There are few linear motion applications where the load is perfectly centered on the support bearing. On the other hand, most applications involve cantilever loads, meaning they are displaced from the bearing and induce a momentary load.
In this context, the term “bearing” can mean a single bearing or a system of bearings, for example two rails in parallel, with two bearings each, which together support a load.
The moment caused by a cantilever load (or driving force) produces two reaction forces on the bearing of equal and opposite magnitudes. These reaction forces, multiplied by the bearing's coefficient of friction, determine the frictional forces that oppose the bearing's movement. For the bearing to move, the driving force must be greater than the frictional forces; otherwise, binding or lack of movement will occur. The solution to overcoming the constraint is not to apply a greater driving force.
The solution lies in what is commonly called the 2:1 ratio (also known as the “2:1 rule” or “binding ratio”).
The 2:1 ratio is the relationship between the length of the bearing and the distance the cantilever load (or driving force) is from the bearing. In reality, the 2:1 ratio is not always 2:1. As shown by the equation below, the acceptable relationship between moment arm distance (D 1 ) and bearing length (L 1 ) that will prevent seizure depends on the bearing friction coefficient (μ).
Using the generally accepted coefficient of friction of 0.25 for plain bearings, the ratio is 2:1. If the coefficient of friction is lower, for example 0.10, the ratio will be 5:1. And if it is greater, by 0.50, for example, the proportion becomes 1:1.
This is why recirculating bearings rarely have bonding problems with cantilever loads: their coefficient of friction is usually around 0.001, so the acceptable ratio of moment arm distance to bearing length is 500:1.
As mentioned above, when the 2:1 ratio is exceeded, applying more driving force will not cause the bearing to move. The only ways to counteract the restriction are to 1) reduce the moment arm distance, 2) increase the bearing length, or 3) reduce the coefficient of friction.
An important design guideline for plain bearing systems is the following: When two rails or shafts are used (as in the 2-rail, 4-bearing arrangement shown below), the rail-mounted bearings are closest to the load cantilever ( or drive). driving force) must be fixed and bearings mounted on the rail furthest from the cantilever load (or driving force) must be floating. The fixed floating arrangement allows the bearing system to compensate for minor misalignments and helps prevent unnecessary wear.
In a 2-rail, 4-bearing arrangement, the two bearings closest to the cantilever load or driving force must be fixed and the other bearings must be floating.
