Calculation formula and method of bearing life

1. Basic rating life and basic dynamic load rating

(1) Lifespan

The total number of revolutions before fatigue pitting occurs for the first time in the material of any element of a rolling bearing or the number of hours of operation at a given constant speed.

(2) Basic rating life

For a batch of bearings of the same type, under the same operating conditions, 90% of them can run the total number of revolutions before fatigue pitting or the total number of working hours that can run at a given speed. Its reliability is 90%, denoted by the symbol L10 or Lh10.

(3) Basic dynamic load rating

The basic rated life of the bearing is one million (106) revolutions and the maximum load it can bear is the basic dynamic load rating of the bearing, expressed in Cr.

Under the basic dynamic load rating, the reliability of the bearing can rotate 106 revolutions without pitting failure is 90%.

Pure Radial Load - Radial Bearing Basic Dynamic Load Rating C Pure Axial Loads - Thrust Bearings Refers to the radial component of the load that causes relative radial displacement between the rings - angular contact ball bearings and tapered roller bearings

2. Equivalent dynamic load

Definition: Convert the actual load into an imaginary load with equivalent effect and consistent with the load conditions for determining the basic dynamic load rating. This imaginary load is called the equivalent dynamic load P.

It is understood as: the bearing life under the action of the equivalent dynamic load P is the same as the bearing life under the actual combined load

(1) For bearings that can only bear radial load R (N, NA bearings)

P=R

(2) For bearings that can only withstand axial load A (thrust ball (5) and thrust roller (8))

P=A

(3) Bearings subject to radial load R and axial load A at the same time

P=XR+YA

X—radial load factor, Y—axial load factor, X, Y—see Table 14.13

3. Calculation of axial force of radial angular contact bearing

This type of bearing is subjected to R→ to generate a derived axial force S, so it should be used in pairs and installed symmetrically.

(1) The magnitude and direction of the derived axial force:

a) Formal installation (face to face), the fulcrum span is small, and it is suitable for the transmission parts to be located between the two supports;

b) Reverse installation (back-to-back), the actual support distance becomes larger, which is suitable for the transmission parts at the overhanging end

(2) Determination of the actual axial load A

1) When Fa+S2>S1

The shaft has a tendency to move to the left, so that the bearing 1 is "compressed" and the bearing 2 is "relaxed". The compressed outer ring of the bearing 1 will generate a balance force S on the inner ring and the shaft to prevent it from moving to the left through the rolling elements, so that 

∴The actual axial load of bearing 1 is

Axial force on bearing 2, given by the equilibrium condition of the force

- its own derived axial force

2) When Fa+S2<S1

The shaft has a tendency to move to the right, bearing 2 is "compressed", bearing 1 is "relaxed", and a balance force  is generated on "2", making 

∴The actual axial force of bearing 2 is

The actual axial force on bearing 1 is determined by the balance condition of the force

- inherently derived axial force

Conclusion: - Calculation method of actual axial force A

1) Analyze the derived axial force and applied axial load on the shaft, and determine the "compressed" and "relaxed" bearings.

2) The axial force of the "compressed" end bearing is equal to the algebraic sum of all other axial forces on the shaft except the axial force derived from itself.

3) The axial force of the "relaxed" end bearing is equal to its own derived axial force

4. Life calculation of rolling bearing

The relationship between the load P and the life L of the bearing is shown in the figure, and its equation is

PεL10=constant

where P - equivalent dynamic load (N)

L10—Basic rating life (106r)

ε-life coefficient, ball bearing ε=3, roller bearing ε=10/3.

It is known that the basic dynamic load rating when the basic rated life of the bearing is one million revolutions (1×106r) is Cr,

Here is the life formula

If the life is expressed in working hours, we have

where n—the working speed of the bearing (r/min);

fp—load factor, considering the correction of the load due to vibration and impact when the machine is working,

After the bearing life is calculated, it should meet the

Lh≥[Lh]