Abstract: It is difficult to select the half cone angle of a fully loaded cross tapered roller turntable bearing. This article simplifies the tedious calculation process of selecting the half cone angle of the roller by referring to a table, greatly improving the design efficiency.
Keywords: large bearings; Conical roller bearings; Rotary table bearings; Roller; Half cone angle; select
Symbol Explanation
d - Inner diameter of bearing inner ring
D - Outer diameter of bearing outer ring
T - Total height of bearings
C - Height of outer ring of bearing
B - Inner ring height of bearing
h - Distance from the reference end face of the inner ring to the non reference end face of the outer ring
φ - Half cone angle of roller
Dw - Large end diameter of tapered roller
Dwp - Roller group pitch diameter
ε - Total clearance of the raceway circumference when fully loaded with rollers
Z - Number of rollers fully loaded
Extra large rotary bearings are special structural bearings that can simultaneously withstand large axial loads, radial loads, overturning moments, and other comprehensive loads. Generally, turntable bearings are equipped with mounting holes, lubricating oil holes, and sealing devices. Compared with crossed cylindrical roller turntable bearings, crossed tapered roller turntable bearings have higher static load capacity and are widely used in large slewing supports such as lifting and transportation machinery, mining machinery, construction machinery, and port machinery due to their pre interference energy, which gives the bearings greater support stiffness and higher rotational accuracy. The fully loaded cross tapered roller turntable bearing can accommodate a large number of rollers, providing greater static load capacity and support stiffness, and is suitable for use in low-speed and heavy-duty conditions. It is a high value-added product. However, when designing a fully loaded cross tapered roller turntable bearing, it is necessary to ensure that the total clearance ε of the raceway circumference is within a reasonable range after selecting a reasonable roller diameter. However, ε is greatly affected by the half cone angle φ of the roller, and their functional relationship is complex, which makes the selection difficult. Often, satisfactory results can only be found after multiple calculations. This article provides a fast method for selecting the half cone angle of a roller by analyzing the relationship between various parameters.
1. Structural characteristics and calculation process
1.1 Structural Features
The structure of the fully loaded cross tapered roller turntable bearing is shown in Figure 1, consisting of an outer ring, an inner ring, rollers, sealing rings, and connecting screws. The outer or inner ring is a two-part structure, which is connected by connecting screws after assembly. Adjacent tapered rollers are arranged in a cross pattern in the raceway, with all spherical end faces facing outward. The extension lines of the two inner and outer raceways intersect with the centerline of the rollers, so that half of the rollers bear axial loads in one direction and the other half bear axial loads in the opposite direction. This type of bearing can form negative clearance under a certain preload, improving support stiffness and rotational accuracy.
Figure 1
For the convenience of design and manufacturing, the angle between the two outer raceways is usually taken as 90 °, and it forms a 45 ° angle with the radial direction. The angle between the two inner raceways is 90 °+4 °, and the radial angle is 45 °+2 °. O2 is the center of the roller pitch circle, OO2 is the radius of the roller group pitch circle, Dwp=2 OO2, and the intersection point A of the extension lines of the two outer raceways is on OO2. O1 is the intersection point between the extension lines of the inner and outer raceways and the centerline of the bearing rotation, and OO1 is the centerline of the bearing rotation. Make O2 M ⊥ O1 O2 and intersect with O1A at point M, where N is the intersection point of the roller centerline and the roller end face.
1.2 Calculation process
Calculate the number of rollers using the KDw roller diameter coefficient in the formula
Take the maximum even number less than π/ω for Z.
Calculate the theoretical total clearance of the raceway circumference when fully loaded with rollers
In the formula, the total clearance coefficient of the fully loaded roller is λ
1.3 Constraints
Roller big end diameter Dw
Total clearance of the raceway circumference ε
The diameter Dw of the large end of the roller can be adjusted appropriately according to the installation hole positions of the inner and outer rings, and equation (8) is a necessary condition that must be met.
From equations (1) and (4), it can be seen that the number of rollers Z is a function of the half cone angle of the rollers, and is independent of the pitch circle diameter Dwp of the roller group.
According to equations (2) and (3), the large end diameter of the roller is a function of Dwp and φ. Although Dwp can be adjusted appropriately according to the installation hole positions of the inner and outer rings, its adjustment range is very small compared to its own value, generally not greater than 0 01 Dwp , The impact on the roller diameter is very small, and it is usually not adjusted by adjusting Dwp to adjust the roller diameter. Therefore, when the Dwp value is selected, the diameter of the large end of the roller depends on φ.
From equations (1), (4), and (6), it can be seen that λ is a function of φ.
Based on the above, when Dwp and φ are selected, Dw, Z, and λ can be determined. Among them, Z and λ are functions of φ, independent of the diameter Dwp of the roller group pitch circle.
2. Formulation of Tables
The value of φ that satisfies both equations (7) and (8) is not unique, but the calculation formula is complex and difficult to find. Through design practice, commonly used values of φ are listed in Table 1 and selected by referring to the table during design.
Table 1
The selection range of the diameter value is from 0 ° 36 ′ 15 ″ to 1 ° 13 ′, and the diameter value beyond this range is basically not used in the actual design process. The K value is the value of KDw rounded to three decimal places for the convenience of table lookup. The steps for using Table 1 are as follows: (1) Determine the diameter Dwp of the roller group pitch circle based on the external dimensions and structural characteristics of the bearing, determine the range of values for the diameter Dw of the large end of the roller, and then take the middle value of Dw within the range as the initial value. (2) By looking up the table according to the value of K, we can obtain the corresponding number of rollers Z, track clearance coefficient λ, and roller diameter coefficient KDw for the corresponding value of φ.
3. Calculation examples
The external dimensions of a certain model of fully loaded cross tapered roller turntable bearing are known to be as follows:
(1) Dwp = 2515 mm,38 ≤Dw ≤43 mm, Dw = 40.5 mm.
4. Conclusion
The tedious calculation process of selecting the half cone angle of the roller is simplified by referring to a table, greatly improving the design efficiency. Determine the required value of φ as several finite values with appropriate intervals. After analysis, selecting two adjacent parameters, the difference in bearing capacity is minimal. And the table has a considerable range of applicability, and in the actual design process, the commonly used value of φ is even less, which is conducive to achieving the serialization and standardization of roller parameters.
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