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Ball bearings – Load distribution for rolling bearings
Ball bearings and other rolling bearings are installed in numerous machines. The installed bearings transfer the radial or axial forces that occur to the machine housing and thus permit the use of various moving components. The forces that occur and the resulting load in the bearing must already be determined during the design process. The load distribution in the bearing and the matching contact point geometry is crucial for the expected service life, function and efficiency of the bearing. In this article, we will look at the load exerted on a rolling bearing and how contact surface geometry affects load distribution in the rolling bearing.
Roller bearings fundamentals
Rolling bearings are rotary bearings that guide moving parts in relation to each other and brace them against the surrounding components. During this process, they absorb forces and transfer them as a connecting element between dormant and moving components. Their main functions are to carry and guide the components moving relative to each other. Not insignificant forces are in this case exerted on the surfaces of the rolling bearing and the rolling elements.
Loads exerted on rolling bearings on component contact
The main load of rolling bearings is usually perpendicular to the contact plane. This load concentrates within the rolling bearing on comparatively small contact surfaces between the rolling body and the inner or outer ring. The incident forces lead to a surface compression, which depends, among other things, on the shape of the race and rolling body and also on the force direction and number of rolling elements under load at the same time. The resulting surface compression affects the service life and wear, and also the maximum allowable load capacity of the bearing. For better appreciation, the extent of the compression in the pressure-bearing surfaces can be determined using the Hertz equations.
Hertz compression describes the local pressure distribution that occurs at the contact surface of two curved bodies under load. Using the calculations, the pressure-bearing surface area, deformation and surface load can be determined. For the ideal calculation, the following conditions are assumed: a linear-elastic material behavior, the contact surfaces are comparatively small, contact is friction-free, and pressure is exerted vertically. In practice, these conditions are not always precisely met in rolling bearings, but the Hertz formula still provides sufficiently accurate results to assess maximum area compression. On the basis of these, rolling bearings can be designed better and the maximum load for ball bearings can also be determined.
Impact of contact surface geometry on load distribution
The geometry of the contact surface changes depending on the race geometry and the types of rolling elements used. It has a direct influence on load distribution. For example, a so-called point contact forms for balls, while a line contact forms for cylindrical rolling elements. The point contact leads to a compression under load. Both the ball and the track deform elastically. This deformation creates an elliptical contact surface with different compression distribution. The compression is at its maximum (maximum deformation) in the center of the contact surface created by the deformation and then decreases outward.
The point contact occurring in the grooved ball bearing creates a comparatively high surface compression. Cylindrical roller bearings or barrel bearings are therefore more recommended for high radial loads. The line contact of cylindrical rolling elements distributes the pressure over a larger area. The rolling elements and races deform even with cylindrical roller bearings under load. Due to the shape of the rolling elements, the compressive load ends abruptly at the ends of the rolling elements, so that pressure peaks occur at these points.
Drum rollers are for example used to avoid the abrupt discontinuity of the compressive load. For symmetric drum rollers, the outer surface is slightly curved over the length of the cylinder, which creates an elliptical pressure distribution. For non-symmetrical barrel bearings, the compressive load shifts minimally towards the larger curvature. This for example permits compensating for misalignments.
Other rolling element types with line contact include the tapered roller and the needle-shaped rolling element. The load direction on a tapered roller corresponds to the taper angle. Both axial and radial loads can be accommodated. The misalignment also permits absorbing particularly high combined loads. For needle-shaped rolling elements, the pressure peaks at the end are minimized by the extended line contact thanks to the needle shape.
Instructions for designing ball bearings
The design of the bearing significantly influences the function and service life of ball bearings. The relative movement of a bearing ring can have a negative effect on the service life. The movement is frequently caused by incorrect assembly: The bearing ring is not aligned correctly or is not secured properly. During installation, it is therefore essential to ensure that the roller bearing fastening of the rings (inner ring and outer ring) and also the washers on the axle or housing bore are properly installed. Do not allow these to slip under load.
But not only an overly loose installation, but also an excessively tight installation can have negative consequences: If bearing rings are too tight or deformed due to excessive force during assembly, this leads to an uneven load distribution. Load spikes may occur resulting in premature failure of the material and the risk of cracking. A deformed bearing ring may create new contact surfaces for friction and heat generation, which also negatively affects service life.
