The tensile stress in the outer fiber of such a beam is z m i m ym. Effect of interference fits on roller bearing fatigue life. Stefan ghimisi, constantin brancusi university of targu jiu abstract. It allows for the prediction of contact area, pressure, compression and the resulting stresses between to continuous nonconforming solids under a load. Contact stress analysis in wheelrail by hertzian method and. Researchers have reported that al 2 o 3 maintains an elastic hertzian response up to a mean contact pressure of 5 gpa maximum pressure 7. 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 surface fatigue mechanism is not definitively understood. A frictionless, augmented lagrange method was used to control the contact between the shaft and bushing. Based on the data the stress values can be optimized by modifying either the load parameter or the roller size.
Contact stress analysis in wheelrail by hertzian method and finite element method. Failure analysis and design of a heavily loaded pin joint by nader farzaneh submitted to the department of mechanical engineering on march 27, 2002, in partial fulfillment of the requirements for the degree of master of science in mechanical engineering abstract. Nov 10, 2011 hertzian predictions were most accurate in the coc pairs. The results from the analysis show that contact stresses. However, more sophisticated problems require that the action of forces be described in terms of stress, that is, force divided by area.
The application performs all calculations automatically. An analysis was performed to determine the effects of innerring speed and press fits on roller bearing fatigue life. We can compare the maximum y compressive stress values to a summary listing of the maximum stresses output for the cylinder and base plate from text report. 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. Pdf hertz contact stress analysis and validation using finite. Comparison of hertzian and jkr theories with a finite element. Hertzwin is a free hertzian contact stress calculator. Contact stress analysis of spur gear for different materials. It gives the contact stress as a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies.
Palmgren revisited a basis for bearing life prediction. Zaretsky lewis research center cleveland, ohio prepared for the stle annual meeting sponsored by the society of tribologists and lubrication engineers kansas city, missouri, may 1822, 1997 national aeronautics and space administration. This kind of stress may not be significant most of the time, but may cause. Next disadvantage of these equations is the fact that they do not respect the. Hertz developed a theory to calculate the contact area and pressure between the two. The effects of the resultant hoop and radial stresses on the principal stresses were considered. Hertzian static contact stress acceptance criteria physics. The equation for b that you posted in your comment assumes a different definition of the reduced elastic modulus 1e, while the equations posted in the wiki, assume 2e, see its definition after equation 1. The small contact areas that result often cause design. Tutorial of hertzian contact stress analysis university of arizona. Based on the result from the contact stress analysis the hardness of the gear tooth profile can be. 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.
Me en 7960 precision machine design contact stresses and deformations 7 sphere vs. Normally, you wouldnt calculate a contact stress as might be done with ball bearings you just work with the average stress in the area and assume there will be some local yielding. That means that the primary unknown will be the generalized displacements. Hertzian contact stress forms the foundation for the equations for load bearing capabilities and fatigue life in bearings, gears, and any other bodies where two surfaces are in contact. 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. The stresses that are exported from this analysis are pointing out not only the necessity for an elastoplastic model to be created, but also the importance of. It can be used to calculate mechanical point and line contact dimensions and material stresses. This paper presents a study by the finite element method fem of the contact tensions between two bodies and the results obtained are compared with the calculations obtained on basis of the relations of the theory of h. My problems lies that there is no acceptance criteria. Lsdyna implicit finite element analysis is used to investigate these contact stresses in the workpiece material under imposed hertzian pressure loading. Ai palmgren revisited a basis for bearing life prediction erwin v. Stresses on spur gear teeth the two primary failure modes for gears are. Apr 22, 20 step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench.
Unusually high stresses may occur when a load is applied over a small area of contact. The hertzian contact stress calculations give the contact stress that is induced in flawless steels no inclusions, when the contactforce is constant across the cam and camfollower see also contact assumptions, below. 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. Though it has been shown through experimentation the hertzian equations maybe on the conservative side but in many cases the stresses can be mitigated with simple design changes. Contact stresses and deformations curved surfaces in contact. For the analysis, the bottom of the sample was fixed on the x and y axes, and the center axis of the sample and the coating layer was fixed on the y axis. Step by step procedure of how to do static structural analysis of hertzian contact analysis ansys workbench.
