Elsevier

Mechanism and Machine Theory

Volume 41, Issue 11, November 2006, Pages 1359-1376
Mechanism and Machine Theory

Modelling of rollers in calculation of slewing bearing with the use of finite elements

https://doi.org/10.1016/j.mechmachtheory.2005.12.007Get rights and content

Abstract

During the operation the slewing bearings are a subject to a large deformation. It is the cause of unequal load of the rolling elements. Deformation of the bearing can be calculated by the FE models, in which the rolling elements are replaced by the truss elements. These elements ought to have a right load–deformation characteristic. In the paper the method of calculating such a characteristics for the roller slewing bearings is presented. The type and the parameters of the roller generator correction have the largest influence on the analysed characteristics, considerably smaller is an effect of the plastic deformations in the contact zone of the roller and the bearing raceway.

Streszczenie

Łożyska wieńcowe ulegają podczas eksploatacji dużym deformacjom. Powoduje to nierównomierne obciążenie cze˛ści tocznych. Deformacje łożysk oblicza sie˛ wykorzystując modele MES, w których cze˛ści toczne zaste˛puje sie˛ elementami pre˛towymi. Elementy te powinny mieć właściwą charakterystyke˛ deformacja–obcia˛z˙enie. W pracy przedstawiono sposób obliczania takich charakterystyk dla łożysk wieńcowych wałeczkowych. Na analizowane charakterystyki najsilniej wpływa rodzaj i wartość korekcji tworzącej wałeczka, w znacznie mniejszym stopniu odkształcenia plastyczne w strefie styku wałeczka z bieżnią łożyska.

Introduction

Slewing bearings perform, within working machines, the function of rotational connections. These machine assemblies are in a large way responsible for the operational reliability and correct operation of the whole machine. These bearings possess a many of characteristic features, which different them from standard commonly used rolling bearings. Aside from their most significant feature, being the capability to taking of the overturning moment load, may have also a big size of diameter (sometimes even several or more meters) while the diameter of the slewing bearing is usually 50 or more times greater than the diameter of the rolling elements. The typical structural solutions for such bearings are illustrated in Fig. 1. The main criterion for the choice of slewing bearings is their static load carrying capacity. In brand catalogues, this feature is referred to as the catalogue load carrying capacity while it is often obtained by rigid bearing rings. The slewing bearings are fastened using an assembly of bolts to the body of the supporting machine, which can be subjected to somewhat significant deformations. This has an important effect on the load of the rolling elements as well as the load carrying capacity of the bearing. The catalogue load carrying capacity does not incorporate such effects. Because of that it is necessary to apply more precise methods for the calculations of bearings, which include effect of supporting structures deforming on the load carrying capacity of the bearings.

Analysis of support structures deformation is a complex process. Analytical solutions e.g. [1], [2] include massive simplifications. Using the finite element methods helps us achieve better results. Simple FEM model of the bearing without supporting structures has been developed by Wozniak [3]. Rings of the bearing are modeled using beam elements but rolling elements using linear elastic elements. Brändlein [4] used FEM for modeling large diameter bearings housing structures, but slew bearing was being modeled separately (analytically) using beam girders with constant cross-section. Rolling elements were not modeled. Gibczyńska and Marciniec [5] used FEM for analysis of bearing support construction deformation, and the bearing itself was computed using analytical methods. Interaction between rolling elements and bearing raceway was replaced with contact forces. Similar solution was adapted by Zupan and Prebil [6], [7]. They were carrying out calculations of the load distribution in the bearing using iteration method. Using FEM they calculated influence coefficients of supporting machine deformation for contact forces. The next step was solving the bearing balance equation. Rolling elements in the bearing were not modeled.

Using FEM does not remove all difficulties appearing in slew bearing computation. One of these is the proper modelling of rolling elements. Large number of these elements (several dozen or more) causes, that building of a full bearing model, taking into account the shape of the rolling elements and the modelling of the contact problem of each of them is practically impossible. Fig. 2 represents mesh of three-row roller bearing model, which is a part of a bigger working machine model. In this particular model rollers were replaced with truss elements. This type of a simplification allows for avoiding the multiple modelling of the contact problem but does however introduce the requirement of specifying of nonlinear load–deformation characteristics of the truss element, which is modelling the rolling elements. The similar solution in rolling bearings models was used by Smolnicki. In that purpose he developed ‘superelement’ consisting of two beam elements with high stiffness joined by truss element and contact element. Smolnicki [8], [9] used FEM for modeling of slew bearings with reinforcement structures. For roller bearings modeling Smolnicki et al. [10] used simplification in form of his ‘superelement’ linear characteristic. This could be the reason of errors in the calculation of the bearing load carrying capacity.

Due to the specific nature of the effects occurring in the contact zones of the rollers or balls with the bearing raceway, the issue of the determining of the characteristics of the truss elements should be considered separately for balls and for the rollers. The following report has been dedicated to the modelling of roller bearings. The analysis has been performed for the structure of a three-row bearing (Fig. 1a).

Section snippets

Analytical model of the contact zone of the bearing roller with the bearing raceway

All analytical models of the contact zone of the roller with the raceway are based on the Hertz’s theory of the contact of two cylinders with an infinite length. The analytical model used in the calculations of slewing bearings requires to bear in mind two issues:

  • The determining of the maximum force with which the roller can be pressed to the raceway and the maximum deformations of the raceway–roller–raceway zone the roller caused by it.

  • The determining of the relation of the deformation of the

Algorithm for the determination of equivalent characteristics

As mentioned above, in the process of modelling of slewing bearings by means of finite elements, the rolling elements are replaced by truss elements. In this purpose 2-node truss elements (Fig. 3a) with nonlinear-elastic material with stress–strain characteristic as shown in Fig. 3b and with computational section area At, were used. It is for these elements that the load–deformation characteristics are determined. Those characteristics should:

  • assure the same value and the same course of the

Results of performed calculations

The calculations of the load–deformation characteristics for the contact zones of the roller with the slewing bearing raceway and the equivalent characteristic of the truss element for the slewing bearing FEM model have been worked out by using the earlier completed models. The limiting loads of the roller have been calculated using formula (6). It has been assumed that for slewing bearings, the hardness of the bearing raceway does not exceed 58 HRC (the bearing rings are made from 41Cr4,

Conclusion

On the basis of the obtained numerical calculation results it is possible to state that when performing a modelling of slewing bearings by using the FEM and the substituting of bearing rollers with truss elements, it is necessary to define the equivalent characteristic for such elements because the dependence between the load and the deformation of the element differs significantly from the dependence used in analytical calculations of carrying load capacity of slewing bearings. The resulting

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