Basic Dynamic Load Rating and Rating Life
The principal requirements of rolling bearings are :
High load capabilities
Smooth and quiet rotation
High rigidity
Low friction
High accuracy
Reliability
The reliability or durability requirement sets the time frame over which all other requirements are to be maintained. The reliability requirement (life in the broad sense) includes grease and acoustic life, as well as fatigue life. Reliability is reduced by various types of damage and degradation.
Improper handling, mounting, lubrication, and fits are the major causes of problems leading to lower-than-calculated bearing life. Regardless of how well they are maintained or mounted or handled, dynamic bearings will eventually fail from rolling fatigue generated by the repetitive stress of bearing load.
The service life of a bearing can be examined from two perspectives: 1)If, from inspection, a trace of fatigue becomes noticeable, the bearing should be deemed not suitable for further use; or 2) length of bearing life in hours or revolutions can be predefined as a limit beyond which the bearing is automatically replaced.
Since calculated fatigue life will vary with the size and type of bearings used under identical load conditions, great care must be taken in the analysis of the load conditions and the final choice of bearings to satisfy the application requirements. Fatigue lives of individual bearing are dispersed. When a group of identical bearings operate under the same conditions, the statistical
phenomenon of dispersion will appear. Use of average life is not an adequate criterion for selecting rolling contact bearings. Instead, it is more appropriate to consider a limit (hours or numbers of revolutions) which a large percentage of the operating bearings can attain. Accordingly, the rating life and basic dynamic load rating Cr or Ca are defined using the following definition:
? Basic rating life is defined as the total number of revolutions (or total operating hours at some given constant speed) that 90% of a
group of identical bearings operated individually under equal conditions can complete without suffering material damage from rolling fatigue.
? Basic dynamic load rating (Cr or Ca) is defined as a bearing load of constant direction and size that ends the bearing life after a million revolutions.
Constant-direction radial or thrust loads are used as the basis of the ratings.The rating life of bearings is calculated by formula 1 & formula 2
L_{10}=(C/P)^{3} ( Formula 1 )
If the speed is constant, it is often to calculate the life e expressed in operating hours.
L_{10h}=L_{10}¡¤10^{6}/(60¡¤n)=(C/P)^{3}¡¤10^{6}/(60¡¤n) £¨Formula 2£©
Where:
L_{10}: basic rating life of ball bearings with 90 % reliability [106 revolutions]
L_{10h}: Basic rating life in operating hours
C : Basic dynamic load rating (N)
P : Bearing load (dynamic equivalent load) (N)
n : Rotating speed (rpm)
The dynamic equivalent load, with its direction and magnitude to the bearing, is defined as the load which is able to achieve the same life as the actual bearing load and rotation conditions. It is a radial load for radial bearings, or an axial load for axial bearings. The dynamic equivalent load, which as a theoretical parameter can be found by applying the values listed in the Tables 1 and 2 to the Formula 3 functions as a replacement for the actual axial and radial bearing load.
P = X¡¤Fr + Y¡¤Fa ( Formula 3 )
ThFr |
actual radial bearing load [N] |
Fa |
actual axial bearing load [N] |
X |
radial factor taken from Table 1 and 2 depending on the ratio Fa / Fr |
Y |
axial factor taken from Table 1 and 2 depending on the ratio Fa / Fr |
e |
limit value for the ratio Fa / Fr for selecting the factors X and Y |
In the following two Tables 1 and 2 the calculation factors X and Y for calculation of the dynamic equivalent load are summarized for single and double row deep groove ball bearings as well as angular contact ball bearings.
The calculation factors depend on the ratio Fa / Fr and the operational radial clearance after assembling the bearing. The values in the following tables are based on common fits for shaft and housing.
Table 1: Calculation factors X and Y for single and double row deep groove ball bearings
Bearing Type | Relative Axial Load(N) | Single Row Radial Ball Bearing | Double Row Radial Ball Bearing | e | ||||||
Fa/Fr¡Üe | Fa/Fr£¾e | Fa/Fr¡Üe | Fa/Fr£¾e | |||||||
h_{0}*Fa/C_{0} | X | Y | X | Y | X | Y | X | Y | ||
Radial Ball Bearing (CN) | 0.172 | 1 | 0 | 0.56 | 2.30 | 1 | 0 | 0.56 | 2.30 | 0.19 |
0.345 | 1.99 | 1.99 | 0.22 | |||||||
0.689 | 1.71 | 1.71 | 0.26 | |||||||
1.030 | 1.55 | 1.55 | 0.28 | |||||||
1.380 | 1.45 | 1.45 | 0.30 | |||||||
2.070 | 1.31 | 1.31 | 0.34 | |||||||
3.450 | 1.15 | 1.15 | 0.38 | |||||||
5.170 | 1.04 | 1.04 | 0.42 | |||||||
6.890 | 1.00 | 1.00 | 0.44 | |||||||
Radial Ball Bearing (C3) | 0.172 | 1 | 0 | 0.46 | 1.88 | 1 | 2.18 | 0.75 | 3.06 | 0.29 |
0.345 | 1.71 | 1.96 | 2.78 | 0.32 | ||||||
0.689 | 1.52 | 1.76 | 2.47 | 0.36 | ||||||
1.030 | 1.41 | 1.63 | 2.29 | 0.38 | ||||||
1.380 | 1.34 | 1.55 | 2.18 | 0.40 | ||||||
2.070 | 1.23 | 1.42 | 2.00 | 0.44 | ||||||
3.450 | 1.10 | 1.27 | 1.79 | 0.49 | ||||||
5.170 | 1.01 | 1.17 | 1.64 | 0.54 | ||||||
6.890 | 1.00 | 1.16 | 1.63 | 0.54 | ||||||
Radial Ball Bearing (C4) | 0.172 | 1 | 0 | 0.44 | 1.47 | 1 | 1.65 | 0.72 | 2.39 | 0.38 |
0.345 | 1.40 | 1.57 | 2.28 | 0.40 | ||||||
0.689 | 1.30 | 1.46 | 2.11 | 0.43 | ||||||
1.030 | 1.23 | 1.38 | 2.00 | 0.46 | ||||||
1.380 | 1.19 | 1.34 | 1.93 | 0.47 | ||||||
2.070 | 1.12 | 1.28 | 1.82 | 0.50 | ||||||
3.450 | 1.02 | 1.14 | 1.66 | 0.55 | ||||||
5.170 | 1.00 | 1.12 | 1.63 | 0.56 | ||||||
6.890 | 1.00 | 1.12 | 1.63 | 0.56 |
* Relevant: The bearing operational clearance in the mounted condition.
Table 2: Calculation factors X and Y for angular contact ball bearings
Bearing Type | Axial Load Rating(N) | Single Row Radial Ball Bearing | Double Row Radial Ball Bearing | e | ||||||
Fa/Fr¡Üe | Fa/Fr£¾e | Fa/Fr¡Üe | Fa/Fr£¾e | |||||||
X | Y | X | Y | X | Y | X | Y | |||
Contact Angle 40¡ã | ¡ª¡ª | 1 | 0 | 0.35 | 0.57 | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | 1.14 |
Contact Angle 25¡ã | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | 1 | 0.92 | 0.67 | 1.41 | 0.68 |
Contact Angle 30¡ã | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | ¡ª¡ª | 1 | 0.78 | 0.63 | 1.24 | 0.8 |
Fa |
axial bearing load [N] |
C_{0} |
basic static load rating [N] (Deep Groove Ball Bearings) |
h_{0} |
relative axial load (Deep Groove Ball Bearings) |