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6. Life and Load Rating

Bearing Life

• The raceway and raceway surface of the inner/outer rings of the bearing continuously receive a repeated load, when rotated with a load applied. This causes material fatigue that results in a damage called flaking. The total rotational frequency to this point is called rolling fatigue life.
• The life of a bearing is based on a statistical value because there is a considerably large variation even though the same dimensions, material and heat treatment processing method are used to operate the bearing under the same conditions. Therefore, generally, the total rotating speed in which 90% of the bearings can be operated without the occurrence of flaking is called the basic rating life.

Basic Dynamic Load Rating

The basic dynamic load rating is the constant load applied in a direction under which the basic rating life of the bearing reaches 1 million revolutions. This is the centric radial load in radial bearings, and the centric axial load in thrust bearings. Also, for duplex bearings that consist of two single-row radial bearings with adjusted standouts, the basic dynamic load rating is converted by about 1.62 times that of a single-row bearing.

Life Equation

The relationships between the basic dynamic load rating, dynamic equivalent load, and the basic rating life of ball bearings are as follows.

How to select basic rating life L_10h

Selection method of bearings in consideration of life for the operating conditions

When a large dynamic equivalent load P close to the basic dynamic load rating C is applied to a bearing, the bearing life is reduced in a very short time. However, when a bearing rotates at a high speed with high acceleration, or beyond the limiting speed x 0.5, it is necessary to set to P/C ≥ 1% in general, in order to prevent the occurrence of damage due to the sliding of the balls and the raceway surface.
A suitable bearing type must be selected based on C_min = P×(L_10h×n/16667)^1/3 by clarifying the operating conditions of the machine (dynamic equivalent load P, rotating speed n) and the required lifetime L_10h in advance.

As shown in the following table and graph, generally, it is necessary to consider selection of a bearing using [dynamic equivalent load] / [dynamic load rating] = P/C = [normal load ratio: 6 to 12%] as a guide.

When P/C and n are known, rating life: L_10h can be obtained easily using the following graph.

If P and n are known based on L_10h= 50,000 hours as a reference, the minimum basic dynamic load rating: C_min can be obtained easily using the following graph. It is recommended to select a bearing type with a basic dynamic load rating: C higher than this C_min. However, rotating speed: n must not exceed the limiting speed of the selected bearing type.

Modification of Life Equation

Generally, the life can be calculated by the above equation, however, it is insufficient when a high reliability of 90% or more is required depending on the application. Since the fatigue life of bearings has been prolonged due to improved bearing steel in recent years, and the relationship between the lubricant and the bearing life has also been clarified, the following modified life equation is used in ISO281.

(1) Life modification factor for reliability a₁

When calculating the life with a reliability of 90% or more, modify the value according to the following factor a₁.

Values of life modification factor for reliability a₁

(2) Life modification factor for bearing characteristics a₂

When the fatigue life is prolonged due to improvements in the manufacturing method and heat treatment condition, etc. of the bearing material, modify the value according to the life modification factor for bearing characteristics a₂. In the case of the standard bearing material of our company, modify the value to a₂=1.

(3) Life modification factor for operating conditions a₃

In the operating conditions of a bearing, the modification factors which originate in the conditions of the lubrication, temperature and load, etc. is called “the life modification factor for operating conditions a₃. In the case of favorable lubrication conditions, where there is no metal contact due to a lubricating film applied between the raceway surface and balls, and dynamic viscosity of lubricant is above 13 mm²/s（13cSt), then a₃=1 is used for the effect of the lubrication on the life.
When the operating conditions are not favorable (dmn ≦ 10,000, deterioration of lubricant, large inclination of inner/outer rings), a₃＜1 is used. If the operating temperature exceeds 120 ºC, the life becomes shorter because the dimensional change becomes larger, and also the hardness deteriorates. The operating temperature and the life modification factor in such a case are based on the following table.

