Archive > 2020 > December 2020 > Rolling Bearing Performance Rating Parameters Review and Engineering Assessment

# Rolling Bearing Performance Rating Parameters Review and Engineering Assessment

**Abbrevations**

Introduction

The main function of rolling bearings is to support load and transmit rotational movement with minimum energy loss. In order to achieve this, bearings are manufactured with particularly good quality fatigue resistance materials, proper design and tight manufacturing tolerances. Particular emphasis is put in both the macro, and micro geometry of the working shapes and surfaces of the raceways. Rolling bearings come in many types and sizes as ball and roller bearings for radial and thrust loads. For many years, the selection of the proper bearing for an application has relied on the matching of two main aspects:

- An adequate definition of the performance rating parameters related to the actual manufacturing process and quality of the bearing, usually performed by the bearing manufacturer.
- An adequate definition of the operating conditions and of the safety factors of the particular application, usually performed by the application engineer.

The first aspect requires: i) a quality control and assurance system during manufacturing process, and ii) a methodology for the assessment and validation of the performance parameters that are applied to bearing products. Usually this is done using load rating models that are validated by dedicated tests of the product.

The second aspect requires measurements, experimentation and good engineering knowledge of the specific application. This includes: i) dynamic load variations and transient conditions, and ii) the effect of the environment that may influence the performance of the bearing in use.

The current paper focuses on the first aspect of the engineering selection process, critically reviewing the methodologies that are applied in bearing performance rating and their relation to bearing manufacturing quality and experimental validation.

International standards are very important here. A frequently employed standard is the ISO 281 (Ref. 1) which establishes the definitions of the dynamic load ratings of rolling bearings. This standard provides the methodology for the simple calculation of dynamic load capacity of rolling bearings based on the main geometrical parameters of the bearing and standard high quality material.

However, the standard has important limitations that users often overlook. The standard applies only to good quality bearings. In other words, bearings that represent the “status of the art” of rolling bearing manufacturing technology. In practice, this means, by quoting the standard: *“rolling bearings manufactured from contemporary, commonly used, high quality hardened bearing steel, in accordance with good manufacturing practices.”* Unfortunately, no quantitative measure of this definition of bearing quality is given in ISO 281. This, in turn, let the undifferentiated application of ISO performance parameters and dynamic load ratings to the large variety of rolling bearings that are produced today.

Verification of the ISO 281 dynamic load ratings would require the use of proper, statistically meaningful, endurance testing of rolling bearings population samples to determine the life L10. However, standards of bearing endurance testing for the verification of dynamic load ratings of rolling bearings are not part of ISO or any other standard. This leads to the present situation in which bearing manufacturers typically apply ISO ratings to describe the performance of their products. However, only very few, generally well-established companies with a long tradition in quality and testing, actually verify the performance parameters of their products by means of dedicated endurance testing (Ref. 2).

Today mechanical engineers have to decide choosing a bearing among different manufacturers. In some cases, significantly different load ratings for seemingly similar bearings type and size are given without a clear explanation of the reasons behind the applied load ratings or whether or not these values are routinely supported with a quality control system and endurance testing practices. This situation is further complicated by the fact that, given the very high costs involved in bearing fatigue life testing, the results of endurance testing are usually proprietary information of the bearing manufacturer that is not released into the public domain.

This paper addresses these issues by reviewing the calculation methodologies of the most relevant load rating parameters of rolling bearings. Their definition, origin and significance in terms of fatigue life of the bearing are clarified. Verification methods of these performance parameters are also discussed. This includes the required endurance testing and the basic statistics that are used in this field.

Objective of this Paper

The intent is to critically review the most important rating parameters used in the prediction of rolling bearing performance. To discuss their origin, definitions and significance in terms of fatigue life of the bearing. To clarify their limitations and applicability in bearing selection and machine design.

**Bearing life rating parameters.** Life in rolling bearings depends on many parameters and application influence, like lubrication conditions, sealing effects, solid and liquid contamination, variable loading and speed conditions, etc. However, to select the size of a bearing, rating life calculations are used. The standard ISO 281 (Ref. 1) describes the modified bearing rating life with 90% survival probability as:

**(1)**

Where L* _{10}* is the bearing rating life for 90% survival probability,

*C*is the dynamic load rating,

*P*is the equivalent load in the bearing and

*p*is a constant exponent that depends on the bearing type (3 for ball bearings and 10/3 for roller bearings). The life factor α

*is given in (Ref. 1) in dedicated charts and equations for the different lubrication and contamination conditions of the bearing. However, the basic theory comes from Ioannides et al. (Ref. 3) where a more detailed description of this life factor is given. Therefore, herewith it will not be denoted as α*

_{ISO}*but (as in (Ref. 3) as α*

_{ISO}*to avoid confusion with the standard:*

_{SLF}**(2)**

With, A being a scaling constant, P* _{u}* is the fatigue limit load (C

*in ISO 281 nomenclature), is a stress penalty factor (environmental factor) described in (Ref. 2) as η = η*

_{u}*∙ η*

_{a}*∙ η*

_{b}*. In which: η*

_{c}*is a macro-scale “parasitic” stress aggravation affecting the bearing. This may be originated by: i) bearing mounting, ii) hoop tension or, iii) residual stresses from heat treatment and manufacturing processes. The factor η*

_{a}*is the lubrication factor that depends on the lubrication quality κ, as defined in the ISO 281. Finally, the contamination η*

_{b}*(in ISO 281 nomenclature e*

_{c}*) is the stress penalty for stress concentrations developed on the bearing raceways due to solid particles contamination denting. The remaining constants of Equation (2) are the*

_{c}*w*exponent (related to the bearing type), the fatigue exponent

*c*of the stress-life equation, and

*e*that is the Weibull exponent.

