18. Calculation formula for rolling bearings

1. Bearing life

When rolling bearings are loaded and operated for extended periods of time, either the raceway surface or the rolling elements are damaged by material exhaustion (scaly scratches, called flaking). The total number of revolutions (or the time at a constant rotation speed) until the damage occurs is called the rolling exhaustion life (abbreviated as life).

However, the above-mentioned exhaustion life has a large variation even with the same material and processing method, so it is industrially arranged according to the rated life.

<Rated life & gt; Total number of revolutions (or time at constant rotational speed) that allows 90% of the same bearings to rotate individually under the same conditions without causing material damage due to rolling fatigue.
Bearing life calculation formula Symbol description and unit
(1) Rated life(L) (1-1) Ball bearings

L=(C/P)3 [106 rotate]
L=
C: Basic dynamic load rating[kgf]
P: Bearing load (Dynamic equivalent load)
(1-2) Roller bearing

L=(C/P)10/3 [106 rotate]
L=
C: Basic dynamic load rating[kgf]
P:Bearing load(Dynamic equivalent load)
(2) Rated life time
(Lh)
(2-1) Ball bearings

Lh=106/(60*n)*L=106/(60*n)*(C/P)3 [hr]
Lh=
C:Basic dynamic load rating[kgf]
P: Bearing load(Dynamic equivalent load)
n: Rotation speed per minute[rpm]
(2-2) Roller bearing

Lh=106/(60*n)*L=106/(60*n)*(C/P)10/3 [hr]
Lh=
C: Basic dynamic load rating[kgf]
P:Bearing load(Dynamic equivalent load)
n: Rotation speed per minute[rpm]
(3) Rated life date(Ld) (3-1) Ball bearings

Ld=Lh/A=106/(60*n*A)*(C/P)3 [day]
Ld=
C:Basic dynamic load rating[kgf]
P: Bearing load(Dynamic equivalent load)
n: Rotation speed per minute[rpm]
A: Old uptime[day]
(3-2)Roller bearing

Ld=Lh/A=106/(60*n*A)*(C/P)10/3 [day]
Ld=
C: Basic dynamic load rating[kgf]
P: Bearing load(Dynamic equivalent load)
n: Rotation speed per minute[rpm]
A:Daily working hours[Hr]
2. Basic dynamic load rating(C)

The basic dynamic rated load is a load that represents the load capacity of rolling bearings, and has a rated life of 1 million under the condition that the inner ring is rotated and the outer ring is stationary. rotate(106rev)It means a load that does not fluctuate in the direction and the large screwdriver. In thrust bearings, the thrust load acting on the central axis, Radial bearings take a radial load, but single-row angular contact bearings have relative displacements of the inner and outer rings only in the radial direction. Take the radial component of the load。

The calculation method of the basic dynamic load rating (C) is determined by JIS B 1518, and the numerical value is described in the catalog of each manufacturer.

This dynamic rated load is based on a rated life of 500 hours.106 The rotation speed, which is 500 hours after rotation, is 33.3r / mn.
3. Dynamic equivalent load(P)

A load that does not fluctuate in direction and large xa, and that gives the same life as under actual load and rotation conditions. Radial bearing, radial Both bearings take a constant radial or thrust load when the inner ring is rotated and the outer ring is stationary.
References: "Machine Design Handbook for Engineers" (Revised version by Saburo Kano) Shaft system and bearing Shaft gully bearing, pp. 329, 330 Quoted from shaft gully bearing design.