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Radial internal clearance =δ Axial internal clearance =δ1+δ2
Fig. 9.1 Bearing Internal Clearance
Bearing Internal Clearance
As shown in Fig. 9.1, prior to mounting the bearing on the shaft and housing, when either the inner or outer ring is in a fixed position the amount of transfer when the counterpart is moved in the radial or axial direction is called radial internal clearance or axial internal clearance. This internal clearance is standardized by ISO 5753 (JIS B 1520). Radial internal clearance for deep groove ball bearings is given as an example in Table 9.1. For details, see "A54 - 65 of the "NTN Ball and Roller Bearings catalog". Measurement load is of course applied when measuring clearance. Measurement load and correction values have been established as shown in Table 9.2 due to elastic deformation caused by measurement load, particularly for ball bearings.
 
 
Table 9.1 Radial Internal Clearance for Deep Groove Ball Bearings                                     Click for Table
 
Table 9.2 Radial Internal Clearance Correction Values for Measurement Load                  Click for Table
 
Internal Clearance Selection
During operation, clearance largely affects bearing performance such as bearing life, heat, vibration and sound. It is therefore necessary to select the clearance that matches operating conditions. If the clearance is theoretically slightly negative, optimal bearing life values are given, but if the clearance is further to the negative side, life decreases radically. Operating conditions are likely to fluctuate during operation due to a variety of factors. Generally speaking, you should therefore select initial bearing internal clearance so that operating clearance is slightly larger than 0. Internal clearance during operation is calculated by the following equation:

δeff=δo-(δf+δt)⋯⋯⋯⋯⋯⋯(9.1)

Where:
δeff : Operating clearance (mm)
δo : Bearing initial internal clearance (mm)
δf : Internal clearance reduction due to interference (mm)
δt : Internal clearance reduction due to the difference in temperature of the inner and outer rings (mm)
 
1. Internal clearance reduction due to interference
 
If the inner and outer rings are mounted on the shaft or housing with interference, the inner ring expands, the outer ring contracts, and internal clearance decreases by that amount. The amount of reduction differs according to the type of bearing, shape of shaft or housing, dimensions and material, but it is approximately 70 - 90% of effective interference.

δf= (0.70~0.90) Δeff ⋯⋯⋯⋯⋯⋯(9.2)

δf : Internal clearance reduction due to interference (mm)

Δeff : Effective interference (mm)

To calculate more precisely, you can take material, shape and dimensional shape of each part into consideration. Dimension tolerance is supposed to be normal distribution, and is generally calculated by 3σ.
 
2. Internal clearance reduction due to the difference in temperature of the inner and outer rings
  As for bearing temperature during operation, temperature of the outer ring is generally 5 - 10°C lower than that of the inner ring or rolling elements. When heat radiation of the housing and shaft are connected to the heat source, temperature difference further increases. Internal clearance decreases by precisely the amount of the inner and outer rings expand due to the difference in temperature.

δt=α・ΔT・Do ⋯⋯⋯⋯⋯⋯⋯⋯(9.3)

δt : Internal clearance reduction due to the difference in temperature of the inner and outer rings

α : Coefficient of linear expansion for bearing materials 12.5×10-6/°C

ΔT : Difference in temperature of the inner and outer rings (°C)

Do : Raceway diameter of the outer ring (mm) Raceway diameter of outer ring is approximated by the following equation. For ball bearings and self-aligning roller bearings

Do=0.2 (d+4D) ………………………(9.4)

For ball bearings and self-aligning roller bearings

Do=0.25 (d+3D) ……………………(9.5)

d : Bearing bore diameter
D : Bearing outside diameter
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