Hertzian contact equations for elliptical, spherical and. Hertz contact stress analysis and validation using finite element analysis 3,744 views. We can also do wear analysis due to frictional rubbing between the contact surfaces. Closure to discussions of rocket motor gear tooth analysis hertzian contact stresses and times 1960, asme j. Calculating maximum contact pressure on a heavily loaded journal bearing fea calculation using the ansys staticstructural package, fea calculations were made to calculate the contact stress. Hertz contact stress analysis and validation using finite. Vicura ab is an engineering company that delivers products which are used in. Hertz contact stress analysis and validation using finite element analysis. Also, theres a paper available on lifting beam design that includes an analysis of the lifting eyes. Ind august, 1960 constitutive equations for solid propellants. Using the hertzs surface pressures and the mohrs circles the substance of pitting start is derived and the stress distributions using the elementary joists. 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.
Jan 21, 2014 2014w engr380 lecture18 spur gear design lewis equation for tooth bending stress, part i duration. These contact stresses are called hertz contact stresses. The deformation is elastic in general, although some plastic deformation is also possible. Analysis of fatigue stress in a hertzian form prof. Numerical modeling and simulation of the deformation. Nonhertzian contact stress analysis for an elastic half space. Finite element analysis of stresses due to normal and. Mech designer is perfectly capable of calculating the hertzian contact stress. Hertzian stress analysis and characterization of thermal. Hertz contact stress calculations and graphs with hertzwin.
Hertz contact stress calculations hertzwin is a free hertzian contact stress calculator. He computed and verified by experiment the load distributions over the contact area and solved for the stresses in the body through use of the. All other items of interest will mainly depend on the. Contact mechanics in gears chalmers publication library. Pdf hertz contact stress analysis and validation using.
Hertz theory for contact stress is an important tool for analysis in optomechanical design. The bending stress obtained by finite element analysis method is compared with bending stress obtained by lewis equation and the contact stress obtained by finite element analysis method is compared with contact stress obtained by hertzian equation. Analysis by finite element method is a modern method for studying various contacts, allowing the determination of important parameters for the study of various contacts. Failure analysis and design of a heavily loaded pin joint.
Keywordscontact stress, spur gear, contact ratio, finite elements. Yet, this volumetric density implies an element edge length of 0. Hertzian contact stress allowable hertzian contact stress transverse pressure angle. Contact stresses and deformations mechanical engineering. Journal of applied mechanics, june 1953 6 nicholas lecain, tutorial of hertzian contact stress analysis college of optical sciences, university of arizona. Investigation of contact stress in spur gear using lewis equation and finite element method ashish v kadu1 and sanjay s deshmukh1 corresponding author. It applies to normal contact between two elastic solids that are smooth and can be described locally with orthogonal radii of. Zaretsky national aeronautics and space administration lewis research center cleveland, ohio 445 summary bearing technology, as well as the bearing industry, began to. International journal for research in applied science. Contact stress analysis of spur gear for different.
The paper attempts to perform contact analysis and obtain appropriate stress values induced at the. Contact stress analysis in wheelrail by hertzian method. Pdf contact stress analysis in wheelrail by hertzian. Contact stress analysis of spur gear ijert journal.
Jan 24, 2012 i have calculated a static contact stress of 670 nmm2 using formula from mechanical engineering design, shigley, 5th edition. See some of the pressure vessel handbooks for typical details. Introduction itting is a surface fatigue failure resulting from repetitions of high contact stress. Hertz s analysis of contact stress involves the following set of assumptions. The maximum shear stresses below the hertzian contact were determined for different condl. In addition to delivering a computer based tool for analyzing contact mechanics in gears the project has also attempted to answer the following questions. Tutorial hertz contact stress brian taylor opti521 fall 2016, sid. Proceedings of the 1st international and 16th national conference on machines and mechanisms inacomm20, iit roorkee, india, dec 1820 20 an approximate analysis for hertzian elliptical wheelrail contact problem jay prakash srivastava department of. Keywords hertz contact stress, contact fe analysis, stresses within. These stresses were first studied by the german physicist heinrich hertz in 1881. An approximate analysis for hertzian elliptical wheelrail. This paper discusses the hertz contact theory validation using finite element analysis. Axisymmetric elements were chosen for this analysis, and plane stress was assumed to analyze the indentation on the coating system.
Contact fatigue has been identified in metal alloys both ferrous and nonferrous and in ceramics and cer mets. Rocket motor gear tooth analysis hertzian contract. Contact fatigue differs from classic structural fatigue bending or torsional in that it results from. C contact mechanicsi the theory developed by hertz in 1880 remains the foundation for most contact problems encountered in engineering. Assessment of the applicability of hertzian contact theory to. Contact stress analysis of spur gear for different materials using ansys and hertz equation putti srinivasa rao1, nadipalli sriraj2, mohammad farookh2 1professor, dept.
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