Analysis for clearance calculation of four points angular contact ball bearing

Abstract: Geometrical relationship between clearance and contact angle was explored and calculation method of clearance was modified by measuring, calculating and analyzing of three points angular contact ball bearing and four points angular contact ball bearings.

Key words: angular contact ball bearing; clearance; analysis

The symbols and their meanings involved in the text:

α— Contact angle,

Pd - Radial measurement clearance,

Pe - Axial measurement clearance,

Ri - radius of curvature of inner groove,

Re - radius of curvature of outer groove,

Dw - Steel ball diameter,

As - gasket angle at three point contact,

β S - gasket angle at four point contact,

Xi - The abscissa of the center of the curvature radius of the inner ring groove,

Xe - The abscissa of the center of the curvature radius of the outer ring groove.

1. Introduction

Three point and four point angular contact ball bearings are widely used in situations that simultaneously withstand axial and radial forces, and are widely used in aviation and marine machinery. In practical use, there are significant differences in the calculation and measurement of the clearance between this type of bearing and ordinary angular contact bearings. This article attempts to conduct a simple analysis of the calculation and measurement of three point and four point bearings, and provide a reasonable geometric relationship.

In ordinary angular contact ball bearings, the geometric relationship between contact angle and bearing clearance is relatively simple:

In the three-point angular contact ball bearing, due to the deviation of the center of the groove radius, the geometric relationship also changes accordingly. At this time, it is necessary to first restore the geometric relationship in the three-point angular contact ball bearing to the ordinary angular contact shape, and then calculate according to the ordinary angular contact shape.

2. Structure of three and four point angular contact ball bearings

2.1 Three point angular contact ball bearing (Figure 1)

2.1.1 Double half outer ring angular contact ball bearing Double half outer ring angular contact ball bearing, the inner ring is consistent with the inner ring of the same size outer ring slope angular contact ball bearing, while the outer ring undergoes lateral displacement at the groove center position.

2.1.2 Double half inner ring angular contact ball bearing The outer ring of the double half inner ring angular contact ball bearing is consistent with the outer ring of the same size inner ring slope angular contact ball bearing, while the inner ring undergoes lateral displacement at the groove center position.

2.2 Four point angular contact ball bearings

Four point angular contact ball bearings generally have an integral outer ring and a double half inner ring. The outer ring is a whole, and the channel is divided into two parts, sometimes with a retraction groove, and sometimes without; The inner ring is a double half inner ring. Its structural form is shown in Figure 2.

Figure 1 Three point angular contact ball bearing

Figure 2 Four point angular contact ball bearing

3. Internal geometric relationship of bearings

3.1 Double half outer ring three-point angular contact ball bearing

3.1.1 Radial clearance and contact angle

3.1.2 Axial clearance and contact angle

3.1.3 Radial and axial clearance

3.2 Double half inner ring three-point angular contact ball bearing

3.2.1 Radial clearance and contact angle

3.2.2 Axial clearance and contact angle

3.2.3 Radial and axial clearance

3.3 Four point angular contact ball bearings

The geometric relationship of four point angular contact ball bearings is relatively complex, and it is necessary to consider the impact of changes in the position of the inner and outer ring groove centers on the clearance.

3.3.1 Radial clearance and contact angle

After simplification, it can be concluded that:

3.3.2 Axial clearance and contact angle

3.3.3 Radial clearance and axial clearance

4. Comparative analysis

4.1 Three point contact

Parameters of a certain type of double half inner ring angular contact ball bearing: steel ball diameter 22.225 mm, outer groove curvature radius 11.45^+0.06 mm, inner groove curvature radius 11.55+^0.06mm, gasket angle 25 °, center horizontal coordinate of inner groove curvature radius 0.185+^0.015mm, radial clearance 0.229mm~0.274mm.

(1) According to the previous formula, the contact angle is 33.2°~41.5°, axial clearance: 0.537mm~0.698mm.

(2) According to the improved formula, the contact angle is calculated as 34.6°~40.0°, axial clearance: 0.602mm~0.848mm.

4.2 Four point contact

Parameters of a certain type of double half inner ring angular contact ball bearing: steel ball diameter 24.606mm, outer groove radius 13.04+^0.05mm, inner groove radius 12.795+^0.05mm, gasket angle 26°, inner groove curvature radius center horizontal coordinate 0.208+^0.021mm, outer groove curvature radius center horizontal coordinate 0.3115+^0.021 radial clearance 0.15mm~0.18mm.

(1) According to the previous formula, the contact angle is 25.3 °~34.1 °, and the axial clearance is 0.182mm~0.457mm.

(2) According to the improved formula, the contact angle is 30.8 °~34.3 °, and the axial clearance is 0.769mm~1.520mm. From the above calculation results, it can be seen that there are significant differences in the contact angle and clearance conversion before and after the improvement, mainly due to the fact that previous calculation formulas did not consider the changes in clearance caused by offset displacement.

5. Conclusion

Three point and four point angular contact ball bearings are special forms of ordinary angular contact ball bearings. There are basic common principles. 3、 The measured clearance of four point angular contact ball bearings is different from that of ordinary angular contact ball bearings. The measured clearance of ordinary angular contact is its calculated clearance, while the measured clearance of three and four point angular contact ball bearings is not its calculated clearance. Calculating clearance requires calculation. The improved contact angle and clearance conversion formula is more in line with the internal geometric relationship of the bearing, and provides more reasonable guidance for production services than previous calculation formulas.

More about KYOCM Slewing Bearing ：

Rotary bearings consist of an inner ring and an outer ring, one of which usually contains a gear. Together with the connecting holes in the two rings, they enable optimized power transmission through simple and fast connections between adjacent machine parts. Bearing raceways are designed with rolling elements, cages or gaskets to accommodate loads acting individually or in combination in any direction.

Features and advantages:

High carrying capacity

High stiffness for rigid bearing applications

Low friction

Long service life

Surface protection and corrosion resistance

Integrate other features including:

Driving mechanism

Control device

Lubrication system

Monitoring system

Sealed cassette tape

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