Simplified Solution for Elliptical-Contact Deformation Between Two Elastic Solids

Brewe, D. E.; Hamrock, B. J.

doi:10.1115/1.3453245

Cited by 131 publications

(83 citation statements)

References 4 publications

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“…The following analysis will assume that the curvature is positive for convex surfaces and negative for concave surfaces [19]. The geometry between two solids in contact ( and ) can be expressed in terms of the curvature sum ( ) and the curvature difference ( ) as follows [20,21]:…”

Section: Geometry Of Contacting Elastic Solidsmentioning

confidence: 99%

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Simple and Versatile Dynamic Model of Spherical Roller Bearing

Ghalamchi

Sopanen

Mikkola

2013

International Journal of Rotating Machinery

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Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-offreedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.

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Section: Geometry Of Contacting Elastic Solidsmentioning

confidence: 99%

“…Brewe and Hamrock [20] used numerical iteration and curve fitting techniques to find the following approximation formulas for the ellipticity parameter and the elliptical integrals of the first and second kinds as follows: …”

Section: Geometry Of Contacting Elastic Solidsmentioning

confidence: 99%

Simple and Versatile Dynamic Model of Spherical Roller Bearing

Ghalamchi

Sopanen

Mikkola

2013

International Journal of Rotating Machinery

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“…Simplified expressions for κ, ξ and ε, derived using linear regression, can be found in Brewe and Hamrock [15]. If K inn and K out are the stiffness parameters for inner and outer raceway contacts respectively, defined by equation 2, then effective stiffness parameter for a rolling-element can be calculated as [16]:…”

Section: Determination Of Internal Load Distributionmentioning

confidence: 99%

A dynamic model to predict the occurrence of skidding in wind-turbine bearings

Jain¹,

Hunt²

2011

J. Phys.: Conf. Ser.

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Abstract. Despite use of the best in current design practices, high-speed shaft (HSS) bearings, in a wind-turbine gearbox, continue to exhibit a high rate of premature failure. As HSS bearings operate under low loads and high speeds, these bearings are prone to skidding. However, most of the existing methods for analyzing skidding are quasi-static in nature and cannot be used to study dynamic operating conditions. This paper proposes a dynamic model, which includes gyroscopic and centrifugal effects, to study the skidding characteristics of angularcontact ball-bearings. Traction forces between rolling-elements and raceways are obtained using elastohydrodynamic (EHD) lubrication theory. Underlying gross-sliding mechanisms for pure axial loads, and combined radial and axial loads are also studied. The proposed model will enable engineers to improve bearing reliability at the design stage, by estimating the amount of skidding. IntroductionWind energy is the fastest growing renewable energy sector with an average annual growth rate of around 30% during last 10 years. In order to harvest energy most efficiently and reliably, various wind-turbine design concepts have been developed over the years. Most of the modern wind-turbine designs utilize a gearbox which connects the rotor-shaft to high-speed shaft, and increases rotational speed from 15-30 rpm (at blades) to 1000-1800 rpm -the speed required by most generators to produce electricity. As wind-turbines have grown larger, gearbox failure rates have gone up as well. Since gearbox is one of the most expensive components of a wind turbine, higher-than-expected failure rates increase the cost of energy production. For a typical turbine, 20% of the downtime is due to gearbox failures and an average gearbox failure takes about 250 hours to repair [1].Most of the problems in wind turbine gearboxes appear to emanate from bearings [2]. Bearings supporting the high speed shaft exhibit a high rate of premature failure and are identified as one of the most critical components [1,2]. These bearings operate under low loads and high speeds, and therefore, are prone to skidding, i.e., gross-sliding of rolling-elements on raceways. Sliding can lead to rolling surface distress and eventually to premature failure. Hence, skidding is an important design criterion for wind-turbine bearings. Both ball-bearings and roller-bearings are commonly used to support HSS. The focus of this work is on angular-contact ball-bearings.Researchers have developed numerous analytical and numerical models of varying complexity to understand the skidding behaviour of bearings. Jones [3,4] developed the first mathematical theory to analyze the motion of rolling-elements in ball bearings. He evaluated the frictional

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“…The classical Hertzian solution can be simplified using a linear regression by the method of least squares [21,22]. The load-deflection constants between the ball and each race, K ij and K oj , can be expressed as…”

Section: Ball Equilibriummentioning

confidence: 99%

Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

Chen

Zhang

2007

Nonlinear Dyn

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This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.

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Simplified Solution for Elliptical-Contact Deformation Between Two Elastic Solids

Cited by 131 publications

References 4 publications

Simple and Versatile Dynamic Model of Spherical Roller Bearing

Simple and Versatile Dynamic Model of Spherical Roller Bearing

A dynamic model to predict the occurrence of skidding in wind-turbine bearings

Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

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