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# Calculation of dynamic bearing loads

The loads acting on a bearing can be calculated according to the laws of mechanics if the external forces (e.g. forces from power transmission, work forces or inertia forces) are known or can be calculated. When calculating the load components for a single bearing, the shaft is considered as a beam resting on rigid, moment-free supports for the sake of simplification. 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 a bearing arrangement is to be calculated using readily available aids such as a pocket calculator. 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. In these programs, the bearings, shaft and housing are considered as resilient components of a system.
External forces that arise, for example, from the inherent weight of the shaft and the components that it carries, or from the weight of a vehicle, and the other inertia forces are either known or can be calculated. However, when determining the work forces (rolling forces, cutting forces in machine tools etc.), shock forces and additional dynamic forces, e.g. as a result of unbalance, it is often necessary to rely on estimates based on experience with similar machines or bearing arrangements.

## Gear trains

With gear trains, 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 in the gear itself or by the input drive or power take-off. Additional dynamic forces in gears result from form errors of the teeth and from unbalanced rotating components. Because of the requirements for quiet running, gears are made to high standards of accuracy and these forces are generally so small that they can be neglected when making bearing calculations.
Additional forces arising from the type and mode of operation of the machines coupled to the gear can only be determined when the operating conditions are known. Their influence on the rating lives of the bearings is considered using an "operation" factor that takes shock loads and the efficiency of the gear into account. Values of this factor for different operating conditions can usually be found in information published by the gear manufacturer.

## Belt drives

For belt drives it is necessary to take the effective belt pull (circumferential force) into account, which is dependent on the transmitted torque, when calculating bearing loads. The belt pull must be multiplied by a factor, which is dependent on the type of belt, its preload, belt tension and any additional dynamic forces. Belt manufacturers usually publish values. However, should information not be available, the following values can be used for
 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 when the distance between shafts is short, for heavy or shock-type duty, or where belt tension is high.