February 21, 2012 - Rockford, IL- Simplicity® self-lubricating linear bearings work well in cantilevered load situations when specified design guidelines are followed. Use these formulas and examples when using Simplicity bearings with a cantilevered load.
Maximum Ratio - 2:1
1X = bearing separation on same shaft
2X = distance from shaft to load or force
Example: If 2X equals 10” then 1X must be at least 5”
CAUTION: Binding will occur if the 2:1 ratio is exceeded!
Note: This principle is NOT load dependent. It is NOT due to edge loading. It is also NOT dependent on the driving force used. The bearings will bind whether hand or mechanically driven. The 2:1 principle for linear plain bearings and the resulting binding is a product of friction.
Working through the following equation will explain why this is a product of friction:
P = force being applied
L = distance out from shaft that P is being applied
s = center to center spacing of bearings
f = resultant force on bearings by shaft
F = friction force on each bearing
µ = coefficient of friction (about 0.25 when not moving)
Balance the Moments: f * s = L * P
L / s = f / P
Compute Friction Force: F = f * µ
Note: Total friction force pushing up is 2 * F. To lock up the slide, the total friction force must be equal to (or greater than) P.
P = 2 * F = 2 * f * µ
Substitute for P: L / s = f / ( 2 * f * µ ) = 1 / ( 2 * µ ) = > L / s = 1 / ( 2 * µ )
Note: The forces drop out of the equation
Assume static coefficient of friction is 0.25 (µ = 0.25) then L / s = 2. That is the 2:1 ratio.
There are many other factors that add to the braking effect, but the coefficient of friction is the main cause.
Note: Added lubrication can help to drop friction and extend the 2:1 ratio.
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