Source: AST BearingsSource: AST BearingsBearings are found in virtually every rotating assembly in equipment and power transmission applications. They produce smooth rotary motion and reduce friction and wear. When sized and used properly, most bearings will operate for many years without requiring replacement. The terms and formulas in this article will help the design engineer with bearing selection.

Rotary bearing is a broad term that includes plain bearings, hydrostatic and hydrodynamic bearings, magnetic bearings and rolling element bearings. Rolling element bearings can be further broken down by rolling element type — ball, roller and needle roller. This article focuses on radial and angular contact ball bearings, and roller bearings, which are the most commonly used rolling element bearings.

Every mechanical design engineer incorporating ball or roller bearings in their assembly should be familiar with calculations for bearing life and bearing load. Knowledge of these basic formulas will help ensure a robust design optimized for long life.

Terms and definitions

The American Bearing Manufacturers Association (ABMA) and International Organization for Standardization (ISO) have developed terms and definitions concerning bearing life and load. Bearing manufacturers publish static and dynamic load ratings for each bearing type according to:

Bearing life is a function of bearing load, and understanding the terminology and definitions for life and load is important before performing any calculations.

Bearing life

Bearing life (L) is defined as the number of hours the bearing can run at a given constant speed before it displays the first signs of fatigue in the material of either bearing ring or any of the rolling elements.

Bearing rating life (L10) is the life in hours at a specific constant speed that 90% of a group of apparently identical bearings will complete or exceed. Rating life also refers to life for a single bearing associated with 90% reliability. Bearing rating life for bearings that operate at a constant speed can also be expressed in hours and is referred to as L10h. The units for rating life are in millions of revolutions (106rev).

Bearing load ratings

Bearing load is expressed with different terms, each with a unique definition. Static loads refer to loads on a non-rotating bearing.

Basic load rating (CB) is a calculated constant load for radial and angular contact bearings. It is the load that a group of apparently identical bearings can endure for one million revolutions of the inner ring while the outer ring is held stationary. The units for basic load rating are pounds (lb) or Newtons (N).

The basic static load rating (Co) is the radial load on a non-rotating bearing corresponding to a calculated contact stress at the most heavily loaded point of contact between the rolling element and raceway that produces a total permanent deformation of the rolling element and raceway of 0.0001 of the rolling element diameter. The units for basic static load rating are pounds (lb) or Newtons (N).

Static equivalent load (Po) is a calculated static, radial load. It is defined as the load that would cause the same total permanent deformation at the most heavily stressed rolling element and raceway contact as that which occurs under the actual loading condition. The units for static equivalent load rating are pounds (lb) or Newtons (N).

The basic dynamic load rating (C) is the calculated constant radial load that a group of apparently identical bearings with a stationary outer ring can statistically endure one million revolutions of the inner ring. The units for basic dynamic load rating are pounds (lb) or Newtons (N).

Dynamic equivalent load (P) is one of the factors used in bearing life equations. It is a constant, hypothetical radial load, that has the same impact on bearing life as that which occurs under the actual loading condition. The units for dynamic equivalent load rating are pounds (lb) or Newtons (N).

Calculations

Bearing life (L10) can be calculated with the following formula. Variables required are basic dynamic load rating (C) and the dynamic equivalent load of the bearing (P).

L10 = (C/P)3

L10 = rating life (106rev); C = basic dynamic load rating (lb or N); P = dynamic equivalent load (lb or N)

To convert from revolutions to hours divide by the speed (rpm).

L10hrs = (C/P)3 x [(106rev) / (N rpm x 60min/hr)] = 16667/N x (C/P)3

N = speed (rpm)

The dynamic equivalent load (P) is a function of the radial and axial loads and a radial and thrust factor. Even bearings whose primary loading is radial will most likely experience some axial loading as well. These loads can be combined to determine the dynamic equivalent load. For most bearing types with filling notches for balls, use the higher of the two values given by the following formulas.

1. P = VFr

2. P = XVFr + YFa

P = dynamic equivalent load; V = rotation factor; X = radial factor; Y = thrust factor; Fr = radial load; Fa = axial load

When the bearing outside diameter (OD) is equal to or less than 0.625 in, the following values can be used: X = 0.56, Y = 2.10 and e = 0.16. For bearings larger than 0.625 in in diameter, refer to the table below. Factor “e”, shown in the last column of the table below, represents the ratio of Fa/VFr. If Fa /VFr < e, then formula (1) is used; if Fa/VFr > e, then formula (2) is used.

X, V and Y Bearing Factors; Source: New Hampshire Ball Bearings, Inc.X, V and Y Bearing Factors; Source: New Hampshire Ball Bearings, Inc.

While these formulas offer a good starting point, other factors can also influence effective bearing life and load ratings.

  • In some applications, the loads and speed may vary during operation. This can be factored into bearing load calculations if the load and speed variations are known variables.
  • Lubrication is another factor that can have a significant impact on bearing life. For sealed bearings, the life of the lubricant often determines the life of the bearing.
  • Environmental conditions and contamination can also adversely affect bearing life.
  • Bearing material may also influence performance. For example, load ratings for 440C stainless steel should be reduced by approximately 20% compared to 52100 bearing steel. Bearing life is not an exact science due to these factors and others, however, use of these formulas will help engineers develop a safe and reliable design for their assemblies.

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