If you have already clicked through the texts on the calculation principles for linear guides and screw drives on linearwizard.com, you will already know that various factors and formulas must be taken into account when designing linear systems. This is no different for ball bushings, which is why you will find everything that is important for their calculation in this article. The topics range from tolerances, load ratings, the static safety factor, maintenance and lubrication to the calculation of the nominal service life.
Tolerances
With ball bushings, the amount of clearance on the shaft must always be considered. Depending on which standard the ball bushings comply with (ISO or JIS), the enveloping circle tolerance of the ball bushing varies. For the same shaft fit, as can be seen in the table using the example of a ball bushing ⌀ 20, the radial clearance varies. Due to the different standards on which ball bushings can be based, preload and clearance are possible on the same shaft. This means, for example, that one ball bushing can tilt due to clearance, while another runs completely without clearance or with preload. It should also be noted that ball bushings are generally less suitable for applications that require preload; in such cases, linear guides are a better alternative.
Load ratings
Both the static and dynamic load ratings of ball bushings are calculated in accordance with DIN ISO 14728-2. The static load rating C0 describes the constant axial load that generates a total plastic deformation of 0.00001 times the ball diameter.
The dynamic load rating Ca refers to an axial load that is not variable in size and direction and at which a ball bushing achieves a nominal service life of 5 x 104 meters.
The static safety factor fs
For ball bushings, it is also important to calculate the static safety factors fs in order to avoid impermissible plastic deformations caused by load peaks. These events, which are difficult to predict, occur due to impacts and blows to the ball bushings, for example.
The static safety factor fs is the ratio of the static load rating C0 to the maximum occurring load F0max . This refers to the highest amplitude; even very short-term amplitudes are considered. The function of the static safety factor fs is to prevent impermissible plastic deformation of the raceways and rolling elements.
To calculate the static safety factor fs , the static load rating must be divided by the maximum equivalent load. The value of the static load rating can be influenced by three additional factors, the contact factor fc , the hardness factor fH and the temperature factor fT .
Formula 9
![\[f_s=\frac{f_H\times f_T\times f_C\times C_{0}}{F_{\mathrm{max}}}\]](https://linearwizard.com/wp-content/ql-cache/quicklatex.com-74042e4a00850aee18c92022ae743e60_l3.png "Rendered by QuickLaTeX.com")
| fs | Static safety factor |
| fc | Contact factor |
| fH | Hardness factor |
| fT | Temperature factor |
| C0 | Static load rating [kN] |
| Fmax | Maximum equivalent load [kN] |
The formula for the static safety factor fs is identical, regardless of whether you calculate it for ball bushings or linear guides.
The contact factor fc is used if several ball bushings are located at a small distance from each other. In this case, it is assumed that not all ball bushings can absorb the same load due to assembly tolerances. It must therefore be assumed that the load absorption is generally lower than theoretically possible.
The hardness factor fH changes the static load rating if ball bushings are made of a material that does not achieve the same hardness as rolling bearing steel. This applies to stainless steel, for example.
temperature factor fT in turn, is used at operating temperatures above 100 °C. At temperatures above this limit, the hardness of the steel of the ball bushings decreases.
The nominal service life L
The nominal service life L bdescribes the mileage that a ball bushing covers before the first signs of material fatigue appear. It is generally calculated in meters. The same formula is used here as for calculating the service life of linear guides; this is based on a calculation of 5 x 104 meters. In practice, however, the service life of ball bushings is rarely calculated.
Formula 10
![\[L = \left( \left(\frac{f_H \times f_c \times f_T}{f_w} \times \frac{C}{F_m}\right)^3 \times 5 \times 10^4 \right)\]](https://linearwizard.com/wp-content/ql-cache/quicklatex.com-439891f33e707e1c814e47252b42acfa_l3.png "Rendered by QuickLaTeX.com")
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Two birds with one stone: You only need to know one formula to calculate the service life of linear guides and ball bushings.
It is important to note that the operating conditions play a central role in the design of fw factor. The intensity of vibrations and shocks is of particular importance. A distinction is made between five levels and the more challenging the environmental conditions, the higher this load factor must be.
Operating conditions | Speed (m/s) | Load factor |
No or very low vibrations and shocks | ≤ 0.25 | 1.0 … 1.2 |
Low vibrations and shocks | 0.25 … ≤ 1.0 | 1.2 … 1.5 |
Medium vibrations and shocks | 1.0 … ≤ 2.0 | 1.5 … 2.0 |
Strong vibrations and shocks | >2 | 2.0 … 3.5 |
Short-stroke applications | 3.5 … 5.0 |
The factor fw considers the presence of oscillations and vibrations and their negative influence on the service life of ball bushings.
As an alternative to the “meter“ unit, the nominal service life L10 can also be converted into hours (Lh) and cycles (L#). These two units are calculated as indicated.
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|
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| Lh | Nominal service life (m) | L# | Nominal service life (cycles) |
| s | Stroke (m) | s | Stroke (m) |
| n | Number of strokes (min⁻¹ ) | ||
![\[ L_h = \frac{L}{2 \times s \times n \times 60} \]](https://linearwizard.com/wp-content/ql-cache/quicklatex.com-79acd1cfcbb28e8ab476b2346b52d8bd_l3.png "Rendered by QuickLaTeX.com")
![\[L\# = \frac{L}{2 \times s} \]](https://linearwizard.com/wp-content/ql-cache/quicklatex.com-3ffbd11ea620c0208cd23545d16b3809_l3.png "Rendered by QuickLaTeX.com")
Maintenance and lubrication
As you may have already read in the article on the variants of ball bushings, most ball bushings do not offer the option of relubrication. If this is necessary, however, there are three lubrication types to choose from; lubrication is then possible either via a grease gun, an automatic lubricator or centralised lubrication systems or oil mist lubrication, whereby centralized lubrication systems or oil mist lubrication are used extremely rarely due to the very low lubricant requirement. The relubrication intervals and relubrication quantity must also be determined depending on the ambient conditions. The choice of the right lubricant is also of great importance – it must be noted that ball bushings must never be lubricated with a lubricant containing solid lubricants, as this very quickly leads to blockage of the ball recirculation and thus to failure of the ball bushings!
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