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Static Carrying Capacity of a Single-Row Ball Slewing Bearing Taking into Account Drive Transmission Conditions Cover

Static Carrying Capacity of a Single-Row Ball Slewing Bearing Taking into Account Drive Transmission Conditions

Acta Mechanica et Automatica
Volume 19 (2025): Issue 1 (March 2025)
By: Szczepan Śpiewak  
Open Access
|Mar 2025

Figures & Tables

Fig. 1.

Basic geometric parameters of the single-row ball slewing bearing
Basic geometric parameters of the single-row ball slewing bearing

Fig. 2.

The basic geometric parameter of a pinion and a toothed ring
The basic geometric parameter of a pinion and a toothed ring

Fig. 3.

A visualisation of finite elements of single-row ball slewing bearing, coupled with a drive pinion
A visualisation of finite elements of single-row ball slewing bearing, coupled with a drive pinion

Fig. 4.

Schematic position of bearing rings and replacement elements in a state before (a) and after (b) load inflicted with mapping changing of contact angle of balls in slewing bearing (c)
Schematic position of bearing rings and replacement elements in a state before (a) and after (b) load inflicted with mapping changing of contact angle of balls in slewing bearing (c)

Fig. 5.

Characteristic of the contact zone replacement
Characteristic of the contact zone replacement

Fig. 6.

Juxtaposition of static carrying capacity curves of the single-row ball slewing bearings loaded by radial forces directed positively with and without taken into consideration gear condition
Juxtaposition of static carrying capacity curves of the single-row ball slewing bearings loaded by radial forces directed positively with and without taken into consideration gear condition

Fig. 7.

Comparison of distributions of the forces acting on balls of the single-row ball slewing bearing for the points of work: I and II according to Fig. 6, β- angular coordinate
Comparison of distributions of the forces acting on balls of the single-row ball slewing bearing for the points of work: I and II according to Fig. 6, β- angular coordinate

Fig. 8.

Comparison of distribution of the forces acting on balls of the single-row ball slewing bearing for the maximum radial force with taken into consideration (Hmax=5,977 [MN]) and without(Hmax=3,3 MN) the gear condition, β- angular coordinate
Comparison of distribution of the forces acting on balls of the single-row ball slewing bearing for the maximum radial force with taken into consideration (Hmax=5,977 [MN]) and without(Hmax=3,3 MN) the gear condition, β- angular coordinate

Fig. 9.

The distribution of displacements in the direction of the radial force HM for operation points marked in Fig. 6 as II
The distribution of displacements in the direction of the radial force HM for operation points marked in Fig. 6 as II

Fig. A1.

Juxtaposition of static carrying capacity curves of the single- row ball slewing bearing loaded by constant values of the radial forces defined positively, negatively and orthogonaly
Juxtaposition of static carrying capacity curves of the single- row ball slewing bearing loaded by constant values of the radial forces defined positively, negatively and orthogonaly

Fig. A2.

uxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by the main radial forces HM defined positively
uxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by the main radial forces HM defined positively

Fig. A3.

Juxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by the main radial forces HM defined negatively
Juxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by the main radial forces HM defined negatively

Fig. A4.

Juxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by radial forces HN defined orthogonally
Juxtaposition of static carrying capacity curves of the single-row ball slewing bearing loaded by radial forces HN defined orthogonally

Fig. B1.

Distributions of the effective stress for the tested meshes of the contact zone model
Distributions of the effective stress for the tested meshes of the contact zone model

Fig. B2.

Distributions of the displacements for the tested meshes of the slewing bearing ring model
Distributions of the displacements for the tested meshes of the slewing bearing ring model

Fig. B3.

