One of the most misunderstood principles regarding linear bearings is something called the 2:1 Ratio. Understanding it will help engineers avoid the problem of stick-slip.



Back in the 1980s, Pacific Bearing Co. (PBC) invented and commercialized plain bearings, which were sized to be interchangeable with linear ball bearings.

Plain bearings worked very well in certain applications—mainly those in environments that were hot, cold, or dirty, or included high vibrations, high static loads, or non-lubricated and short strokes less than twice the bearing’s length. These were just the sort of applications in which recirculating ball bearings failed miserably.

But plain bearings were quickly found to be unacceptable replacements in applications requiring low coefficients of friction, high speeds, or high moment loads. In fact, some applications with high moment loads caused plain bearings to simply bind up; all motion would cease or become jerky (also known as stick-slip motion). Early on, the assumption was that plain bearings could not handle the same moment loads as equivalently sized recirculating ball bearings.

What engineers failed to realize was that there is a geometric relationship that describe the allowable working space of plain bearings. This went unrecognized until PBC published the Binding Ratio (aka, 2:1 Ratio) in the 1990s. Two decades later, some engineers still don’t realize the scope of this rule and that it applies to all linear motion systems, not just plain bearings. They also don’t know that the Binding Ratio isn’t always 2:1. It varies with the application and can be larger or smaller than 2:1.

The Binding Ratio
The “Binding Ratio” is defined as the maximum ratio of moment-arm distance to bearing length that will not bind (prevent motion). It is often displayed numerically as X:Y, where X is the moment-arm distance and Y is bearing length. Typically, X is divided by Y so that the ratio can be expressed as X∕Y:1. It is commonly simplified to 2:1.