Tutorial on hertz contact stress university of arizona. Hertz contact stresses have a significant effect on bearing dynamic load capacity and l10 life. Area of contact is dependent on the force applied due to elastic deformation. Hertz contact stress calculations and graphs with hertzwin.
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. In reality, a small contact area is being created through elastic deformation, thereby limiting the stresses considerably. 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. If we determine the size and shape of this contact area and the distribution of normal pressure, then the interval stresses and deformation can be calculated. 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 stresses shigleys mechanical engineering. This is fine when it comes to bending and shear stresses etc, however im not sure what to do with hertz stresses. This paper discusses the hertz contact theory validation. 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. In the solution for contact stresses, an expression for the distance between corresponding points on the surfaces near the point of contact is required. Contact pressure and yield stress phoenix tribology. Using trescas criterion, a minimum yield stress of 422 nmm2 will be required for ductile materials.
Contact is a point or line when there are no applied forces or moments. Hertzian static contact stress acceptance criteria. An example of pitch line contact fatigue is shown in fig. Pdf hertz contact stress analysis and validation using. Contact failure in gears is currently predicted by comparing the. Contact stress analysis of spur gear ijert journal. 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.
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. Pdf application of hertzs theory of contact stresses to. They arise when materials meet at a common surface. Hence, the hertz equation for contact stresses in the teeth becomes, 3 where rp1 and rp2 are the pitch radii of the pinion and gear and. Shigleys mechanical engineering design tutorial 319. Heinrich hertz introduced the idea on contact mechanics in 1982. Hertz contact stress involutes gear tooth contact stress analysis one of the main gear tooth failure is pitting which is a surface fatigue failure due to many repetition of high contact stresses occurring in the gear tooth surface while a pair of teeth is transmitting power. The stresses considered in this section are examples of surface stresses or contact stresses. I found the original pdf benchmaks report yesterday and try to reproduce it with salomeprepomaxcalculix, but still the results shows a little penetration about 0. These stresses were first studied by the german physicist heinrich hertz in 1881. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress.
I am designing some equipment for a customer who requires i use a safety factor of 4 on proof strength and 6 on ultimate strength. A clearly laidout window allows you to enter material properties, dimensions and loads. The current project aims to arriving at these very solutions. 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. To study the influence of interacting wheel and rail profile topology of standard rail uic60, the standard wheel profile as per. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. The contact area will change depending on the magnitude of the contact stress. View notes hertz contact stresses from stat 2 at qatar university. What are hertz contact stresses and how do they affect. Tables of hertzian contactstress coefficients duane h. This paper discusses the hertz contact theory validation using finite element analysis.
By theory of elasticity, developed by hertz, in 1881. 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. Cooper abstract formulations are given for the coefficients x, u, u defined by h. Specify boundary conditions for symmetry, base and contact confirmation. In their 1947 paper 6, lundberg and palmgren state, hertz theory is valid under the assumptions that. The roller bearing assembly and spur gear pair assembly is an example were the assembly undergoes fatigue failure due to contact stresses.
On the compression of a cylinder in contact with a plane. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. Therefore, it is very imporant to calculate the actual stress at the point of contact, the socalled contact stress. Contact stress analysis of spur gear for different. 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. Unusually high stresses may occur when a load is applied over a small area of contact. 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. Hertzwin is a free hertzian contact stress calculator. 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.
In mechanical engineering and tribology, hertzian contact stress is a description. 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 contact stresses characteristics of contact stresses 1. Shear stresses, which cause fatigue a primary mode of failure of rolling elements are proportional to.
This all means that for a tresca material the mean contact pressure for initiation of yield is about 1. Contact stress and shear stress analysis of spur gear. Contact stresses and deformations curved surfaces in contact. B are the balls normal deformation of nut a and nut b. Other examples would be seawater pressurising a gas cylinder in deep water and the stress exerted by a train wheel on a train track. For analyses of adverse loading, hertzian theory may be useful and applicable provided that the following key assumptions of the theory are approximately. Please can anyone help with using hertz contact stresses. High contact stress may lead to failures such as cracks, pits and flaking in the surface material. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench.
But yes, in static cases you can often allow for higher stress. 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. 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 fully elastic models hertz analyzed the stresses at the contact of two elastic solids, and thereby assumed small strains within the elastic limit. Iwill try improving the mesh now is free mostly hexa. International journal for research in applied science. The application performs all calculations automatically. Usually, hertz contact stresses are judged by the shear stress just below the surface. Hertzian contact stress theory university of arizona. Contact stress hertz equation the stresses on the surfaces of gear teeth are usually determined using formula derived from the work of h. Contact between two continuous, nonconforming solids is initially a point or line. Palmgren later recanted his doubts about the validity of hertz theory. Assessment of the applicability of hertzian contact theory.
It can be used to calculate mechanical point and line contact dimensions and material stresses. Stresses surface tractions and sliding contact cylinder. Hertz determined the width of the contact band and the stress pattern when various geometric shapes were. 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 geometry of tooth mesh is such that rolling occurs at the pitch line while sliding oc curs at the addendum as the gears come out of mesh. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Contact mechanics is the study of the deformation of solids that touch each other at one or more points. The pitting problems, design needs and safety requirements make far in depth and complicated study of this contact. The mathematical theory for the general threedimensional contact problem was first developed by hertz in 1881. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. Nonadhesive, meaning the two surfaces require no force to separate. Patil3 1 2 3head of the department of mechanical engineering, sgdcoe, jalgaon, india. This page focuses mainly on the normal direction, i.
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 mechanics is the study of the deformation of solids that touch each other at one or more. It is determined by the contact shape of the screwnuts and the material properties 18, 19. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. Hertzian contact stress forms the foundation for the equations for load bearing. Under the action of a load the solids deform and a contact area is formed as shown in figure 1. Palmgren revisited a basis for bearing life prediction. Calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and mesys tool analysis. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Application of hertzs theory of contact stresses to cocoa pod deformation.
Analyze the model and inspect the contact stresses. Keywords hertz contact stress, contact fe analysis, stresses within rollers, roller contact analysis and. But note that the surface material is still elastic there is a miniscule plastic enclave under the surface. Contact fatigue occurs in gears along the pitch line. Contact stress calculations using hertz equation 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. You could divide the hertz stresses by the same factors before comparing them to your allowables. These contact stresses are called hertz contact stresses.
Hertz stress refers to the stress and deformation generated on two cylindrical rollers in contact under applied load. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. 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. Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. Hertz contact stress mechanical engineering general. Contact stress causes deformation, plastic or elastic. The stresses in between two rollers are critical, as a single line contact takes place between the rollers as. Hertz contact theory maintains both surfaces are frictionless. This tutorial addresses the basics of hertzian contact stress. Create the geometry for the cylinder and the base plate. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces.
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