In addition to ensuring the correct fit, the desired load type should also be defined before installation. Alternatively, one can assess what type of load the ring will be exposed to. The load type defines how the bearing ring is secured or moved relative to the load source and which bearing seat to select. There are the following types:
- Circumferential load: A circumferential load on the bearing occurs when the ring is running relative to the load direction. The entire ring is stressed once during the revolution. If the seat is loose, the ring can migrate, so a tight seat should be selected.
- Point load: A point load on the bearing occurs when the ring is positioned relative to the load direction. The same point is consistently under load. Even when the seat is loose, the ring does not migrate.
The following table shows different load cases of radial bearings:
| Load case | Simplified scheme | Description | Adjustment |
|---|---|---|---|
| Outer ring: Point load |  |
Inner ring: circumferential Housing and load: stationary |
fixed fit: inner ring loose fit permitted: outer ring |
 |
Inner ring: stationary Outer ring: Housing and load: circumferential |
||
| Inner ring: Point load |  |
Shaft and load: stationary Outer ring circumferential |
fixed fit: outer ring loose fit permitted: inner ring |
 |
Shaft and load: circumferential Outer ring: stationary |
Both load types have different applications. In most cases, however, the circumferential load will be the intended uniform load sharing option. Tolerances for bearings and bearing seats in general can be found on our ISO fits and tolerances for shafts and bores blog.
Design-based solutions for floating and fixed bearings
For rolling bearings, there are two common bearing configurations: Floating bearings and fixed bearings. Fixed bearings are designed to absorb radial and also axial forces. Locking the shaft in the axial direction prevents it from moving. Suitable fixed bearings include double-row angular contact ball bearings. Floating bearings are used exclusively to absorb radial forces. Both bearing types are usually arranged such that they can ideally absorb these loads and compensate for thermal changes in length of the supported shaft or housing. Suitable floating bearings include cylindrical roller bearings and needle bearings. The roller sprocket can move along the race of the ribless bearing ring.
The following two figures show the different load distribution when installing a groove ball bearing with different preload (fit):
A minimum of two bearings should be used to support a shaft. Such multiple bearings consist of a fixed bearing and any number of floating bearings. The floating bearings of a rotating shaft are designed to absorb radial forces while allowing axial movement. Thus, the thermal expansion of the shaft and housing can be balanced.
The following instructions apply when designing the bearing and fit:
- Check shaft alignment: For a shaft offset, oscillating bearings are an option (in the compensation range of the oscillating bearing).
- Ensure optimal load distribution and even distribution on the rolling elements (the rings must not slip in the circumferential direction, take into account fixed and floating bearings).
- Ensure runout and planarity.
Influence factors on the performance and service life of rolling bearings
In addition to correct installation, other parameters affect the performance and service life of ball bearings and rolling bearings. As already mentioned, the dynamic load distribution of the bearing also has an influence. Below we will look at the dynamic load rating for bearings and ball bearings as well as the static load rating in detail. We will also show how to calculate the dynamic and static load rating for bearings. We will then also briefly consider temperature as an example for further influencing factors.
Influence of dynamic and static load rating
Ball bearings can be described by the dynamic and static load rating. The dynamic load rating C is used to calculate the nominal service life of a bearing under the influence of a load X. The standard according to ISO 281 is that the bearing is in use for at least 1 million revolutions. The static load rating C0 in turn indicates the maximum load that can be exerted on the bearing at rest without permanent deformation (or a maximum deformation of 1/10000). The higher the dynamic load rating, the higher loads that can act on the bearing in operation. The higher the static load rating, the better the bearing is protected from deformation under heavy loads.
The dynamic load rating is usually specified by the manufacturer. The dynamic bearing load is calculated, which is then compared to the dynamic load rating. The dynamic bearing load is calculated as follows:
P = X \times F_{r} \times F_{a} \times Y
- P = Dynamic bearing load in N
- Fr = radial force in N
- Fa = axial force in N
- X = radial load factor
- Y = axial load factor
- The load factors X and Y depend on the selected bearing type and the ratio of Fr and Fa (usually manufacturer's specifications)
The dynamic load rating C should be greater than or equal to the determined dynamic bearing load P, otherwise there is a risk of overloading the bearing. The static load rating C0 can be calculated as follows:
C_{0} = P_{0} \times S_{0}
- C0 = Static load rating in N
- P0 = Equivalent static bearing load
- S0 = Static load-carrying safety factor, depending on operating mode and smoothness requirements
The bearing load is affected by different temperatures. High temperatures reduce the material strength of rolling elements and races. For this purpose, there are downgrading factors that must be taken into account for uses at higher temperature conditions when designing rolling bearings.
