Schaeffler KG introduced the “Expanded calculation of the adjusted rating life” in 1997. This method was standardised for the first time in DIN ISO 281 Appendix 1 and has been a constituent part of the international standard ISO 281 since 2007.

As part of the international standardisation work, the life adjustment factor a_DIN was renamed as a_ISO but without any change to the calculation method.

The basis of the rating life calculation in accordance with ISO 281 is Lundberg and Palmgren's fatigue theory which always gives a final rating life.

However, modern, high quality bearings can exceed by a considerable margin the values calculated for the basic rating life under favourable operating conditions. Ioannides and Harris have developed a further model of fatigue in rolling contact that expands on the Lundberg/Palmgren theory and gives a better description of the performance capability of modern bearings.

The method “Expanded calculation of the adjusted rating life” takes account of the following influences:

• the bearing load
• the fatigue limit of the material
• the extent to which the surfaces are separated by the lubricant
• the cleanliness in the lubrication gap
• additives in the lubricant
• the internal load distribution and frictional conditions in the bearing.

The influencing factors, especially those relating to contamination, are extremely complex. A great deal of experience is essential for an accurate assessment. As a result the Engineering Service of Schaeffler Group Industrial should be consulted for further advice.

The tables and diagrams can only give guide values.

The required size of a rolling bearing is dependent on the demands made on its:

• rating life
• load carrying capacity
• operational reliability.

The dynamic load carrying capacity is described in terms of the basic dynamic load ratings. The basic dynamic load ratings are based on DIN ISO 281.

The basic dynamic load ratings for rolling bearings are matched to empirically proven performance standards and those published in previous FAG and INA catalogues.

The fatigue behaviour of the material determines the dynamic load carrying capacity of the rolling bearing.

The dynamic load carrying capacity is described in terms of the basic dynamic load rating and the basic rating life.

The fatigue life is dependent on:

• the load
• the operating speed
• the statistical probability of the first appearance of failure.

The basic dynamic load rating C applies to rotating rolling bearings. It is:

• a constant radial load C_r for radial bearings
• a constant, concentrically acting axial load C_a for axial bearings.

The basic dynamic load rating C is that load of constant magnitude and direction which a sufficiently large number of apparently identical bearings can endure for a basic rating life of one million revolutions.

The methods for calculating the rating life are:

• basic rating life L₁₀ and L_10h to ISO 281, see link
• adjusted rating life L_na to DIN ISO 281:1990 (no longer a constituent part of ISO 281), see link
• expanded adjusted rating life L_nm to ISO 281, see link.

The basic rating life L₁₀ and L_10h is calculated as follows:

The equivalent dynamic load P is a calculated value. This value is constant in size and direction; it is a radial load for radial bearings and an axial load for axial bearings.

The load value P gives the same rating life as the combined load occurring in practice.

This calculation cannot be applied to radial needle roller bearings, axial needle roller bearings and axial cylindrical roller bearings. Combined loads are not permissible with these bearings.

The adjusted rating life L_na can be calculated if, in addition to the load and speed, other influences are known such as:

• special material characteristics
• lubrication

or

• if a requisite reliability other than 90% is specified.

This calculation method was replaced in ISO 281:2007 by the calculation of the expanded adjusted rating life L_nm, see link.

The viscosity ratio κ is determined according to the formula on link.

The viscosity ratio κ is an indication of the quality of lubricant film formation:

The reference viscosity ν₁ is determined from the mean bearing diameter d_M = (D + d)/2 and the operating speed n, Figure 2.

The nominal viscosity of the oil at +40 °C is determined from the required operating viscosity ν and the operating temperature ϑ, Figure 3. In the case of greases, ν is the operating viscosity of the base oil.

In the case of heavily loaded bearings with a high proportion of sliding contact, the temperature in the contact area of the rolling elements may be up to 20 K higher than the temperature measured on the stationary ring (without the influence of any external heat).

Taking account of EP additives in calculation of the expanded adjusted rating life L_nm: see link.

The calculation of the expanded adjusted rating life L_nm was standardised in DIN ISO 281 Appendix 1. Since 2007, it has been standardised in the worldwide standard ISO 281. Computer-aided calculation in accordance with DIN ISO 281 Appendix 4 has been specified since 2008 in ISO/TS 16 281.

L_nm is calculated as follows:

The values for the life adjustment factor a₁ were redefined in ISO 281:2007 and differ from the previous data.

The standardised method for calculating the life adjustment factor a_ISO essentially takes account of:

• the load on the bearing
• the lubrication conditions (viscosity and type of lubricant, speed, bearing size, additives)
• the fatigue limit of the material
• the type of bearing
• the residual stress in the material
• the environmental conditions
• contamination in the lubricant.

In accordance with ISO 281, EP additives can be taken into consideration in the following way:

• For a viscosity ratio κ ＜ 1 and a contamination factor e_C ≧ 0,2, calculation can be carried out using the value κ = 1 for lubricants with EP additives that have proven effective. With severe contamination (contamination factor e_C ＜ 0,2), the effectiveness of the additives under these contamination conditions must be proven. The effectiveness of the EP additives can be demonstrated in the actual application or on a rolling bearing test rig FE 8 to DIN 51 819-1.If the EP additives are proven effective and calculation is carried out using the value κ = 1, the life adjustment factor must be restricted to a_ISO ≦ 3. If the value a_ISO calculated for the actual κ is greater than 3, this value can be used in calculation.

The fatigue limit load C_u in accordance with ISO 281 is defined as the load below which, under laboratory conditions, no fatigue occurs in the material.

The life adjustment factor for contamination e_c takes into consideration the influence of contamination in the lubrication gap on the rating life, see table.

