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Influence of Radial Clearance on Radial Stiffness of Cylindrical Roller Bearings

Influence of Radial Clearance on Radial Stiffness of Cylindrical Roller Bearings

Abstract: The relationship between relative radial displacement of inner and outer rings of bearings and radial clear-
ance is deduced based on Palmgren formula. The calculation method of radial stiffness of cylindrical roller bearings un-
der different radial clearance is obtained,and the influence of radial clearance on radial stiffness of bearings is ana-
lyzed. The results show that with decreasing radial clearance in a certain range,the load distribution of rollers is more
uniform,the number of loaded rollers becomes more,the maximum load of rollers is reduced;the relative radial displace-
ment of inner and outer rings caused by radial load is decreased,and the radial stiffness of bearings is increased.

Cylindrical roller bearings in the work of the main bearing radial load, when the performance index is lower than the work requirements, bearing failure or failure, resulting in mechanical equipment stop, abnormal work. Especially as the cylindrical roller bearing of the RV reducer, the radial stiffness directly affects the transmission accuracy of the RV reducer, so it is necessary to study the factors influencing the radial stiffness of the cylindrical roller bearing. The radial clearance is an important performance index of the bearing, which has important influence on the bearing's life, roller load distribution and other performance. When the radial clearance is too large, the roller load distribution is not equal due to the small number of bearing rollers, which can reduce the bearing's running accuracy, bearing capacity and stability, causing bearing failure or failure.

In view of this, the relationship between the relative radial displacement and the radial clearance of the cylindrical roller bearings under specific radial loads is deduced by the Palmgren formula, and the influence of radial clearance on the radial stiffness of the bearing is further analyzed.

1 relation between the contact load and displacement of roller and raceway

The elasticity of rolling bearings is approaching

In the formula: Q is the roller load; L is the effective length of the roller; Ν1,ν
2 Poisson's ratio of roller and ferrule material respectively; E 1, E 2 is the elastic modulus of the rollers and ferrule materials, respectively.
However, the (1) formula is only suitable for rolling bearings with a raceway diameter of ~70 mm for the elasticity of the approaching amount δ calculation. Considering the roller and raceway diameter and the smoothness of curvature, the (1) Type correction

In the formula: D W is the diameter of the roller; D R for Raceway diameter; "+" on behalf of the Inner Raceway, "-" on behalf of the outer Raceway.
When the rollers are in contact with the inner and outer raceways at the same time, the elastic approaching of the inner and outer raceway contacts is obtained by the (2) type respectively.

The total normal displacement of the rollers in contact with the inner and outer raceways is

The relation between the relative radial displacement of bearing inner ring and radial clearance is deduced by Palmgren formula, and the calculation method of radial stiffness of cylindrical roller bearing is obtained.
Radial clearance has a great influence on the radial stiffness of the bearing.
When the bearing bearing conditions are the same, with the radial clearance decreasing, the bearing load distribution angle increases, the bearing roller number increases, the maximum contact load of the rollers decreases,
The relative radial displacement of the inner and outer ring decreases.
Measures for the proper preload of cylindrical roller bearings: the micro-interference fit between the inner ring and the shaft can improve the radial stiffness of the bearing.

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