To engineer a contact condition like that the cylinder needs a profile with end reliefs. Archive of applied mechanics 70 2000 255268 o springer. Hertz contact stress involutes gear tooth contact stress analysis. 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. The theory of contact stress based on this concept is known as the hertz contact theory. On the theory of hertzian fracture proceedings of the royal. Keywords hertz contact stress, contact fe analysis, stresses within rollers, roller contact analysis and. The second missing element was a comprehensive life theory that would fit the observations of palmgren. 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. Hertzwin is a free hertzian contact stress calculator. A theoretical background to the hertz contact theory can be found here. The results are compared, following the analysis, to the results calculated on basis of the relations in h.
Dynamic model of 6206 deep groove ball bearing with the abovementioned bearing faults has been established by finite element method. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems. Hertz contact stress calculations and graphs with hertzwin. Rectangular contact area with semielliptical pressure distribution me en 7960 precision machine design contact stresses and deformations 710. 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 another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface. This paper presents to determine the contact stress of large diameter ball bearings using analytical and numerical methods. An approximate analysis for hertzian elliptical wheelrail contact problem. 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.
Therefore, it is very imporant to calculate the actual stress at the point of contact, the socalled contact stress. Palmgren, as will be discussed, distrusted hertz theory 12 and depended on a loadlife relation. Hertzian dipole, defined as a finite oscillating current over an infinitesimal length at a specified position. Contact stress analysis of spur gear for different materials using ansys and hertz equation putti srinivasa rao1, nadipalli sriraj2, mohammad farookh2 1professor, dept.
Contact stresses and deformations mechanical engineering. To speed up the process of calculation and accurate the model, fischer et. Palmgren revisited a basis for bearing life prediction. Under the action of a load the solids deform and a contact area is formed as shown in figure 1.
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. Relation between hertz stresslife exponent, ballrace. A vibration model of ball bearings with a localized defect. Hertzian contact theory indicates that the contact area between the ball and the raceway is an elliptical contact surface.
Cooper abstract formulations are given for the coefficients x, u, u defined by h. Hertz 1882 contact model is both elastic and quasistatic in nature. For example, the hct is applied in 2, 3 to investigate the growth of shelltype defects in the head of a railroad rail. The contact area will change depending on the magnitude of the contact stress. Contact mechanics is the study of the deformation of solids that touch each other at one or more. Hertzian contact stress, localized stresses that develop as two curved surfaces come in contact and deform slightly under imposed loads. Jones 10 relates the hertz contact theory for the stresses of nonconforming bodies in contact for both ball and roller bearings. 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.
These elevated stresses are beyond the hertzian field. International journal for research in applied science. Hertzian cone, the cone produced when an object passes through a solid, such as a bullet through glass. Assessment of the applicability of hertzian contact theory. 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. 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.
The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. The previous numerical algorithm is used to treat counterformal contacts, and convergent results can always be obtained. This paper is a revised and expanded version of an article entitled, contact stress analysis in wheelrail by hertzian method and finite element method presented in national conference on recent advancements in mechanical engineering held at north east regional institute of science and technology, arunachal pradesh. There the elastohydrodynamic oil film is minimal and the load is less distributed. In analytical method the contact stress is found out using the hertzian elliptical contact theory. Hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. The contactaffected zone, in the absence of surface shearing tractions, entertains compressive principal stresses. A clearly laidout window allows you to enter material properties, dimensions and loads. This is true for tires, needle bearings and other roller type of devices. The finite element analysis also performed to predict contact pressure in. Jan 24, 2012 i have calculated a static contact stress of 670 nmm2 using formula from mechanical engineering design, shigley, 5th edition. Review of hertzs contact stress theory basic assumptions the decision to rejector accept an established theory for modelling a specific physical system requires a comparison of the features of the system with the complete set of assumptions or axioms on which the theory is based. Hertzian contact models hertz contact model is nonlinear model which takes in account elastic deformation of spherical solids and changing contact radius.
That would explain why the stresses werent evenly distributed. Such as the hertzian theory, the jkr solution is also restricted to elastic sphere contacts. Abstractcontact stress analysis between two spur gear. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. Me en 7960 precision machine design contact stresses and deformations 78 spheres in contact vertical stress distribution at center of contact area plot shows material with poissons ratio. After hertzs work, people do a lot of study on the stresses arising from the contact between two elastic bodies. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. The limits normally adopted for hertzs contact stresses are 4 times the allowable stress for linear contact and 5. Hertzian contact stress hertzian contact theory is a classical theory of.
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. 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. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. Contact stress causes deformation, plastic or elastic. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Hertz theory does not account for tangential forces that may develop in. In reality, a small contact area is being created through elastic deformation, thereby limiting the stresses considerably. 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. For the hertzian contact stress theory, the fundamental. Contact between two continuous, nonconforming solids is initially a point or line.
The theory of contact between elastic bodies can be used to find contact areas and. 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. Pdf hertz contact stress analysis and validation using finite. This paper discusses the hertz contact theory validation using finite element analysis. Koos made the first effort at creating a stress theory with the profile of trouble p.
