BEARING LIFE CALCULATION

The working principle of the bearing is to minimize the friction between machine parts that behave in different ways such as two different speeds, opposite directions, or a rotating surface and a fixed surface.

Although can't be perceived by the eye, the roller or the balls in the bearing goes through a deformation at micron level, which occurs when their rigidity is determined based on specific speeds and specific loads. With these forces, the balls and the rollers, which normally apply linear or point pressures, apply force to a much wider surface instead of having linear or point contact , that is, they create friction by spreading over a certain area, thereby providing rotation of the balls within the bearing. All bearings must be operated with a slight force.

There is no specific rules for bearing selection, and each designer can use different bearings on the same machines. The important thing is to meet the working conditions.

For this reason, the following primary features should be considered;

• Axial and radial (vertical to the axis) load
• Operating speed
• Operating time
• Bearing life expectancy
• Lubrication type
• Selection of sealing materials
• Operating temperature
• Noise level
• The amount of vibration during operation
• Type of assembly

Most of the designers and engineers in our country are choosing bearings based on inner diameter, outer diameter and load. This leads to serious mistakes. Instead of calculating values such as design load, life expectancy and temperature, it is now possible to find these values in the catalog of each company.

EQUIVALENT DYNAMIC LOAD (P)

The resultant force of radial and axial loads is the main factor that determines life expectancy of the bearing.

In bearing literature, resultant force is called "Equivalent dynamic load (P), and its formula is P (N) = Fr * cos β + Fa * sin β.

The values of sinβ and cosβ vary based on the type and size of the bearing and these are given as the coefficients of X and Y in the bearing catalog. Thus;

P = X * Fr + Y * Fa

If Fa is below a certain value, the second term is assumed to be 0 and the formula changes to P = X * Fr.

Whether the value of Fa is to be taken into consideration is determined by the coefficient of "e" given in the catalog.

If Fa / Fr> e then P = X * Fr + Y * Fa is used

If Fa / Fr

Here Fr: Radial load (N)

Fa: Axial load (N)

The calculated equivalent dynamic load (P) is the main parameter used to calculate the bearing life expectancy.

L10= (C/P)p

L10 : L10: Bearing life expectancy in millions of rotations

C : Dynamic load number in Newtonian

P : Equivalent dynamic load in Newtonian

p : This value is always 3 for ball bearings and 10/3 for roller bearings.

EQUIVALENT STATIC LOAD (P0)

The "dynamic load number (C)" used in the calculation of life expectancy is obtained from the table for the corresponding bearing in the catalog. In the tables, a "static load number (C0)" is given along with C.

The static load number (C0) is taken into account in situations when the rpm of the bearings is very low, the bearing shows slow oscillation movement, the bearing is under a load while being motionless, and most importantly when the bearing will be subjected to shock impacts. In these cases, the factor that determines the bearing performance is not the fatigue, but the permanent deformation caused by the static load. This deformation causes increased noise, vibration and friction in the bearings. In order to ensure that the ball bearing operates without reaching the low performance limit, the static equivalent load P0 (N) to be used in the calculations, is calculated with the following formulas.

P0 = X0*Fr+Y0*Fa

C0 = s0*P0, s0 = C0 / P0

C0 :static load number is taken from the respective bearing catalog.

s0: static safety factor

X0, Y0 are provided on the relevant pages of the bearing catalog. The required ratio between static load number C0 and the equivalent static load P0 is provided in the s0 static safety factor table. (In the absence of shock loads, this ratio is less than 1 in ball bearings.) If the calculated value is less than the S0 value on the table, the bearing with the larger C0 value should be selected.

Devendra Singh