The maximum sealing capability of high pressure oring seal designs is dependent on seal activation as discussed earlier and is not solely dependent on the initial contact pressure as determined by the compression of the seal in its housing groove. Vicura ab is an engineering company that delivers products which are used in different mechanical transmission systems and electrical drivelines. 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. A change in designed surface topology may result from wear that brings in a wide change in contact geometry and stresses. Hertzian loaddisplacement relation holds for spherical. 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 hertzian contact hertz 1881, 1882 is referred to the frictionless contact between two bodies. Assessment of the applicability of hertzian contact theory to. The theory governing the wheelrail contact is hertz theory. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. To study the influence of interacting wheel and rail profile topology of standard rail uic60, the standard wheel profile as per. Hertzian contact stress wolfram demonstrations project. Design of hard coated hertzian contacts for precision equipment submitted to precision engineering as the repeatability of kinematic couplings is coupled with surface finish, it is still necessary to preserve the finish of the contact patches if tens of nanometer repeatability is desired. So, as long as you use linear material properties and your displacements are in the realm of a linear solution, such a.
Glaser department of civil and environmental engineering, university of california, berkeley, 621a sutardja dai. Under the action of a load the solids deform and a contact area is formed as shown in figure 1. Hertz contact stress analysis and validation using. In this example problem, a steel cylinder with a radius of 5 is pressed against a 2 deep aluminum base. I need to write up my calcs and submit to my customer. 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 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. Alternatively, you could revert to a nonhertzian contact theory. Introduction study of deformation of solids under contact is called contact mechanics, comprising of mechanics of material and continuum. Hertz contact stress calculations hertzwin is a free hertzian contact stress calculator. Prex could you please give me a reference for your advice the limits normally adopted for hertz s contact stresses are 4 times the allowable stress for linear contact and 5.
However for low pressure designs, an analysis of the contact stress makes it possible to. This theory introduces characteristic material length. In 1882, heinrich hertz published a theory concerning circular contact areas and elastic deformations in the case of contact between two spheres1. The classical threedimensional hertz contact problem is reexamined in the present work within the context of couplestress elasticity. Contact between two continuous, nonconforming solids is initially a point or line.
So, as long as you use linear material properties and your displacements are in the realm of a linear solution, such a capability would suffice for hertz contact. International journal for research in applied science. This kind of stress may not be significant most of the time, but may cause. In this video, i have talked about the way in which the analysis is to be done of a cylinder being compressed between two rectangular plates in ansys. In another failure mode, called contact or hertzian fatigue, repeated stresses cause surface cracks and detachment of metal fragments from the tooth contact surface. Hertz contact theory is the classical theory to evaluate the contact stress in a contact between parabolic surfaces. Keywords hertz contact stress, contact fe analysis, stresses within rollers, roller contact analysis and. The following calculation presents an analysis of hertzian contact stresses when a sphere is pressed against a surface flat, convex and concave surfaces are considered. Hertzian theory when two curved bodies are brought into contact they initially contact at a single point or along a line.
Nov 28, 2014 this paper discusses the hertz contact theory validation using finite element analysis. 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. Keywords hertz contact stress, contact fe analysis, stresses. 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. The problem is linear except the contact condition at the base which is modeled using the contact pair approach. This paper presents the results of a study carried out using the finite element method, on the contact stresses between two bodies. Unusually high stresses may occur when a load is applied over a small area of contact. In the early stage, approximate modelling establishes whether the concept will work at all, and identifies the combination of material properties that maximize performance. Hertzian loaddisplacement relation holds for spherical indentation on soft elastic solids undergoing large deformations chenen wua, kenghui linb, jiayang juanga,n a department of mechanical engineering, national taiwan university, taipei 10617, taiwan. 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. If the vshaped notches are wide apart and contact only occurs at these notches then you might be able to consider each notch separately using hertz theory. Over a century ago hertz established a theory of contact mechanics that is still used today by engineers working in tribology. For the simplest model to calculate the stresses, one uses the hertz theory and evaluates the effect of the weight only. 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.