When loads are applied to the bodies, their surfaces deform elastically near the point. Hertzian static contact stress acceptance criteria physics. 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. In this thesis, an attempt is made to analyze contact stress using hertz theory. The surface fatigue mechanism is not definitively understood. This condition is modeled as a pair of cylinders in line contact, and a hertzian contact stress. Hertzian contact stress forms the foundation for the equations for load bearing. Contact mechanics, in principles and techniques for desiging precision machines. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies. Present study utilizes the application of hertz contact theory to the wheelrail contact problem to study the effect of variation of wheel. An improvement over the hertzian theory was provided by johnson et al. 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. Contact stress analysis of spur gear ijert journal.
In accordance with the hertzian contact theory 11, 12, the pressure in the plane of xoy in the contact area as showed in figure 2 is distributed as an elliptical curve, and the pressure. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. Pure hertzian model only describes normal deformation of spheres. Hertz contact stress of deep groove ball bearing sciencedirect. Bearing faults are commonly shown as the defects such as rolling body fracture, rolling body, and surface pitting, etc. For example, in mechanical engineering and tribology, hertzian contact stress is a description of the stress within mating parts. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a flat surface. 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. It can be used to calculate mechanical point and line contact dimensions and material stresses. Jan 21, 2014 2014w engr380 lecture18 spur gear design lewis equation for tooth bending stress, part i duration.
You could divide the hertz stresses by the same factors before comparing them to your allowables. Hertzian contact stress theory university of arizona. Contact fatigue differs from classic structural fatigue bending or torsional in that it results from a contact or hertzian stress state. Some account must be taken for the shape and size of the. Tables of hertzian contactstress coefficients duane h. The simplest modification is to crown the cylinder that the contact is of double radius type, just as hertzian theory handles. In 1882, hertz solved the contact problem of two elastic bodies with curved surfaces. Sep 17, 2016 since the area in contact between two bodies is sufficiently small compared to the surface of the bodies, the problems can be analyzed by superposing the basic solutions. In mechanical engineering and tribology, hertzian contact stress is a description. Hertzian contact pressure is applied in a fatigue life model to.
The finite element analysis also performed to predict contact pressure in ball and raceway. The equations for two cylinders in contact are also valid for. Hertzian contact stress hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. The application performs all calculations automatically. Bearing failure is one of the most important factors influencing performance, accuracy and reliability of rotating machineries. Pdf hertz contact stress analysis and validation using. The company was founded in 2011 and is majority owned by fouriertransform ab. Contact fatigue has been identified in metal alloys both ferrous and nonferrous and in ceramics and cer mets. Contact stresses and deformations curved surfaces in contact. This stillrelevant classical solution provides a foundation for modern problems in contact mechanics. Since the area in contact between two bodies is sufficiently small compared to the surface of the bodies, the problems can be analyzed by superposing the basic solutions. These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. Keywordscontact stress, spur gear, contact ratio, finite elements. The displacement of the points on the surface in the contact area between an originally even surface and a rigid sphere of radius r is equal to uz d.
From contact mechanics2 demonstrating the change in area during conditions of load. This is in accordance with the known experimental facts about the hertzian crack, particularly the fact that the crack at the surface forms systematically outside the edge of the circle of contact, at which the maximum tensile stress occurs. Me 383s bryant february 17, 2006 1 contact mechanical interaction of bodies via surfaces surfaces must touch forces press bodies together size area of contact dependent on forces, materials, geometry, temperature, etc. Tutorial on hertz contact stress university of arizona. Failure analysis of rolling bearings based on explicit. Contact stress analysis of spur gear for different.
Introduction itting is a surface fatigue failure resulting from repetitions of high contact stress. This paper presents the results of a study carried out using the finite element method, on the contact stresses between two bodies. Assessment of the applicability of hertzian contact theory to. 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. Hertzian contact equations for elliptical, spherical and.
Apr 22, 20 step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench. Later extensions of the model add viscosity, shear response including friction and adhesion. My problems lies that there is no acceptance criteria. The tensile stress in the outer fiber of such a beam is z m i m ym. Equations 7 and 8 can be used to determine the contact parameters between a cylinder and an internal spherical surface or a. We can also do wear analysis due to frictional rubbing between the contact surfaces. The contact pressure is intensified near the pitch circle, where the contact is pure rolling with zero sliding velocity. Another contact case entails friction that causes shear stresses on the contact zone. Contact stress analysis in wheelrail by hertzian method and. Hertzian contact pressure is applied in a fatigue life model to describe the damage of wheels in 4. By theory of elasticity, developed by hertz, in 1881.
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 stress mechanical engineering general. Part i history and definition of stress theory this first body of research led to the first efforts of development of family stress theory burr, 1989 by sociologist earl koos 1946. Hertzian contact theory contact between elastic curved bodies initial contact bodies spheres touch at. Hertz contact stress calculations hertzwin is a free hertzian contact stress calculator. Contact stress analysis in wheelrail by hertzian method. An approximate analysis for hertzian elliptical wheelrail. On the theory of hertzian fracture proceedings of the.