For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. Contact stress two spheres in contact equation equations. The free flexhinge software application enables you to quickly calculate the stiffnesses and material stress of a flexure hinge. Shear stresses, which cause fatigue a primary mode of failure of rolling elements are proportional to the maximum hertz. New version of hertzian contact stress calculation mesys ag. Why hertz stress is the best indicator of contact reliability. The typical results we want to see are the peak contact stress, the contact radius and stress variation through depth under peak contact stress.
The following equation will determine the contact stress between two balls or spheres of known radius, youngs modulus and applied load. Unlike the hertz contact stress theory the finite element method evaluated the induced surface stresses within the topology of the orange which are found to be tensile forces and are greater than the compressive normal principal stresses evaluated using hertz contact stress theory. You could divide the hertz stresses by the same factors before comparing them to your allowables. Pdf hertz contact stress analysis and validation using finite. It uses a color function to visualize the contact zone between a statically loaded pair of contact models, a sphere and a torus. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Pdf hertz contact stress of deep groove ball bearing. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. Oct 23, 2014 the typical results we want to see are the peak contact stress, the contact radius and stress variation through depth under peak contact stress. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. I found a nice paper giving the theoretical solution for a 2d plane strain problem here. The problem is linear except for the contact condition between the two parts. 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.
For 9th and 8thpower hertz stress life exponents for ball and roller bearings, respectively, the lundbergpalmgren model best predicts life. Connector contact springs are generally made from copper alloys, which fall in a limited range of. This kind of stress may not be significant most of the time, but may cause. Design for limit stresses of orange fruits citrus sinensis. In practice, the rollers is are of finite length and at the ends of the rollers higher stress can occur. 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. Hertz contact stress theory ppt video online download slideplayer. The problem is linear except the contact condition at the base which is modeled using the contact pair approach. A simple matlab code for calculation of hertz solution hertz model for line, point and elliptical contacts.
To study the influence of interacting wheel and rail profile topology of standard rail uic60, the standard wheel profile as per. 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. It causes serious problems if not take it into account in some cases. The hertz contact problem studied consists of two identical, infinitely long cylinders pressed into each other. Contact stresses are due to weight, driving forces and other types of unusual, mainly dynamic, forces. Evaluation of subsurface contact stresses in railroad. 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. In bearing engineering, the equalized terms are between balls and an inner or outer ring. Also shows a plot of resultant pressure and deflection not for elliptical contact. Even more complicated theories consider the driving and other forces as a percentage of weight. Hertzian cone, the cone produced when an object passes through a solid, such as a bullet through glass. The software calculates hertzian contact stress and the subsurface stressen of the general contact of two elliptical bodies according to the hertzian theorie. Please see below for the options available which we can assist you. This demonstration presents the hertzian contact stress distribution and elastic deformations.
The calculation procedure consists of calculation of maximum contact pressure at different loads using analytical formulas and comparison of results with mesys. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. Use the following categories below to email us regarding your questions or comments. Hertzian contact stress wolfram demonstrations project. The subject investigated of this paper is a kind of large. The following equation will determine the contact stress between a sphere and a flat surface with known youngs modulus and applied load. Useful solutions to standard problems in introduction and synopsis modelling is a key part of design. Applicability of the hertz contact theory to rolling rubber. Questions on hertz contact problem spherical contact problem equations about spherical contact problem calculations based on equations calculations based on equations calculations based on nastran incadwrong result. The calculation is done using a tribology simulator software, which is available for download here its free to use. Rolling bearing life prediction, theory, and application.
The description of functionality of rolling bearing calculation for slewing rings. The hertz contact problem massachusetts institute of. Other important limitations are that the dimensions of the contact patch must remain. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified position. An understanding of the hertz theory of contact pressure. 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 mechanics in gears chalmers publication library. Tutorial on hertz contact stress university of arizona. Hertz contact theory hct is a study of contact stress and deformation which is widely used in many engineering fields. It is however, not only the contact stress which causes failure of tooth surface but also the relative sliding speed of the tooth surfaces which affects the surface failure in combination with. The limits normally adopted for hertz s contact stresses are 4 times the allowable stress for linear contact and 5. 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 simulator uses a boundary element method bem with fast fourier transform and conjugate gradient method to obtain the contact pressure and. 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. E youngs modulus f load r 1, r 2 radii v poissons ratio. Jan 27, 2012 an other issue is that in line contacts, the hertzequations assume infinite length of the rollers. Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. Ciavarellab,1 adepartment of mechanical engineering and applied mechanics, university of michigan, ann arbor, mi 481092125, usa bdepartment of engineering science, university of oxford, parks road, oxford, ox1 3pj, uk abstract contact problems are central to solid mechanics, because contact is the principal method of applying loads to a.
