, and contact zone parameters, amp journal of.
These contact stresses are called hertz contact stresses. Pdf contact stress analysis in wheelrail by hertzian. I am told that the compressive stress produced around the contact region of the pin b and the link, is explained by the hertzian stress. Pdf hertz contact stress of deep groove ball bearing. A multihertzian contact model considering plasticity. In many cases, the resultant stresses are not of design significance, but in some cases failure can. Hertzian of or relating to the physicist heinrich hertz or. The hertzian contact theory is approximated according to a concept by tanaka 2001. Pdf calculation of hertz contact stress between the deep groove. Contact stress analysis in wheelrail by hertzian method. Usually, hertz contact stresses are judged by the shear stress just below the surface. The application performs all calculations automatically. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. The contact radius a is considered significantly smaller than the radius of curvature r, and the two contacting surfaces, as depicted in figure 1, assumed to be nonconformal.
The note describes a simple and highly accurate numerical routine for calculating contact pressure and dimensions in elliptical hertzian contacts. The stresses considered in this section are examples of surface stresses or contact stresses. A general method of numerical solution in the nonhertzian elastic contact problem is developed using rectangular subdivisions. Another contact case entails friction that causes shear stresses on the contact zone. Under the action of a load the solids deform and a contact area is formed as shown in figure 1. The normal deflection uz of the surface, outside the contact region, is given by.
1371 784 1081 1007 819 1131 781 1214 74 871 1008 393 1279 1312 614 232 1601 1002 1067 1210 591 80 528 645 381 1127 863 901 443 164 1324