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

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. A1.

Fig. A2.

Fig. A3.

Fig. A4.

Fig. B1.

Fig. B2.

Fig. B3.

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

	Parametr of the bearing	Value
1	The track diameter of the bearing dt [mm] (Fig. 1)	1105
2	The ball diameter dk [mm]	44
3	Quotient rays of ball and receway kp [2, 34]	0,96
4	Dimension dzp[mm] (Fig. 1)	1260
5	Dimension dzo [mm] (Fig. 1)	1200
6	Dimension dwo[mm] (Fig. 1)	1010
7	Dimension dwp [mm] (Fig. 1)	960
8	High of the bering h [mm]	137
9	Dimension a [mm] (Fig 1)	10
10	Dimension b [mm] (Fig. 1)	71
11	Dimension hw [mm] (Fig. 1)	117
12	Dimension hz [mm] (Fig. 1)	122
13	Axial clearance [mm]	0,5
14	The clearance between the rings Lp [mm] (Fig. 1)	7
15	Nominal contact angle αo[°]	45
16	Row fill facctor	0,83
17	Number of bearing balls	64
18	The surface balls hardness	62HRC
19	The surface raceway hardness	56HRC
20	Number of the bolts mounting in the internal/external ring	42/42
21	The size and strength class mounting bolts by [DIN] [31]	M24-12.9
22	Mounting tension force Sw [kN]	242

Statistical data of the FE model of the slewing bearing

The modeled object	Finite element type	Number of finite elements
The ball as a Superelement	Truss	128
	Beam	512
Inner ring	3D-Solid	3584
Outer ring	3D-Solid	3584
Bolts	Beam	84
Heads of the mounting bolts	3D-Solid	5040
Upper support structure	3D-Solid	3392
lower support structure	3D-Solid	3392
Płyta	3D-Solid	1
Toothed rim	3D-Solid	56340
Pinion	3D-Solid	37651

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

Feature of the presented model		Reference number
1	The 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],[*]
2	Taking into account the support structures in slewing bearings	[2], [7], [9], [10], [11], [25], [26], [32], [33], [35], [36], [38], [*]
3	Taking into account interactions between the bearing and bolts	[1], [2], [7], [9], [11], [13], [25], [26], [32], [33], [35], [36], [38], [*]
4	Taking into account flexible rings	[1], [2], [7], [9], [10], [11], [13], [15], [18], [24], [25], [26], [32], [33], [35], [36], [37], [38], [*]
5	Taking into account of radial forces	[1], [2], [7], [9], [10], [11], [13], [15], [18], [24], [25], [26], [32], [33], [35], [36], [38], [*]
6	Modeling of the contact zone taking into account the elastic-plastic material model	[2], [7], [11], [15], [18], [24], [26], [33], [35], [36], [*]
7	Modeling 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 parameters		Pinion	Toothed rim
1	Reference diameter [mm]	d1=182	d1=1274
2	Tip diameter [mm]	da1=211,763	da1=1322,823
3	Root diameter [mm]	df1=151,577	df1=1262,637
4	Profile shift coefficient	x1=0,1135	x2=0,7942
5	Number of tooth	z1=13	z2=91
6	Module [mm]	m=14
7	Backlash [mm]	jn=0,56
8	Center distance [mm]	aw=740
9	Reference pressure angle	αn=20°
10	Working pressure angle	αw=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 bearing	External load components			Number of forces	Ball reaction values Fi
	Q [MN]	M [MNm]	HM [MN]		Arythmetic average [kN]	Standard deviation [kN]
Without pinion	0	1,603	1,120	49	108,7	40,7
With pinion	0	2,156	1,120	44	89,5	38,6
Without pinion	0	0	Hmax=3.3	98	81,4	52,4
With pinion	0	0	Hmax=5,977	63	65,5	31,5