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. Frequently asked questions about the contact stress software. Introduction contact stress is a description of the stress within mating parts. Hertz stress as a connector design parameter connector. In this article, a calculation of contact pressure in a rough contact is discussed. Extract the total contact loading at each roller by selection of the contact nodes for each roller. 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. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties which maximize performance.
In this example problem, a steel cylinder with a radius of 5 is pressed against a 2 deep aluminum base. 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. 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. Hertz contact stress analysis and validation using finite. Chapter 6, is expanded, presenting more coverage on electrical strain gages and providing tables of equations.
Contact reliability is therefore critical to product performance and should be a key area of focus for electronic design engineers. Calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and mesys tool analysis. Fine mesh near the contact of fem analysis in principle, the meshing of two involute teeth have similar with the contact two cylinders or. For line contact cylinder on cylinder, the relationship is. This theory introduces characteristic material length.
Where s h is the calculated hertz stress hertz stress cannot be measured, f n is the contact normal force, e is the elastic modulus of the materials in contact, and d is the diameter of the contact area created by the applied normal force. Contact stresses two spheres in contact different youngs modulus and spherical radius. Contact stress calculations are based on hertzian pressure analysis between two cylinders represented by the teeth in contact under compression load. Hertzian contact stress, localized stresses that develop as two curved surfaces come in contact and deform slightly under imposed loads. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. 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. Hertz contact stress calculations and graphs with hertzwin. 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. Applicability of the hertz contact theory to rolling. Pdf calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and. Fortunately there is a proven and near foolproof way to predict spring contact reliability.
The application performs all calculations automatically. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. Itt cannon hertz stress and connector reliability white. Assessment of the applicability of hertzian contact theory.
Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. 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. Hertz is committed to providing our customers with the highest level of service.
The hertz contact problem see timoshenko and goodier, 1951 provides a classic example for verifying the contact capabilities in abaqus. Hertzwin is a free hertzian contact stress calculator. Also the effects of misalignment, causing an unequal stress distribution over the contact area, are not taken into account. Download limit exceeded you have exceeded your daily download allowance. Hertz contact stresses have a significant effect on bearing dynamic load capacity and l10 life. Hertz contact stress mechanical engineering general. 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. Lesson 9 hertz contact problem patran 322 exercise workbook 93 model description. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. Contact stress is damage to the tissue of the body caused by contact between soft tissue and a hard object. Hertzian contact stress refers to the localized stresses that develop as two curved. A simple matlab code for calculation of hertz solution hertz model for line, point and elliptical. Het praktische, gratis programma voert alle hertzcontactberekeningen. It can be used to calculate mechanical point and line contact dimensions and material stresses.
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. High contact stress may lead to failures such as cracks, pits and flaking in the surface material. In this case, we can consider a small area of the contact region da, fig. As the pressure increases, the oring is forced to the low pressure side of the gland. This amount of deformation is dependent on the modulus of elasticity of the material in contact. Hertz contact stress of deep groove ball bearing sciencedirect. E 1, e 2, youngs modulus f load r 1, r 2 radii v 1, v 2 poissons ratio. Spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. A new version of the software for calculation of hertzian contact stress is available.
Contact analysis on large negative clearance fourpoint. Internal contact stress may occur when muscles, nerves, tendons, or other soft tissue rub, or press, against bone or tendons in a way that causes the tissue to bruise or overextend. Contact stresses two spheres in contact same material and differnet spherical radius. For the simplest model to calculate the stresses, one uses the hertz theory and evaluates the effect of the weight only. Pdf the hertz contact problem in couplestress elasticity. These stresses were first studied by the german physicist heinrich hertz in 1881.
In addition, the problem is analyzed under dynamic conditions in abaqusstandard to illustrate the use of contact. It also serves as an excellent illustration of the use of substructuring in abaqusstandard for locally nonlinear cases local surface contact. Simply fill in the material data and dimensions on a clearly laidout window. In this case, we can consider a small area of the contact region. Create a steel semicylinder with a radius of 5 is pressed against a 2 deep aluminum base. Contact mechanics is the study of the deformation of solids that touch each other at one or more. Unusually high stresses may occur when a load is applied over a small area of contact. What are hertz contact stresses and how do they affect. Hertzian theory when two curved bodies are brought into contact they initially contact at a single point.
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