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How to calculate the lifespan of the rolling bearings?

Nov 01, 2022
1.What factors will affect the lifespan of rolling bearings?

Normally the rolling bearings have three kinds of failure forms, including pitting corrosion, permanent deformation, and wear & tear.

①Pitting corrosion

When the bearing works, relative movement occurs between the rolling element and the inner/outer ring. Under load, the contact between the rolling element and the inner/outer ring brings cyclic changes in the contact fatigue stress. Long-term operation will lead the pitting corrosion damage to bearings, so that vibration, noise, and even loss of running accuracy happens after.

②Permanent deformation

Generally fatigue pitting corrosion damage will not happen to the low-speed bearings and intermittent swing bearings, but in the excessive shock load or static load, uneven permanent plastic deformation dents start to appear on the raceway and rolling element, which will increase the friction and reduce the running accuracy eventually.

③Wear & tear

In dusty or poor lubrication working conditions, corrosion happens to the working surface of rolling element and the rings. Exceeded speed will cause gluing, surface heating and even tempering of the rolling element. Other abrasions may be caused due to installation, disassembly, maintenance improperly, etc..

Thus for different bearings with different failure forms, different design guidelines will be adopted, and lifespan calculation, static intensity calculation and limiting speed will all affect the actual lifespan of bearings.

①For slewing rolling bearings, the main failure is caused by corrosion of fatigue points. In general, for these kinds of bearings, bearing life calculation should be carried out.

②For bearings operating under low speed or oscillating bearings, permanent deformation value needs to be strictly controlled, and the static intensity calculation is necessary then.

③For high-speed bearings, mainly due to abrasions and burns by the heat, the limiting speed needs to be calculated besides the lifespan calculation.

2.The definitions of lifespan, and basic nominal life, basic nominal dynamic load

To calculate the lifespan of bearings, first of all, we need to understand properly about the definitions of lifespan, and basic nominal life, basic nominal dynamic load.

①Definition of bearing lifespan

Lifespan:  
Before the first fatigue pitting corrosion occurs to any component of rolling bearing, the total rotating number, or the total operating hours under the given constant speed.

Basic rating life:
A batch of bearings with the same type, under the same operating conditions, the total rotating number of 90% of them before fatigue pitting corrosion occurs, or the total operating hours in a given speed. Its reliability is 90%, with the symbol L10 or Lh10 to indicate.

② Definition of basic nominal dynamic load

The basic nominal dynamic load of the bearing is the maximum load can be withstood by the bearings when their basic nominal life is one million (106) turns, when for the basic rated dynamic load of the bearing, with the symbol Cr to indicate.

Under the basic nominal dynamic load and one million (106) turns, the reliability of bearings without pitting corrosion failure is 90%.

③ Definition of Equivalent dynamic load

The equivalent dynamic bearing load is defined as: a hypothetical load, constant in magnitude and direction, that acts radially on radial bearings, and axially and centrically on thrust bearings.

In another word, bearing lifespan under the equivalent dynamic bearing load technically equals to bearing actual lifespan under the actual load.

3.How to calculate the lifespan of rolling bearings?


The equation for the relationship between the load P and the life L of a bearing is:

PεL10 = constant

Where,
P = equivalent dynamic load (N)
L10 = basic nominal life (106r)
ε = life factor, ε = 3 for ball bearings, and ε = 10/3 for roller bearings.
It is known that the basic nominal life of the bearing is one million turns (1 × 106r) as the basic nominal dynamic load is Cr,
PεL10 = 1 x Crε
Thus, the equation of bearing life(L) is:

L = fp(Cr/P)ε(106r)

The fp is the load factor, considering correction of the load caused by the vibration & shock during machine operation.
If we want to know the total operating hours of a bearing, we take the equation as below:

Ln= fp(Cr/P)ε(106/60n)=16670/n *fp(Cr/P)ε

n = the bearing operation speed (r/min)

4.T
he calculation of bearing static intensity

Basic nominal static load C0 : it depends on the allowable plastic deformation value under normal operation. That is, a certain contact stress value by the contact between the rolling element which bears the maximum load and the centre of raceway is reached.

Spherical ball bearings: 4600Mpa; Other ball bearings: 4200Mpa; Roller bearings: 4000Mpa.

The equivalent bearing static load (hypothetical load): the plastic/permanent deformation value under the equivalent bearing static load equals to the plastic/permanent deformation value under actual bearing load.

R, A = actual radial/axial bearing load
X0, Y0 = static radial/axial bearing load co-efficiency

P0(equivalent static bearing load) = RX0 + AY0

5.The ultimate rotating speed of rolling bearings

The factors affecting the speed of rolling bearings are:
①Grease
②Coiling system
③Precision level
④Clearance
⑤Material of bearing and its gauge
⑥Processing technology

The methods to improve the ultimate rotating speed of rolling bearings are:
①Choosing the right grease/oil for your bearings according to different working temperature/environment, the bearing’s working temperature has to be matched with the lubricant’s allowable operating temperature. Temperature matching will ensure the good fluidity of lubrication.
②As for coiling system, for example, we can remove the dust cover and add a water cooling unit, to cool down the bearings, and keep the stable clearance.
③Precision level will affect the rotating speed as everyone understands.
④Adjusting the clearance is an important way to change the rotating speed.
⑤The smaller the coefficient of the bearing thermal expansion/contraction is, the better the performance of rotating speed will be. And also, wearable materials help improve rotating speed as well.

6.The selection of rolling bearings

In this article, you will get a very complete knowledge of rolling mill bearings. In the following part, you will know how to select the rolling bearings, basically, we select bearings in accordance with the flowing factors such as: actual load(amount, direction, and feature), rotating speed, intensity, assembly precision, and etc..

<1> high rotating speed + small actual load + high rotating precision = ball bearings
   low rotating speed + big actual load(impact load as well) + high rotating precision = roller bearings (while sensitive to skewed axial lines)
<2> Most radial load Fr = radial bearings
   Most axial load Fa + comparatively lower rotating speed = thrust bearings
   Both heavy axial/radial load + high rotating speed = angular contact ball bearings
   Both heavy axial/radial load + low rotating speed = taper roller bearings
   Heavier radial load Fr + smaller axial load Fa = deep groove ball + thrust ball bearings/or, thrust angular contact bearings
<3> Rotating speed should be less than the ultimate rotating speed. Deep groove ball bearings, angular contact ball bearings and cylindrical roller bearings are all with higher ultimate rotating speed.
<4> Asymmetrical bearing bores/or, worse intensity = spherical bearings
<5> Higher rotating precision<runout> = higher tolerance grade (ABEC) + smaller clearance
   Higher rotating speed = higher tolerance grade (ABEC) + bigger clearance

So generally, the most complete common sense of rolling mill bearings has been shared as above. We hope the information will help you make the best choice on selecting the specific bearings you need. And also, if you have any question or anything you feed confused, please feel free to leave a message on our website.
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