Load distribution in a four contact-point slewing bearing

doi:10.1016/S0094-114X(03)00003-X

Mechanism and Machine Theory

Volume 38, Issue 6, June 2003, Pages 479-496

https://doi.org/10.1016/S0094-114X(03)00003-X Get rights and content

Abstract

This article discusses a calculation procedure for determining the load distributions in the rolling elements of a four contact-point slewing bearing with one row of ball bearings, under general load conditions (moment, axial load and radial load). What is discussed here is an extension to four contact-point of the general bearing theory, which calculates the load distributions in two contact-point rolling elements.

Laburpena
Artikulu hau kalkulu-prozedura bat da eta bide ematen du karga orokorreko (momentu, karga axial eta karga erradial) baldintzapean dagoen errenkada bakarreko boladun orientazio-koroa bateko errodadura-elementuetan indar-banaketa kalkulatzeko. Prozedurak errodamenduen teoria orokorra lau ikutze-puntura luzatzen du. Teoria orokor horrek Hertz-en teoria du oinarri eta bi ukitze-puntuko kasuan, errodadura-elementuetan indar-banaketa kalkulatzeko balio du.

Introduction

A slewing bearing is basically a large-sized bearing which may also have gear teeth to receive the energy of a motor, in accordance with the desired application. The field of application of this kind of bearing is very varied, from tower cranes to wind-power generators, excavation machinery and capital goods machinery.

Different types of slewing bearings exist: they can have either a single row of ball bearings, a double row of ball bearings, a row of crossed rollers, two rows of rollers or three rows of rollers. Thus, a slewing bearing is basically divided into rolling elements (which may be spherical ball bearings or rollers) and inner and outer raceways.

Slewing bearing calculation is based on the bearing calculation theory. When the bearings are dimensioned in order to support the loads to be carried, one of the first criteria used is that of limiting the contact pressure created between the rolling elements and the raceways.

It is therefore fundamental to calculate the static capacity, specifying the force to which the rolling element of the heaviest load-carrying bearing is subjected. To do this, the force distribution and the contact angle for the rolling elements of the slewing bearing must be known.

The load distribution in the rolling elements provides us with very useful information for calculating a slewing bearing. On the one hand, it tells us what the maximum load is and indicates which rolling element carries the heaviest load. And it also provides information for determining an equivalent load for calculating the dynamic capacity of the slewing bearing from the particular loads of each rolling element [2], [3], [4].

The two rings which make up the slewing bearing are normally screwed to the structure. The load distribution of the bearing also provides information which helps us to verify these screwed assemblies.

When the load distribution in the bearing is calculated, the relative displacements (axial, radial and rotational) between the bearing rings are calculated, and so the procedure for determining the load distribution also offers information on the general rigidity of the bearing, information which is sometimes fundamental in the case of certain applications.

This article describes the procedure established for determining the load distributions in the rolling elements of a four contact-point slewing bearing [1] with one row of ball bearings, under general load conditions (moment, axial load and radial load), where the effect of the bearing’s clearances is included.

The difference between two contact-point and four contact-point is in the raceway curvatures. Two contact-point slewing bearings have one single curvature for each raceway, while four contact-point bearings have two curvatures per raceway (Fig. 1).

For simplification purposes, the procedure described in this article supposes that the raceways are rigid and only assumes elastic deformations of the contacts of the rolling elements and raceways (Hertz contacts). Neither does it take into account the effects caused by the supporting surface of the bearing.

The deformation of the rings in general (owing, amongst other factors, to the elasticity of the rings themselves or to a lack of rigidity and flatness of the supports) gives rise to a loss of homogeneity in the contact angles and the contact pressures [5].

It is known from previous studies that the main deformation of the bearing on reinforced structures is caused by the contact pressure of the ball bearings on the raceways. In this situation the rings remain practically non-deformable.

The calculation procedure developed has been included in an Excel book macro so that the final user can easily calculate the forces exerted on the ball bearings. In addition to calculating the forces for each ball bearing, the force distribution can be seen in a very visual and graphic way. The displacements taking place in the bearing can also be calculated.

Section snippets

Solution method

In general, the outer loads carried by the slewing bearing are of axial, radial and moment types with respect to its axis. These combined loads cause each one of the ball bearings to carry a different load in accordance with the position it occupies within the bearing and with the geometric characteristics of the raceway and the material properties.

The turning speed of these bearings is low enough for the effects of the gyroscopic forces and centrifugal forces of the ball bearings themselves to

Contact rigidity

The contact rigidity, as mentioned above, is a non-linear function of the material of the ball bearing and raceway and of the relative displacement between them [1].

In each ball bearing/raceway contact, the load on the ball bearing in the direction of the contact is equal to $Q=Kδ^{3/2}$ where K is the contact rigidity and δ is the relative approach between remote points of the bodies in contact. δ is a function of the load on the ball bearing, the sum of the curvatures, the materials of the bodies in

Calculation procedure

The calculation procedure consists of defining the initial and final coordinates of the centres of curvature, studying the contacts between diagonally opposed centres of curvature and defining the non-linear equations.

Implementation

This procedure has been incorporated in a slewing bearing calculation program which allows the final user to easily calculate the forces on the ball bearings. In addition to calculating the forces on each ball bearing, the force distribution can be seen in a very visual and graphical way. It also allows the displacements produced in the bearing to be calculated.

The program is organised according to the diagram in Fig. 11.

To calculate the forces on each ball bearing, data must first be entered

Conclusions

The fundamental conclusion is that a calculation procedure has been developed for discovering the load distribution in the rolling elements of a four contact-point slewing bearing with one row of ball bearings.

This procedure has been implemented in a program for calculating load distribution and allows the rolling element with the greatest load to be observed in a very graphical way, in addition to the value of the load. The program also provides other data, such as the contact area of each

Acknowledgements

This calculation procedure is a result of a collaboration between IKERLAN’s Mechanical Engineering Department and LAULAGUN. The authors would therefore like to thank both IKERLAN and Roberto Esnaola Torres, the Managing Director of LAULAGUN.

With this article, the authors wish to pay tribute to the late José Ignacio “Xasio” Amasorrain (1949–1999). He is the real author of the procedure for calculating four contact-point slewing bearings, and this work has been finished on his behalf.

References (10)

A.H. Tedric, Rolling Bearing Analysis, fourth ed., John Wiley,...
International Standard ISO 76, Rolling Bearings––Static Load Ratings, second ed.,...
International Standard ISO 281, Rolling Bearings––Dynamic Load Ratings and Rating Life, first ed.,...
American National Standard, ANSI/AFMA Std 9-1990, “Load Ratings and Fatigue Life for Ball...
J.I. Amasorrain
Análisis estático de tornillerı́a en coronas de orientación
(1999)

There are more references available in the full text version of this article.

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