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. Hertz contact stress calculations and graphs with hertzwin. It can be used to calculate mechanical point and line contact dimensions and material stresses. Chapter 6, is expanded, presenting more coverage on electrical strain gages and providing tables of equations. The hertz contact problem in couplestress elasticity. Hertzian theory when two curved bodies are brought into contact they initially contact at. Spherical contact is a special case of the hertz contact, which is between two spheres, or between a. Well to calculate the hertz conatact stress i used the folowing.
Contact of bodies occurs in all interfaces transmitting force or motion, or both. Stress concentration in periodically rough hertzian contact. 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. Pdf the hertz contact problem in couplestress elasticity. The contact elliptical area is small so stresses developed will be higher. After hertz s work, people do a lot of study on the stresses arising from the contact between two elastic bodies.
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. Hertz contact stress of deep groove ball bearing sciencedirect. 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. Nov 04, 2017 typically people denote maximum stress according to hertz contact theory as a hertz contact stress. Oct 23, 2014 however, most fea suppliers package a multibody contact capability with a solution for linear materials and linear displacements and call it linear contact. Useful solutions for standard problems thayer school of.
Toward realtime detection of deep tissue injury risk in. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. 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. The company was founded in 2011 and is majority owned by fouriertransform ab. This theory introduces characteristic material length scales that emerge from the underlying microstructure and has proved to be very effective yet rather simple for modeling complex microstructured materials. Typically people denote maximum stress according to hertz contact theory as a hertz contact stress. In a detailed study of butterfly formations in aisi 52100 steel ball bearings by becker ref. Use of contact pair in ansys hertzian stresses on contact. These stresses were first studied by the german physicist heinrich hertz in 1881. Hertz contact stress mechanical engineering general.
Contact stress causes deformation, plastic or elastic. Calculation of hertz contact stress between the deep groove ball bearing and inner race using analytical and mesys tool analysis. The classical threedimensional hertz contact problem is reexamined in the present work within the context of couple stress elasticity. 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. To make his theory accessible for engineering applications, the program calculates a fast and accurate solution. The hertz contact stress usually refers to the stress close to the area of contact between two spheres of different radii. Hertzian contact stress hertzian contact theory is a classical theory of contact mechanics and is a very useful tool for engineers and researchers. Contact stresses and deformations mechanical engineering. However, most fea suppliers package a multibody contact capability with a solution for linear materials and linear displacements and call it linear contact. Tutorial on hertz contact stress university of arizona. The company was founded in 2011 and is majority owned by fouriertransform ab vicura, 20. Lesson 9 hertz contact problem patran 322 exercise workbook 93 model description. The results are compared, following the analysis, to the results calculated on basis of the relations in h.
High contact stress may lead to failures such as cracks, pits and flaking in the surface material. Experimental study of the force pulse and resulting stress waves gregory c. Contact stresses between two cylindrical bodies sciencedirect. Keywords hertz contact stress, contact fe analysis, stresses within rollers, roller contact analysis and hertz contact stress calculations. This paper discusses the hertz contact theory validation using finite element analysis. 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. Hertzian contact problems require the dimensions of the area of contact are small compared to the radii of curvature of the contacting surfaces near the region of contact. Safety and economy of railway traffic is enormously influenced by the contact stress variation caused by wheel rail contact profile changes. Spherical contact is a special case of the hertz contact, which is between two spheres, or between a sphere and the surface of a half space.
These contact stresses are called hertz contact stresses, which was first studies by hertz in 1881. The contact area will change depending on the magnitude of the contact stress. Patterned substrate, surface fraction, stress concentration, real contact area, hertz to softatpunch transition. 8 1 depth below contact area r a ti o of s tress to p ma x. Bearing pressure is a particular case of contact mechanics often occurring in cases where a convex surface male cylinder or sphere contacts a concave surface female cylinder or sphere. For example, butterflies are often associated with high contact stress 2000 to 4000 mpa, as discussed in more detail in the article contact fatigue of hardened steel in this vol ume. Gear tooth surface wear involves removal or displacement of material due to mechanical, chemical or electrical action. Excessive contact pressure can lead to a typical bearing failure such as a plastic deformation similar to peening. Useful solutions for standard problems preface modelling is a key part of design. Introduction contact stress is a description of the stress within mating parts. In your case this assumption fails, because you want to know the influence of your irregularities. Patil3 1 2 3head of the department of mechanical engineering, sgdcoe, jalgaon, india.