Precison Ball Bearing - Selecting a bearing (load rating and rating life)

In general, if bearings are made of high quality steel with high level production skills, the load rating and rating life can be calculated based on the specification defined in JIS and ISO.

Life of a ball bearing

The required life of a ball bearing depends on the application and requirements of the equipment. Because there are many different applications for the equipment, definitions of life also vary. Therefore, life needs to be defined based on the application and requirements.
Some different types of life include rating life, noise life, lubricant life, and performance life.
When noise starts getting louder than that of the setup level, it is the end of noise life. When lubricants lose their function due to degradation, it is the end of lubricant life. When RPM and runout go beyond their setup points, it is the end of performance life.
In this section, the rating life of single row deep groove ball bearing, which is specified in JIS B 1518, is explained. Rating life is a predicted life calculated based on the basic dynamic radial load rating.

Basic rating life (L10)

It is defined as the life associated with 90 percent reliability.
The rating life of a group of apparently identical ball bearings is the life in millions of revolutions, or number of hours, that 90 percent of the group will complete or exceed.

If the RPM is constant, the life is usually expressed in hours. The relationship between basic rating life and life hours is as follows:

Basic dynamic radial load rating (Cr)

It is defined as a calculated, constant radial load which a group of identical bearings can theoretically endure for a rating life of one million revolutions. The calculation is explained in JIS B 1518, and the values are in the dimension tables.

Dynamic equivalent radial load (Pr)

It is defined as "the equivalent radial load to the bearing which will result in the same life as the actual load and rotation conditions". Combined radial and axial loads are converted to equivalent radial loads with the formula and table below.

Pr = XFr + YFa

X, Y	:	These values can be found in the table below.
Fr	:	Radial Load (N)
Fa	:	Axial Load (N)

The ratio of
axial load

Fa
ZDw²

Fa	≦	e
Fr	≦	e

Fa	>	e
Fr	>	e

(N)

0.172
0.345
0.689
1.03
1.38
2.07
3.45
5.17
6.89

0.19
0.22
0.26
0.28
0.30
0.34
0.38
0.42
0.44

0.56

2.30
1.99
1.71
1.55
1.45
1.31
1.15
1.04
1.00

Z	:	Number of balls
Dw	:	Diameter of a ball (mm)
* X,Y,e values, which are not in the above table, can be determined by linear interpolation. * The variables of row are excluded from the formula for calculating the axial load ratio, which is specified in JIS, because the formula is for a single row bearing.

Calculations

Under the conditions below, the L10 life of R-830ZZ is calculated.

Basic dynamic radial load rating (Cr) : 553N
Ball diameter (Dw) : 1.5875mm
Number of balls (Z) : 6 pcs
RPM (n) : 3600 min^-1
Radial load (Fr) : 6N
Axial load (Fa) : 8N

1. Calculate the ratio of axial load

Fa	=	8	=	0.529
ZDw²		6×(1.5875)²

2. Calculate e value relative to the ratio of axial load

e	=	0.22	+	(0.529 - 0.345)	×	(0.26 - 0.22)	=	0.24
				(0.689 - 0.345)

3. Calculate the ratio of radial and axial loads

Fa	=	8	=	1.33
Fr		6

4. Compare the load ratio and e value

Fa	=	1.33, e	=	0.24 ∴	Fa	>	e
Fr					Fr

5. Determine X and Y

X	=	0.56
Y	=	1.99	-	(0.529 - 0.345)	(1.99 - 1.71)	=	1.84
				(0.689 - 0.345)

6. Calculate dynamic equivalent load

Pr = 0.56 × 6 + 1.84 × 8 = 18.08

7. Calculate life hours

L10	=	10⁶	×	553	³	=	132473h
		60 × 3600		18.08
Basic rating life : 132472hrs

The basic static radial load rating and static equivalent radial load of a ball bearing are specified in JIS B 1519, "a calculation method of static load rating of a ball bearing"

Basic static radial load rating (Cor)

It is defined as "The basic static load rating is the amount of static radial load that equates to a stress level of 4200MPa on the most heavily stressed ball/raceway contact area (the center)." A total permanent deformation (ball and raceway) caused by the contact stress is about 0.0001 times the ball diameter. The basic static radial load ratings can be found in the dimension tables.

Static equivalent radial load (Por)

The static equivalent radial load is a static radial load that would cause the same amount of contact stress generated on the most heavily stressed ball/raceway contact area (the center) under the actual load conditions.

Take the larger value calculated with the formula below.

Por = XoFr + YoFa
Por = Fr

Xo,Yo : JIS B 1519

Coefficient of deep groove ball bearing Xo = 0.6
Yo = 0.5

Fr : Radial Load (N)
Fa : Axial Load (N)

Selecting a bearing

6. load rating and rating life