A New Proposal for Explicit Angle Calculation in Angular Contact Ball Bearing

[+] Author and Article Information
J -F. Antoine1

 LGIPM-CEMA, IUT de Thionville-Yutz, 1 impasse Kastler, 57970 YUTZ, Francejf.antoine@enim.fr

G. Abba

 LGIPM-CEMA, Ecole Nationale d’Ingénieurs de Metz, Île du Saulcy, 57045 METZ Cedex, Franceabba@enim.fr

A. Molinari

LPMM, ISGMP, Université de Metz, Île du Saulcy, BP 80794, 57012 METZ Cedex 1, Francemolinari@lpmm.sciences.univ-metz.fr


To whom correspondence should be addressed.

J. Mech. Des 128(2), 468-478 (Jun 09, 2005) (11 pages) doi:10.1115/1.2168467 History: Received October 11, 2004; Revised June 09, 2005

In order to optimize the mechanical behavior of high speed rotors, it is useful to know the load-displacement law of the angular-contact ball bearing. The relationship between preload, speed, and contact angle is studied and a new analytical approach is proposed, giving explicitly and with good precision the contact angle versus preload and rotational speed for the special case of elastically preloaded high speed angular-contact ball bearing.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Free state of the ball

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Figure 2

Preloaded state of ball—parameters

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Figure 3

Dynamic state of the ball under the bearing rotational speed Ω⃗ and the preload F⃗p

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Figure 4

Ball bearing with 7°, 15°, 25°, or 40° contact angle—required iterations number to reach the reference result at 0.1% by the Newton-Raphson method with Harris formulation and with the scheme proposed here

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Figure 5

Convergence of series—returns for given iteration rank and for different free state contact angles

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Figure 6

Relative error on preloaded state contact angle between exact angle value and model for different free state contact angles vs load factor

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Figure 7

Convergence of algorithm for contact angles and ZFc∕Fp term in terms of iteration rank (angular-contact ball bearing 218-Fp=2000N and Ω=15,000rpm)

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Figure 8

Angles given by the third iteration of algorithm (curves) and the numerical solving (symbols) in terms of preload and for different rotational speed in the 218 angular contact bearing case

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Figure 9

Convergence of algorithm for contact angles and ZFc∕Fp term in terms of iteration rank (angular-contact ball bearing VEX 6-Fp=4N and Ω=200,000rpm)

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Figure 10

Angles given by the third iteration of algorithm (curves) compared to numerical results (symbols) for various rotational speed Ω in terms of the applied preload Fp

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Figure 11

Angles given after 3 iterations of the algorithm (curves) compared to those given by numerical solving (symbols) for different values of osculation ratio C=ao∕ai in terms of the rotational speed (Fp=8N)



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