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Bearing Design Considerations for Pumps and Compressors – Part 2

Bearing Design Considerations for Pumps and Compressors – Part 2

In the previous installment of this technical article, we explored the basics of bearing load ratings. Here we will examine bearing life: how to calculate it and when to use life adjustment factors. The following is Part 2 of a four-part post. You can read Part 1 here.

Bearing Life

The inner and outer rings of a radial ball bearing are constantly loaded during rotation. This produces material fatigue which eventually leads to bearing failure. The bearing life of individual bearings can vary considerably, even if they are of the same size, same material, and subject to the same operating conditions. For a statistically large group of identical bearings operating under the same conditions, basic rating life is the number of revolutions reached by 90% of the group of bearings prior to the first evidence of material fatigue. The basic rating life can also be expressed in hours. Examples of typical design life requirements for common operating conditions are shown in Table 1.

Both the ABMA and ISO standards use the same method to determine the basic rating life of a bearing. When the bearing experiences combined loading (both radial and axial loads) the standards provide a method to determine the equivalent radial load, Pr. The equation for the basic rating life of a dynamically loaded ball bearing is as follows:

L10 = (Cr/Pr)3 x 106


L10,h = 16667/n x L10


L10 = Basic Rating Life [revolutions]

Cr = Basic Dynamic Load Rating [N]

Pr = Equivalent Radial Load [N]

L10,h = Basic Rating Life [hours]

n = Operating Speed [rpm]

The basic rating life formula is acceptable for general use and correlates with 90% reliability, common material and manufacturing quality, and conventional operating conditions. However, for many applications where a reliability greater than 90% is required, and/or where there are special bearing properties or a deviation from conventional operating conditions, an adjusted rating life formula is used:

Lna = a1 x a2 x a3 x L10


Lna,h = 16667/n x Lna


Lna = Adjusted Rating Life; Reliability of (100-n) % [revolutions] 

a1 = Life Adjustment Factor for Reliability

a2 = Life Adjustment Factor for Special Bearing Properties (Material Type and Quality)

a3 = Life Adjustment Factor for Operating Conditions 

Lna,h = Adjusted Rating Life; Reliability of (100-n) % [hours] 

n = Operating Speed [rpm]

Life Adjustment Factor for Reliability, a1

Bearing reliability is expressed as the percentage of a group of identical bearings operating under the same conditions that will attain or exceed a specified life. For the basic rating life, L10, the bearing reliability is 90% and a1 = 1. When a reliability greater than 90% is required, the corresponding life adjustment factor should be selected from Table 2.

Life Adjustment Factor for Special Bearing Properties, a2

Special bearing properties can be accounted for by using the life adjustment factor a2. Improvement in manufacturing techniques and heat treatment of bearing components have led to an extended fatigue life for bearings. Most bearing manufacturers commonly use a value of a2 = 1, representing the use of high quality, vacuum degassed steel. However, a value of a2 > 1 may be used if the bearing steel has an extremely low level of impurities. Conversely, if a hardness reduction is caused by a special heat treatment process, a value of a2 < 1 should be applied. It is important to note it is not possible to define relationships between special bearing properties and the values of a2. These values are determined through empirical means and can vary widely between suppliers. Always consult the bearing manufacturer before considering using an a2 factor other than 1.   

Life Adjustment Factor for Operating Conditions, a3

Non-conventional operating conditions related to lubrication, speed, and mounting are considered with the life adjustment factor a3. Under good lubrication conditions, i.e., a permanent oil film exists between the rolling elements and the rings, then a3 = 1. In situations where the lubricant film thickness is less than the composite roughness of the two surfaces, a3 < 1. If the rotational speed of the bearing is very low (mean bearing diameter multiplied by operating speed is ≤ 10,000) then a value a3 < 1 is required. For designs in which a bearing is mounted to a shaft with a loose fit, a value of a3 < 1 should be used.

Life Adjustment Factors – Additional Considerations

Pumps and compressors are often subjected to non-standard loading and operating conditions that may require further consideration beyond the life adjustment factors previously described. Additional life adjustment factors are typically provided by bearing manufacturers, based on empirical data. These include adjustments for:

  • Sinusoidal loading (encountered in rotating and reciprocating machinery)
  • Step loading (due to operating modes and/or external forces)
  • Reversing loads
  • Vibration
  • Oscillation
  • High speeds
  • Inner ring versus outer ring rotation
  • Temperature and environmental effects

Life adjustment factors allow engineers to develop a more accurate approximation for bearing life, specific to the application and/or operating conditions. Bearing manufacturers often use additional, proprietary factors in determining both load ratings and life calculations for their customers. Accordingly, it is important to consult with bearing manufacturers in conjunction with the previously referenced industry standards during the bearing selection process.

In the next installment of Bearing Design Considerations for Pumps and Compressors, AST will discuss bearing fits and material. Look for Part 3, coming May 8, 2024.