Distributions of effective stress for the tested meshes of the contact zone model of a toothed rim and a drive pinion
Distributions of effective stress for the tested meshes of the contact zone model of a toothed rim and a drive pinion

Values of basic parameters of the single-row ball slewing bearing

Parametr of the bearingValue
1The track diameter of the bearing dt [mm] (Fig. 1)1105
2The ball diameter dk [mm]44
3Quotient rays of ball and receway kp [2, 34]0,96
4Dimension dzp[mm] (Fig. 1)1260
5Dimension dzo [mm] (Fig. 1)1200
6Dimension dwo[mm] (Fig. 1)1010
7Dimension dwp [mm] (Fig. 1)960
8High of the bering h [mm]137
9Dimension a [mm] (Fig 1)10
10Dimension b [mm] (Fig. 1)71
11Dimension hw [mm] (Fig. 1)117
12Dimension hz [mm] (Fig. 1)122
13Axial clearance [mm]0,5
14The clearance between the rings Lp [mm] (Fig. 1)7
15Nominal contact angle αo[°]45
16Row fill facctor0,83
17Number of bearing balls64
18The surface balls hardness62HRC
19The surface raceway hardness56HRC
20Number of the bolts mounting in the internal/external ring42/42
21The size and strength class mounting bolts by [DIN] [31]M24-12.9
22Mounting tension force Sw [kN]242

Statistical data of the FE model of the slewing bearing

The modeled objectFinite element typeNumber of finite elements
The ball as a SuperelementTruss128
Beam512
Inner ring3D-Solid3584
Outer ring3D-Solid3584
BoltsBeam84
Heads of the mounting bolts3D-Solid5040
Upper support structure3D-Solid3392
lower support structure3D-Solid3392
Płyta3D-Solid1
Toothed rim3D-Solid56340
Pinion3D-Solid37651

Overview of features characterizing individual FE models of slewing bearings against the model presented in the article [*]

Feature of the presented modelReference number
1The use of replacement elements for modeling rolling parts[1], [2], [7], [9], [11], [13], [15], [18], [24], [25], [26], [32], [33], [35], [36], [37], [38],[*]
2Taking into account the support structures in slewing bearings[2], [7], [9], [10], [11], [25], [26], [32], [33], [35], [36], [38], [*]
3Taking into account interactions between the bearing and bolts[1], [2], [7], [9], [11], [13], [25], [26], [32], [33], [35], [36], [38], [*]
4Taking into account flexible rings[1], [2], [7], [9], [10], [11], [13], [15], [18], [24], [25], [26], [32], [33], [35], [36], [37], [38], [*]
5Taking into account of radial forces[1], [2], [7], [9], [10], [11], [13], [15], [18], [24], [25], [26], [32], [33], [35], [36], [38], [*]
6Modeling of the contact zone taking into account the elastic-plastic material model[2], [7], [11], [15], [18], [24], [26], [33], [35], [36], [*]
7Modeling of the bearing taking into account the cooperation conditions between a toothed bearing’s ring and a drive pinion[*]

Values of gears basic parameters

Name of parametersPinionToothed rim
1Reference diameter [mm]d1=182d1=1274
2Tip diameter [mm]da1=211,763da1=1322,823
3Root diameter [mm]df1=151,577df1=1262,637
4Profile shift coefficientx1=0,1135x2=0,7942
5Number of toothz1=13z2=91
6Module [mm]m=14
7Backlash [mm]jn=0,56
8Center distance [mm]aw=740
9Reference pressure angleαn=20°
10Working pressure angleαw=22,414°

Juxtaposition of statistical parameters describing the nature of the load of ball of single-row ball slewing bearing (Fig_ 8) for the selected points of work I and II (Fig_ 7)

Model of bearingExternal load componentsNumber of forcesBall reaction values Fi
Q [MN]M [MNm]HM [MN]Arythmetic average [kN]Standard deviation [kN]
Without pinion01,6031,12049108,740,7
With pinion02,1561,1204489,538,6
Without pinion00Hmax=3.39881,452,4
With pinion00Hmax=5,9776365,531,5
DOI: https://doi.org/10.2478/ama-2025-0003 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
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Language: English
Page range: 15 - 25
Submitted on: Jan 18, 2024
Accepted on: Apr 1, 2024
Published on: Mar 31, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
slewing bearing,
bearing capacity,
bearing design,
tilting moment,
static limiting load curves,
the toothed ring
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Szczepan Śpiewak, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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