General static load-carrying capacity for the design and selection of four contact point slewing bearings: Finite element calculations and theoretical model validation Josu Aguirrebeitia n , Mikel Abasolo, Rafael Avile ´ s, Igor Ferna ´ ndez de Bustos Department of Mechanical Engineering, ETSI-BILBAO. University of the Basque Country, Alameda de Urquijo, s/n, 48013 Bilbao, Spain article info Article history: Received 2 November 2011 Received in revised form 30 January 2012 Accepted 2 February 2012 Available online 3 March 2012 Keywords: Slewing bearings Load capacity Bearing selection Parametric finite element model abstract In previous publication, the authors developed a theoretical model to evaluate the static load capacity of four contact point slewing bearings. The method culminated in the formulation of an acceptance surface in the load space, in such a way that the validity of a load combination is assured by an inside- surface checking. In the present work a multiparametric Finite Element model has been developed. Three commercial bearings are analyzed using this model and the FE acceptance surfaces are obtained. From the comparison of the theoretical and the FE surfaces, the strengths and weaknesses of the theoretical model are discussed. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Slewing bearings are large sized rotary elements used in applications in which large rotational functional elements are involved, such as boring machines, tower cranes, wind turbine generators, etc. There are many different types of slewing bear- ings depending on the number of rows and on the type of rolling elements. Thus, there are bearings with one, two or three rows, whereas the rolling elements can be balls or rollers. Fig. 1 outlines the topology a four contact point slewing bearing. Fig. 2 shows the usual load system acting on it: axial and radial forces, as well as a tilting moment. In previous publications, several concepts relevant to the assessment of the static load-carrying capacity of four contact point slewing bearings have been examined. Amasorrain et al. [1] developed a procedure to work out the load distribution in this type of bearings when subjected to combinations of axial and radial forces and tilting moments. Liao and Lin [2] developed a similar procedure where only axial and radial forces were taken into account. Both procedures are analogous to the procedure used by Zupan and Prebil [3] to estimate the influence of geometrical and stiffness parameters on the calculation of the load-carrying capacity. The above works propose a generalization of the equations obtained by Jones [4], in which the load distribution is calculated from the known external loads. Never- theless, none of these approaches is useful to work out the load combinations that cause the most loaded ball arrives to its critical contact stress value (4200 MPa according to International Orga- nization for Standardization [5]), i.e. to the static failure. In fact, these load combinations would have to be obtained iteratively, with the consequent high computational cost. In [6] the authors developed a theoretical model under a different focus, which consists on directly calculating the load combinations for which the most loaded element (ball) presents a static failure. In this sense, the works of Sjov¨ all [7] and Rumbarger [8] were generalized in order to obtain this new theoretical approach. Based on the classical geometrical interference model, it enables to obtain a three-dimen- sional acceptance condition in the form of a surface inequation in the load space. This acceptance surface, shown in Fig. 3, can be used by the designer as a straightforward way to select a bearing. Figs. 4–6 show respectively the F A –M T , F A –F R and F R –M T curves, i.e. the coordinate planes, of the acceptance surface. Note that the axial load-carrying capacity C 0a , whose value can be obtained from standards [5] or even experimentally, was used to normalize the axes of the surface. The contact angle of the balls a (see Fig. 2) is assumed to remain constant, a ¼ 451. Diameter d is the ball center diameter, (da þ di)/2 in Fig. 7. The present work presents a multiparametric finite element model of the bearing. It has been used to analyze several commercial bearings and their corresponding acceptance surfaces have been obtained; these surfaces have been compared with the theoretical one so as to validate the theoretical model. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/finel Finite Elements in Analysis and Design 0168-874X/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.finel.2012.02.002 n Corresponding author. Tel.: þ34 94 601 7310; fax: þ34 94 601 4215. E-mail address: josu.aguirrebeitia@ehu.es (J. Aguirrebeitia). Finite Elements in Analysis and Design 55 (2012) 23–30