Remarks: dmn is the rolling element pitch circle diameter (mm) x rotating speed (min^-1).

* The dimensional change of a bearing with normal heat treatment applied becomes larger at temperatures exceeding 120 ºC. Although a reduction in the basic dynamic load rating due to the deterioration of the hardness is unavoidable, the dimensional change can be suppressed even at high temperatures by performing a dimensional stabilization treatment.

Dimensional Stabilization Treatment

System Life of Multiple Bearings

The basic rating life of each bearing has a probability of 90%. The system life of multiple bearings becomes even shorter than the shortest basic rating life of each bearing. Considering all the bearings being used as one bearing system, the system life can be obtained by the following equation.

L=rating life of entire bearing system
L₁、L₂、L₃・・・L_n=rating life of each bearing

Basic Static Load Rating

When a certain static load is applied to a bearing, a local permanent deformation of an indent shape occurs in the contact portion between the balls and raceway surface. This permanent deformation causes a poor rotating condition that also increases noise and vibrations, therefore, the basic static load rating C_o is defined as follows as a reference of the acceptable static load. The basic static load rating of a ball bearing is the static load where the calculated contact stress becomes 4200 MPa（429kgf/mm²） in the contact portion between the balls and raceway, and the sum of the permanent deformation produced between the balls and raceway becomes about 1/10000 of the ball diameter. The value of the basic static load rating C_o is expressed as C_or for radial bearings and C_oa for thrust bearings. In addition, the C_o of duplex bearings that consist of two single-row radial bearings with adjusted standouts is converted by twice that of a single-row bearing.

Calculation of Bearing Load

The loads applied to the bearings include drive loads, such as belts and gears, loads that occur in a machine during operation, and the self-weight of equipment supported by bearings. When a bearing is used, it is difficult to obtain the entire load accurately as the bearing load, because different levels of vibration and impact loads are applied. Normally, the load is obtained by multiplying the various factors based on the experience acquired conventionally with the calculated load value obtained theoretically.

(1) Load factor, gear factor and belt factor

The radial load and axial load applied to a bearing can be obtained by a theoretical calculation. However, the actually applied load becomes larger than the calculated value due to the vibration and impact of the equipment, therefore the load is obtained by multiplying the factors as follows.

Load factor f_w

Gear factor f_g

Belt factor f_b

(2) Load distribution on bearings

(3) Average load of fluctuating load

When the scale and direction of the load applied to a bearing fluctuates, it is necessary to obtain the average load so that it becomes equal to the bearing life under its loading condition.

Dynamic Equivalent Load

Although the load condition is not constant when a bearing is actually used, there are many cases where the load is a combination of the radial load and axial load. In such a case, it is necessary to calculate the load so that the direction and scale become constant. The calculated virtual load is called dynamic equivalent load P, and is expressed as P_r for radial bearings and P_a for thrust bearings.