The rating life is reduced by solid particles in the lubrication gap and is dependent on:

• the type, size, hardness and number of particles
• the relative lubrication film thickness
• the bearing size.

Due to the complex nature of the interaction between these influencing factors­, only an approximate guide value can be attained. The values in the tables are valid for contamination by solid particles (factor e_C). They do not take account of other contamination such as that caused by water or other fluids.

Under severe contamination (e_C → 0) the bearings may fail due to wear. In this case, the operating life is substantially less than the calculated life.

The rating life formulae assume a constant bearing load P and constant bearing speed n. If the load and speed are not constant, equivalent operating values can be determined that induce the same fatigue as the actual conditions.

The equivalent operating values calculated here already take account of the life adjustment factors a₃ or a_ISO. They must not be applied again when calculating the adjusted rating life.

If the load and speed vary over a time period T, the speed n and equivalent bearing load P are calculated as follows:

If the load and speed vary in steps over a time period T, n and P are calculated as follows:

If the function F describes the variation in the load over a time period T and the speed is constant, P is calculated as follows:

If the load varies in steps over a time period T and the speed is constant, P is calculated as follows:

If the speed varies but the load remains constant, the following applies:

If the speed varies in steps, the following applies:

The equivalent speed is calculated as follows:

The formula is valid only if the angle of oscillation is greater than twice the angular pitch of the rolling elements. If the angle of oscillation is smaller, there is a risk of false brinelling.

If no information is available on the rating life, the guide values from the following tables may be used.

Do not overspecify the bearing. If the calculated life is ＞ 60 000 h, this normally means that the bearing arrangement is overspecified. Pay attention to the minimum load for the bearings; see the design and safety guidelines in the product sections.

The operating life is defined as the life actually achieved by the bearing. It may differ significantly from the calculated value.

This may be due to wear or fatigue as a result of:

• deviations in operating conditions
• misalignment between the shaft and housing
• insufficient or excessive operating clearance
• contamination
• insufficient lubrication
• excessive operating temperature
• oscillating bearing motion with very small angles of oscillation (false brinelling)
• high vibration and false brinelling
• very high shock loads (static overloading)
• prior damage during installation.

Due to the wide variety of possible installation and operating conditions, it is not possible to precisely predetermine the operating life. The most reliable way of arriving at a close estimate is by comparison with similar applications.

Radial cylindrical roller bearings used as semi-locating and locating bearings can support axial forces in one or both directions in addition to radial forces.

The axial load carrying capacity is dependent on:

• the size of the sliding surfaces between the ribs and the end faces of the rolling elements
• the sliding velocity at the ribs
• the lubrication on the contact surfaces
• the tilting of the bearing.

Ribs subjected to load must be supported across their entire height.

The permissible axial load F_a per must not be exceeded, in order to avoid unacceptably high temperatures.

The limiting load F_a max must not be exceeded, in order to avoid unacceptable pressure at the contact surfaces.

The ratio F_a/F_r must not exceed a value of 0,4. For bearings of TB design, the value 0,6 is permissible.

Continuous axial loading without simultaneous radial loading is not permissible.

In the case of bearings of TB design, the axial load carrying capacity has been significantly improved through the use of new calculation and manufacturing methods.

Optimum contact conditions between the roller and rib are ensured by means of a special curvature of the roller end faces. As a result, axial surface pressures on the rib are significantly reduced and a lubricant film with improved load-carrying capabilities is achieved. Under normal operating conditions, wear and fatigue at the rib contact running and roller end faces is completely eliminated. The axial frictional torque is reduced by up to 50%. The bearing temperature during operation is therefore significantly lower.

F_a per and F_a max are calculated as follows:

Misalignment caused by shaft deflection for example, may lead to alternating stresses on the inner ring ribs. In this instance, the axial load must be restricted to F_as in accordance with the formula where the bearing is tilted up to a maximum of 2 angular minutes.

For more severe tilting, a separate strength analysis is required.

Very high static loads or shock loads can cause plastic deformation on the raceways and rolling elements. This deformation limits the static load carrying capacity of the rolling bearing with respect to the permissible noise level during operation of the bearing.

If a rolling bearing operates with only infrequent rotary motion or completely without rotary motion, its size is determined in accordance with the basic static load rating C₀.

According to DIN ISO 76, this is:

• a constant radial load C_0r for radial bearings
• a constant, concentrically acting axial load C_0a for axial bearings.

The basic static load rating C₀ is that load under which the Hertzian pressure at the most heavily loaded point between the rolling elements and raceways reaches the following values:

• for roller bearings, 4 000 N/mm²
• for ball bearings, 4 200 N/mm²
• for self-aligning ball bearings, 4 600 N/mm².

Under normal contact conditions, this load causes a permanent deformation at the contact points of approx. 1/10 000 of the rolling element diameter.

In addition to dimensioning on the basis of the fatigue limit life, it is advisable to check the static load safety factor. The guide values and shock loads occurring in operation to table must be taken into consideration, see table, link.

The static load safety factor S₀ is the ratio between the basic static load rating C₀ and the equivalent static load P₀:

Guide values for axial spherical roller bearings and high precision bearings: see corresponding product description.

For drawn cup needle roller bearings, S₀ ≧ 3 is necessary.

The equivalent static load P₀ is a calculated value. It corresponds to a radial load in radial bearings and a concentric axial load in axial bearings.

P₀ induces the same load at the centre point of the most heavily loaded contact point between the rolling element and raceway as the combined load occurring in practice.

This calculation cannot be applied to radial needle roller bearings, axial needle roller bearings and axial cylindrical roller bearings. Combined loads are not permissible with these bearings.

For radial needle roller bearings and all radial cylindrical roller bearings, P₀ = F_0r.