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Linear Bearings: Load/Life Calculation

Linear bearings undergo reciprocating rather than rotary motion so that accelerations are much higher than typically experienced by rotary bearings. Since linear bearings have become important primarily as a result of robotic automation, one must often refer to manufacturer's literature for load/life formulas.

What follows is one way to calculate the life of a linear slide bearing. The symbol L is used to represent the rated life. It is defined as the length of travel endured by the slide under a specified condition. In reality, slide life varies from one slide to another, so that a rating referred to as L10 is typically used in industry. The L10 rating is defined as the length of travel that 90% of all slides (of the same model) will complete before the first sign of failure.

The following factors are used in the calculation of load/life predictions:

1. Factor for Speed

 
where  V =  the speed of the relative carriage/base movement in inches/minute
(use the peak speed value).
  m =  3 for ball slides, 3.3 for roller slides.
NOTE: When the speed is less than 30 inches/minute, fs = 1.

2. Factor for Temperature

Excessive temperature can reduce the hardness of load-bearing slide components and lower the life of the slide due to wear and fatigue. We define the factor for temperature of the slide as "ft" and values are tabulated in the following table. Please note that ft is listed assuming that polymer ball separators are not used. Delrin separators can typically only withstand temperatures less than 180ºF.

Temperature (°F) Factor for Temperature "ft" Hardened Carbon Steel Contacting Elements Factor for Temperature "ft" Stainless Steel Contacting Elements
220 1 1
300 .9 1
400 .75 .9
500 not recommended .75

3. Factor for Load Type

The load endured by a linear slide bearing is a combination of variable forces, vibrations, impacts, occasional loads, etc. We use the load type factor "fw" to account for these varying forces. The values for "fw" are tabulated in the following table.

Load Condition Value of "fw"
Smooth Motion without Impacts 1 to 1.5
Motion with Significant Shock Impacts 2 to 3

Using the factors just defined, the L10 life rating can be expressed as follows:

 
where  L10 =  the life of the slide at 90% of reliability (as defined above in inches)
  C =  catalog "load capacity" of the slide in lbf. (which is a load that corresponds to an L10 life of 10 million inches, provided the factors fs, ft and fw are equal to 1.
  Pc =  calculated effective load that the slide experiences in lbf. (fs, ft and fw are factors as described above.)
  m =  3 for ball slides, or 3.3 for roller slides.

4. Factor for other than 90% Reliability

If other than the 90% reliability is required, the known value of L10 shall be multiplied by a reliability factor "fr" such that:

Ln = fr × L10
where Ln = rated life at the reliability of K% (n = 100 - K).

The values of the factor "fr" are presented in the following table.

Reliability, % "Ln"
rated life
"fr"
reliability factor
50 L50 5.00
90 L10 1.00
95 L5 0.62
97 L3 0.44
99 L1 0.21

Adding the "fr" factor in front of the previous equation, the L10 life rating can be expressed as follows, with each factor remaining as before.
 

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