Equivalent dynamic bearing load, P

The loads acting on a bearing are calculated according to the laws of mechanics using the external forces – such as forces from power transmission, work forces, gravitational or inertial forces – that are known or can be calculated.
In real-world circumstances, the loads acting on a bearing may not be constant, can act both radially and axially, and are subject to other factors that require the load calculations to be modified or, in some cases, simplified.

Calculating Equivalent dynamic bearing load
The load value, P, used in the bearing rating life equations is the equivalent dynamic bearing load. The equivalent dynamic bearing load is defined as: a hypothetical load, constant in magnitude and direction, that acts radially on radial bearings and axially and centrically on thrust bearings.

This hypothetical load, when applied, would have the same influence on bearing life as the actual loads to which the bearing is subjected (fig. 1).

If a bearing is loaded with simultaneously acting radial load Fr and axial load Fa that are constant in magnitude and direction, the equivalent dynamic bearing load P can be obtained from the general equation Perform calculation

where
 P equivalent dynamic bearing load [kN] Fr actual radial bearing load [kN] Fa actual axial bearing load [kN] X radial load factor for the bearing Y axial load factor for the bearing

An axial load only influences the equivalent dynamic load P for a single row radial bearing if the ratio Fa/Fr exceeds a certain limiting factor e. With double row bearings, even light axial loads influence the equivalent load and have to be considered.

The same general equation also applies to spherical roller thrust bearings, which can accommodate both axial and radial loads.

Certain thrust bearings, such as thrust ball bearings and cylindrical and needle roller thrust bearings, can only accommodate pure axial loads. For these bearings, provided the load acts centrically, the equation is simplified to

P = Fa

Information and data required for calculating the equivalent dynamic bearing load for the different bearing types is provided in the relevant product sections.

Other loads may vary with time. For these situations, an equivalent mean load must be calculated.

Mean load within a duty interval

Within each loading interval, the operating conditions can vary slightly from the nominal value. Assuming that the operating conditions, such as speed and load direction, are fairly constant and the magnitude of the load constantly varies between a minimum value Fmin and a maximum value Fmax (diagram 1), the mean load can be obtained from: If, as illustrated in diagram 2, the load on the bearing consists of a load F1, which is constant in magnitude and direction, such as the weight of a rotor, and a rotating constant load F2, such as an unbalanced load, the mean load can be obtained from

Fm = fm (F1 + F2)

Values for the factor fm are provided in diagram 3.

High loads acting for short times (diagram 4) may not influence the mean load used in a fatigue life calculation. Evaluate such peak loads against the bearing static load rating C0, using a suitable static safety factor s0. → Size selection based on static load

Considerations when calculating equivalent dynamic bearing load
For the sake of simplification, when calculating the load components for bearings supporting a shaft, the shaft is considered as a statically determined beam resting on rigid, moment-free supports. Elastic deformations in the bearing, the housing or the machine frame are not considered, nor are the moments produced in the bearing as a result of shaft deflection. These simplifications are necessary if you are making bearing arrangement calculations without the aid of relevant computer software. The standardized methods for calculating basic load ratings and equivalent bearing loads are based on similar assumptions.

It is possible to calculate bearing loads based on the theory of elasticity, without making the above assumptions, but this requires the use of complex computer programs (→ SKF SimPro Quick and SKF SimPro Expert). In these programs, the bearings, shaft and housing are considered as resilient components of a system.

If external forces and loads – such as inertial forces or loads resulting from the weight of a shaft and its components – are not known, they can be calculated. However, when determining work forces and loads – such as rolling forces, moment loads, unbalanced loads and impact loads – it may be necessary to rely on estimates based on experience with similar machines or bearing arrangements.

Geared transmissions

With geared transmissions, the theoretical tooth forces can be calculated from the power transmitted and the design characteristics of the gear teeth. However, there are additional dynamic forces, produced either by the gear, or by the input or output shaft. Additional dynamic forces from gears can be the result of pitch or form errors of the teeth and from unbalanced rotating components. Gears produced to a high level of accuracy have negligible additional forces. For lower precision gears, use the following gear load factors:

• pitch and form errors < 0,02 mm: 1,05 to 1,1
• pitch and form errors 0,02 to 0,1 mm: 1,1 to 1,3
Additional forces arising from the type and mode of operation of the machines that are coupled to the transmission can only be determined when the operating conditions, the inertia of the drive line and the behavior of couplings or other connectors are known. Their influence on the rating lives of the bearings is included by using an “operation” factor that takes into account the dynamic effects of the system.

Belt drives

When calculating bearing loads for belt driven applications, “belt pull” must be taken into consideration. Belt pull, which is a circumferential load, depends on the amount of torque being transmitted. The belt pull must be multiplied by a factor whose value depends on the type of belt, belt tension and any additional dynamic forces. Belt manufacturers usually publish the values. However, should information not be available, the following can be used:

• toothed belts = 1,1 to 1,3
• V-belts = 1,2 to 2,5
• plain belts = 1,5 to 4,5

The larger values apply:

• where the distance between shafts is short
• for heavy or peak load type duty
• where belt tension is high 