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Rotary Bearing: Load/Life Calculation

As we have seen, rotary antifriction bearings are manufactured in a variety of configurations. What we present here is a method for deciding upon a configuration, and then sizing a rotary antifriction bearing. First, we look at a rule of thumb for friction-limited speed of such a bearing.

Friction in rotary bearings: A rule of thumb
Friction in rotary bearings generates heat which can eventually destroy the bearing. With friction in mind, a common rule of thumb used for the allowable speed of ball and straight roller bearings is:

( B + D ) · n/2 < 500,000
Where  = bore diameter in millimeters
= outside diameter in millimeters
= speed in rpm

Selection of an antifriction bearing for a particular application:
We now look at one method for selecting a rotary antifriction bearing given a load/life specification. The following table gives a qualitative overview of the characteristics of each rotary antifriction bearing type. We use this table to select the configuration of the bearing.

Rearing Type Direction of Load Ratio of Load/Bulk Misalignment Capacity
radial axial both high med low high med low
Thrust Ball   y     y       y
Deep Groove Ball y   y   y     y  
Cylindrical Roller y   certain types   y       y
Needle Roller y     y         y
Tapered Roller y y y   y       y
Self-aligning Ball y  y     y y    
Self-aligning Spherical Roller y   y   y   y    
Angular Contact Ball   y y     y     y

Now that we have decided upon the bearing type, we can move on to the more quantitative issue of sizing the bearing. Two metrics that are needed for bearing specification are the static and dynamic load capacities. Static load capacity can specify the bearing if rotational speed is slow, intermittent, and/or subject to shocks. Dynamic load capacity is used when the bearing rotational speed is smooth and relatively constant.

Static Load Specification:

The axial and radial forces acting on the stationary rotary bearing determine the Basic Static Load Rating listed in bearing catalogs. When there are both axial and radial loads on a bearing, the combined static load can be found as follows.

Fstatic = Xsrad · Fsrad + Xsax · Fsax
If only radial forces act,
Fstatic = Fsrad
Where  Fstatic  = The combined, equivalent static bearing load
Fsrad  = The static radial load
Fsax  = The static axial load
Xsrad  = The static radial factor (dimensionless)
Xsax  = The static axial factor (dimensionless)

The basic static load rating coefficient, Co, can be obtained from:

Co = So · Fstatic
Where  Co  = The basic load rating
So  = The static safety factor (dimensionless)
Fstatic  = The combined, equivalent static bearing load

Values of So depend upon the requirements for low-noise operation and the type of bearing, as shown in the following table.

Static Safety Factor (So) Guidelines
Loading Type Noise Irrelevant Normal Operation Quiet Operation
ball roller ball roller ball roller
Smooth Loading 0.5 1 1 1.5 2 3
Normal Loading 0.5 1 1 1.5 2 3.5
Shock Loading > 1.5 > 2.5 > 1.5 > 3 > 2 > 4

If the bearing is stationary for extended periods or rotates slowly and/or intermittently and is subject to shock loads, then the selection is based upon this basic load rating. Values of basic load rating, Co, for each bearing are quoted in the bearing catalogs.

Dynamic Load Specification:
The dynamic load specification of a rotary bearing is dependent on both the dynamic and static forces acting upon the bearing. Therefore, please first calculate the Static Load Specification as outlined above. Axial and radial static forces multiplied by dynamic factors combine to form the equivalent dynamic bearing load, which is calculated as follows.

Fdyn = Xdrad · Fsrad + Xdax · Fsax
Where  Fdyn  = Equivalent dynamic bearing load
Fsrad  = Static radial load on bearing
Fsax  = static axial load on bearing
Xdrad  = radial dynamic factor (dimensionless)
Xdax  = axial dynamic factor (dimensionless)

When Fsax = 0 or is relatively small up to Fsax/Fdyn = e (The values of Fsrad, Fsax, and e are given in the Rotary Bearing Data) then

Fdyn = Fsrad

Since we have calculated the equivalent dynamic bearing load we can now compute the bearing dynamic load rating, which is used to select the bearing. Catalog dynamic load rating values should be chosen higher than the computed value for safety.

The catalog-listed dynamic load ratings are dependent upon both the equivalent dynamic load and the required bearing life. The ISO equation for the basic rating life is:

Where  L =  basic rated life (millions of revolutions)
C =  basic dynamic load rating
P =  equivalent dynamic bearing load
m =  exponent in the life equation,
m = 3 for ball bearings
m = 3.3 for other bearings.

Basic Rated Life of Bearings:
The basic rated life is defined as the number of revolutions that ninety percent of a group of identical bearings would be expected to achieve. It is determined via the life required of the bearing. Typical life requirements for various machine categories are listed below.

Machine Usage Type Life Required of Bearings (Hours)
household appliances — intermittent use 300 - 3000
hand tools, construction equipment — short period use 3000 - 8000
lifts, cranes — high reliability for short periods 8000 - 12000
8h/day gears, motors — full day partial use 10000 - 25000
8h/day machine tools, fans — full day full use 20000 - 30000
continuous use 40000 - 50000