367 Static Load Distributi on in Ball Bearings 

Mário Ricci * 

    Abstract   A numerical procedure for computing the internal loading distribution in statically loaded, single-row, angular-contact ball bearings when subjected to a known combined radial and thrust load is presented.  The combined radial and thrust load must be applied in order to avoid tilting between inner and outer rings. The numerical procedure r equires the iterative solution of Z + 2 simultaneous nonlinear equations –  where Z is the number of the balls – to yield an exact solution for  axial and radial deflections, and contact  angles. Numerical results for a 218 angular-contact ball bearing have been compared with those from the literature and show significant differences in the m agnitudes of the ball loads, contact angles, and the  extent of the loading zone.   Introduction 

Ball and roller bearings, generically called rolling bearings , are commonly used machine elements. They  are employed to permit rotary motions of, or about, s hafts in simple commercial devices and also used in  complex engineering mechanisms.  This work is devoted to the study of the internal loading distribution in statically loaded single-row angularcontact ball bearings. Several researchers have studied the subject [1] [2] [3] [4]. The methods developed by them to calculate distribution of load among the balls and rollers of rolling bearings can be used in most bearing applications because rotational speeds are usually slow to moderate. Under these speed conditions, the effects of rolling element centrifugal forces and gyroscopic moments are negligible. At high  speeds of rotation, these body forc es become significant, tending to alter contact angles and clearance.  Thus, they can affect the static load distribution to a great extent. 

Harris [5] described methods for internal loading distribution in statically loaded bearings addressing pure  radial; pure thrust (centric and ecc entric loads), and combined radial and thrust load. These methods use  radial and thrust integrals introduced in [2] and those initially due to [3] for ball bearings under combined radial, thrust, and moment load.  There are many works describing the parameters variation models under static loads but few demonstrate such variations in practice, even under si mple static loadings. The author believes that the  lack of practical examples is mainly due to the inhe rent difficulties of the numerical procedures that, in  general, deal with the resolution of various non-l inear algebraic equations that must to be solved  simultaneously.   In an attempt to cover this gap, studies are being de veloped in parallel [6] [7]. In this work, a numerical  procedure is described for an internal load distributi on computation in statically loaded, single-row,  angular-contact ball bearings when subjected to a know n external combined radial and thrust load. The  novelty of the method is in the choice of the set of the nonlinear equations, which must be solved  simultaneously. The author did not find in the literature the solution of this problem using the same set of equations.                                                        * National Institute for Space Research, São José dos Campos, São Paulo State, Brazil  

Proceedings of the 40th Aerospace Mechanisms Symposium, NASA Kennedy Space Center, May 12-14, 2010   NASA/CP-2010-216272