An Engineering Approach to Hertzian Contact Elasticity—Part I

International audienceThis paper presents a methodology to calculate the contact pressures on the rolling elements and other significant parameters applicable to raceway bearings used in aeronautical helicopter gearboxes. The mechanism is modelled by a hybrid method where the parts are decomposed in finite elements and the bearings are described by substitution features. This hybrid method accounts for the flexibility of the parts as well as geometrical defects. In this method, the contacts between rolling element and raceways are solved analytically. The Hertz contact theory is used to calculate the contact behaviour. The geometrical defects are included in the model thus changing the value of local displacements. Our paper shows the impact of the flexibility of the different mechanical parts and its geometrical defects, on the behaviour of the bearing raceways. Three most important conclusions are brought to the fore. First the load distribution in the bearing is modified by the flexibility of the parts and the bearing raceways. Second, positioning defects in our assemblies have insignificant effect on the bearing service life. Third orientation defects increase the pressure in roller bearings and the balls orbital speed variation in ball bearings

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“…Refs. [6] or [17] describe, in detail, the calculation method for the pressures. For our study, the methods described in [6] are used.…”

Section: Processing Of the Resultsmentioning

confidence: 99%

“…Houpert [17] has compared the different relationships and has proposed an analytical relationship inspired by the work performed by Tripp [18]. This new relationship introduces the contact length, the material coefficients and the equivalent radius of the cylinders in contact.…”

Section: Modelling Of a Roller Bearingmentioning

confidence: 99%

Impact of geometrical defects on bearing assemblies with integrated raceways in aeronautical gearboxes

Zamponi¹,

Mermoz²,

Linares

et al. 2009

Mechanism and Machine Theory

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“…Using the load-deformation relationship given by Houpert 24,25 for dry contacts and the plateau film thickness formula proposed by Dowson and Toyoda 29 for line contacts, it can be determined that…”

Section: Stiffness and Damping Of Two Rolling Element Rowsmentioning

confidence: 99%

Flexural vibration analysis of an automobile water pump bearing-rotor system with a modified transfer matrix method

Zhou

Tang³

et al. 2012

Proceedings of the Institution of Mechanical Engineers, Part K:

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The loading, elastic deformation and hydrodynamic film effect at each rolling element-raceway contact of automobile water pump bearing are analyzed. Based on this analysis, the total radial stiffness, angular stiffness and radial damping of the two rolling element rows are modelled. These stiffness and damping are taken into the transfer matrix to evaluate the lateral vibration characteristics of a rotor-automobile water pump bearing system. The natural frequencies, mode shapes and unbalance responses of the system are calculated. The effects of the pulley and fan unbalances on the system response under different spindle speeds are studied. The calculation results show that the unbalance response of the system can be reduced by fixing the pulley and fan with the initial phase difference between their unbalances to be 180 , and by increasing the pulley unbalance appropriately when keeping the fan unbalance constant.

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“…In order to solve the elliptical contact problem, one must typically use tables or approximations [2] to obtain values for the elliptical integrals, and the contact properties are then often found using tables or diagrams [3]. Other researchers have provided numerical approaches, and these can be grouped into those that utilize simplified approximations for force-displacement relationships [4], those that attempt to solve the contact parameters through empirical curve fitting [5][6][7][8], and those that use iterative numerical techniques [3,9,10]. These solutions all give satisfactory results for the contact parameters to within some error, but none provide the solution to the contact zone orientation.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Contact Zone Orientation for Normal Elliptical Hertzian Contact

Garland

Rogers

2011

Journal of Applied Mechanics

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Many mechanical designs have parts that come into, or lose, contact with each other. When elastic bodies with second order surface geometries come into contact, the contact patch is expected to be approximately fiat and to have an elliptical boundary. Classic Hertzian contact mechanics can be used to model such contacts, but since there is no closed-form analytical solution to predict the major and minor axes of the contact zone ellipse, approximate numerical methods have been developed, some of which are very accurate. Predictions of the mutual approach of the bodies and the contact pressure distribution can then be made. Although the shape of the contact ellipse has been modeled and solved for, to date there has been no solution for the orientation of the contact ellipse with respect to either of the contacting bodies. The contact ellipse orientation is needed in order to model the shear stress distributions that occur when .sticking friction forces are developed and separate contact zones of sticking and slipping are expected. Using the results of a numerical solution for the conventional contact parameters, this paper presents an analytical solution of the orientation of the contact ellipse, which is shown to depend only on the curvatures and the relative orientation of the contacting bodies. In order to validate the analytical solution, the results are compared with those from ABAQUS finite element simulations for cases of identical bodies and bodies with dissimilar curvatures. The predictions of the contact ellipse orientation angles and the major and minor semi-axes agree very well for all cases considered.

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An Engineering Approach to Hertzian Contact Elasticity—Part I

Cited by 80 publications

References 3 publications

Impact of geometrical defects on bearing assemblies with integrated raceways in aeronautical gearboxes

Impact of geometrical defects on bearing assemblies with integrated raceways in aeronautical gearboxes

Flexural vibration analysis of an automobile water pump bearing-rotor system with a modified transfer matrix method

Solution of the Contact Zone Orientation for Normal Elliptical Hertzian Contact

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