(1) Radial bearings

Bearing Types		Axial Load Ratio	Single-Row Bearings				Double-Row Bearings				ｅ
			X	Y	X	Y	X	Y	X	Y
Deep groove ball bearings			1	0	0.56		1	0	0.56
		0.172 0.345 0.689 1.03 1.38 2.07 3.45 5.17 6.89				2.3 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1				2.3 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1	0.19 0.22 0.26 0.28 0.3 0.34 0.38 0.42 0.44
			1	0	0.56		1		0.78		Single-row bearings	Double-row bearings
Angular contact ball bearings	α=5°	0.172 0.345 0.689 1.03 1.38 2.07 3.45 5.17 6.89				2.3 1.99 1.71 1.55 1.45 1.31 1.15 1.04 1		2.78 2.4 2.07 1.87 1.75 1.58 1.39 1.26 1.21		3.74 3.23 2.78 2.52 2.36 2.13 1.87 1.69 1.63	0.19 0.22 0.26 0.28 0.3 0.34 0.38 0.42 0.44	0.23 0.26 0.3 0.34 0.36 0.4 0.45 0.5 0.52
	α=10°	0.172 0.345 0.689 1.03 1.38 2.07 3.45 5.17 6.89	1	0	0.46	1.88 1.71 1.52 1.41 1.34 1.23 1.1 1.01 1	1	2.18 1.98 1.76 1.63 1.55 1.42 1.27 1.17 1.16	0.75	3.06 2.78 2.47 2.29 2.18 2 1.79 1.64 1.63	0.29 0.32 0.36 0.38 0.4 0.44 0.49 0.54 0.54
	α=15°	0.172 0.345 0.689 1.03 1.38 2.07 3.45 5.17 6.89	1	0	0.44	1.47 1.4 1.3 1.23 1.19 1.12 1.02 1 1	1	1.65 1.57 1.46 1.38 1.34 1.26 1.14 1.12 1.12	0.72	2.39 2.28 2.11 2 1.93 1.82 1.66 1.63 1.63	0.38 0.4 0.43 0.46 0.47 0.5 0.55 0.56 0.56
	α=20° α=25° α=30° α=35° α=40° α=45°	― ― ― ― ― ―	1	0	0.43 0.41 0.39 0.37 0.35 0.33	1 0.87 0.76 0.66 0.57 0.5	1	1.09 0.92 0.78 0.66 0.55 0.47	0.7 0.67 0.63 0.6 0.57 0.54	1.63 1.41 1.24 1.07 0.93 0.81	0.57 0.68 0.8 0.95 1.14 1.34

Dynamic equivalent radial load P_r of a radial bearing is expressed by the following equation.

(2) Thrust bearings

Dynamic equivalent axial load P_a of a thrust bearing is expressed by the following equation.

* Contact angle α of our thrust bearing is 90º.

Static Equivalent Load

The virtual load of the combination of the radial load and axial load that is received when the bearing is static (including very low speed rotations) which is calculated to ensure that the direction and scale become constant is called static equivalent load P₀ and is expressed as P_0r for radial bearings and P_0a for thrust bearings.

The higher value of static equivalent radial load P_0r of a radial bearing is used among the values calculated by the following two equations.

Static equivalent axial load P_0a of a thrust bearing is expressed by the following equation.

* Contact angle α of our thrust bearing is 90º.

Safety Factor

The acceptable static equivalent load of a bearing is determined by the basic static load rating, however, the usage limitations of a bearing differ by the operating conditions and required performance. Therefore, in order to examine the safety integrity, the value can be calculated by the following equation using an experiential safety factor.

Applied Calculation for Life and Load

Calculation Example 1

Assuming that the bearing bore diameter ≦ 10mm, outside diameter ≦ 20mm, and width ≦ 5mm are for the space to assemble a bearing, and the load condition is F_r (radial load) = 120 N and rotating speed n = 1200 min^-1, select the type of single-row deep groove ball bearing with a life factor f_h≧4.

Calculation Example 2

Select the bearing that has the smallest bore diameter, when selection conditions for the bearing are as follows: Material: SUJ2, Deep groove ball bearing: 60 series, Required life time: 10,000 hours or more, Radial load F_r=150N, Axial load F_a=20N, Rotating speed n = 5000 min^-1.

Calculation Example 3

What is the average radial load when the following variable radial load is applied?

Calculation Example 4

What is the system life when the following radial rotational load and radial static load are applied to 6000HZZ, 6202HZZ and 6304HZZ?

Calculation Example 5

What is the lifetime L_10h when radial load 150 N is applied to 688ZZ, and oscillates 1,000 time per minute at an oscillating angle of 30º?

Calculation Example 6

What is the life time L_10h, L_1h where a stainless steel deep groove ball bearing 6706H 2RU is continuously operated at Radial load F_r = 100 N, Axial load F_a = 40 N, Speed n = 1800 min^-1? Also, what is the grease life when 6706H 2RU is continuously operated at a bearing temperature of 80 ° C under the same conditions?