I'm trying to find the static and dynamic loads that the linear ball bearings on the cnc machine I'm helping design will undergo. What I'm trying to do right now is set up an equation in words that I can solve when I get the necessary variables. I see the equation for linear plain bearings is
(Static Load/(Bearing Length * Shaft Diameter)) * velocity
for dynamic loading, but I assume this same equation will not apply for open linear ball bearings.
If there is any confusion, I can try to clarify
you are right in assuming there is something else going on. the equation you described is to calculate the PV of the bearing. where you have the pressure that the bearing cross section is exposed to multiplied by the velocity of the bearing. you calculation might give you a PV of 20000, and you know your fine if you bearing material is rated for 50000. this is all based on wear rates and lubrication conditions.
Rolling element bearings are something different entirely. without going into allot of theory, the rolling element be it a ball or roller deflects against the bearing race, in much the same way a tire deflects against a road. this deflection causes fatigue in the metal of the balls and of the race. Thus the greater the load the less cycles it takes to destroy the bearing. this of course is ignoring a load that would permanently yield the ball or race. the dynamic load rating of a bearing is calculated using empirical formula based on the manufacturers experience and is found in the catalog of the manufacturer. for your purposes it is necessary to know what the manufacturer has based there dynamic load rating on. an example would be 6000 lbs of load at 1000000 inches of travel. or 6000 lbs of load at 1000000 revolutions (for a regular ball bearing). The units very of course. it is just important to know what the manufacture is basing their dynamic load rating on.
once the units are worked out you can describe the relationship of the load vs life with the following two formulas:
L = (C/P) ^3 - for Ball elements
L = (C/P) ^10/3 – for Roller elements
L = Bearing Life (travel length, or revolutions)
P = Equivalent Load (specific to the direction that the baring is designed)
C = Dynamic Load capacity of the bearing
using these formula you can predict, if every thing is perfect, how long the bearings will last. Or at least you chanses are good (usually based on 90% survival rate at specified load at specified life)
hope this helps