From these two equations, the main bearing life rating parameters that depend (or may be affected) by the bearing geometry, material properties, manufacturing process and quality are C, P* _{u}* and ηa. Another important parameter, related to the maximum load safety of the bearing and its performance under low cycle fatigue, is the static load rating C

*which will be discussed in detail later in this paper.*

_{0}Dynamic Load Rating

This parameter (C) was originally invented by Lundberg and Palmgren (Refs. 4–5) when they introduced the equation of the basic rating life of rolling bearings:

**(3)**

Lundberg and Palmgren, in their work, refer to (C) as the basic dynamic capacity of the bearing. It was defined at that time (Ref. 4) as: *“the radial load (or thrust load) which 90% of the bearings can endure for one million revolutions under certain specified conditions of operation.”*

ISO 281 (Ref. 1) re-writes this definition, depending on weather the bearing is radial or thrust, using the following terminology: Basic dynamic radial/axial load rating: *“Constant stationary radial/concentric-axial load which a rolling bearing can theoretically endure for a basic rating life of one million revolutions.”*

ISO 281 (Ref. 1) gives also specific equations to calculate (C* _{0}*) for each bearing type (radial or thrust, ball or roller) which are obtained from the general methodology originally developed by Lundberg and Palmgren (Refs. 4–5).

**General methodology for the calculation of (C).** Hereafter the study follows the same methodology of the original work of Lundberg and Palmgren (Ref. 4); this is done to arrive at an estimation of (C) before any approximations or simplifications are introduced into the equations. From the original work of Lundberg and Palmgren (Ref. 4), the dynamic load rating (C) of a rolling bearing can be calculated directly following the analytical method described in the following equations. The analysis can start by considering Equations (47) and (48) from (Ref. 4). Using the same basic nomenclature as in (Ref. 4) these equations are hereafter re-written as Equations (4) and (5).

**For point contact (ball bearings).**

**(4)**

**For line contact (roller bearings).**

**(5)**

Furthermore, with the basic notation as from (Ref. 4), T = τ_{0}/p_{0}, ε = z_{0}/α p0 = maximum Hertzian pressure. T_{0}, ε_{0}, T1, ε_{1} are functions of T and ε for α/b = 0 and α/b = 1, respectively (a along the rolling direction, minor semi-width).

**(6a)**

**(6b)**

**(7)**

With N = *u*L, ∑* _{ρ}* = curvature summation used in contact theory,

*v*, μ Hertzian functions related to the elliptical integrals. A

_{1}is a proportionality constant determined experimentally from endurance testing of representative populations of rolling bearing samples. A

_{1}is given in the original work (Ref. 4), with bearing loads expressed in (kg) units. For bearing loads given in (N) and bearing dimensions in (mm), consistently with Equation (7) of (Ref. 6) (pages 8 and 11), one gets A

_{1}= 1101.87 and B

_{1}= 1141.096.

Notice that A_{1} and B_{1} need to be further updated to account for the factor bm that was introduced in ISO in 1990, and is used in the current version of ISO 281 (Ref. 1). This will be further discussed in the next section. Detailed parameter description of Equations (6) and (7) are included in Appendix A.

It follows that if Q_{c} is the rolling contact load for the calculation of the dynamic load rating, from the load rating definition, the life is L = 1 million revolutions, then Equations (4) and (5) yield:

**For point contact (ball bearings).**

**(8)**

**For line contact (roller bearings).**

**(9)**

Based on equations (89) and (95) (Ref. 4), for the inner and outer bearing ring (inner – ι, outer – *e*) the bearing external load P can be related to the maximum contact load Q* _{c}* as,

**(10a)**

**(10b)**

Where *J _{r}* is the Sjövall’s radial load distribution integral.

Calculated values of this integral are given in Table 3 of (Ref. 4) depending on the bearing clearance parameter ε. Assuming a bearing with zero clearance, thus (ε = 0.5) one has the following values: *J _{r}* = 0.2288 for a single-row radial ball bearing and

*J*= 0.2453 for a single-row radial roller bearing. The parameters J

_{r}_{1}and J

_{2}are load distribution factors that account for the load variation in the rings due to bearing rotation. For instance, refers to the rotating ring and to the stationary one. Reference 4 in Table 10 gives values for these factors as a function of the bearing clearance; for zero clearance (ε = 0.5) and single-row ball bearings J1=0.5625, J2=0.5275, and for single-row roller bearings J

_{1}=0.5965, J

_{2}=0.6814.

Finally, from Equation (87) (Ref. 4),

**(11)**

Equation (11) represents the most general way of calculating the dynamic load rating of a bearing without using further simplifications, as they have been used (Ref. 4), or the additional modifications formalized in the ISO 281 (Ref. 1) standard.

All the equations discussed above were programmed in a computer code. Calculations were performed to directly determine the value of (C) for radial ball and radial roller bearings of different size and type.

**ISO methodology for the calculation of (C).** The ISO 281 (Ref. 1) methodology for the calculation of the dynamic load rating (C) also introduced further simplifications of the original Lundberg and Palmgren (Refs. 4–5) method, as described above; this is the most widely used methodology in industry. The main simplifications introduced by ISO are related to the calculation of the radial and axial Sjövall’s load distribution integrals *J _{r}* and

*J*. Some numerical values to the exponents

_{a}*c, h, w, ℯ*were also re-defined. Finally, the values of some complex type of functions are given in the form of tabulated values, or as simple heuristic functions to achieve standard ISO equations that can be quickly calculated.

The article "Rolling Bearing Performance Rating Parameters Review and Engineering Assessment" appeared in the December 2020 issue of Power Transmission Engineering.