 # Engineering Statics: Open and Interactive

## Section9.6Journal Bearings

### Subsection9.6.1Journal Bearing Friction

A bearing is a machine element used to support a rotating shaft. Bearing friction exists between the rotating shaft and the supporting bearing. Though other types of bearings exist including, ball, roller and hydrodynamic, we will focus on dry friction journal bearings. Oil lubricated journal bearings require a knowledge of fluid mechanics to analyze, while dry journal bearings have point contact between the shaft and bearing and thus can be analyzed in Statics, they are subject to greater wear and heat build-up than other types of bearings; thus, the use of dry journal bearings is only advisable in situations where there is limited motion.

### Subsection9.6.2Rotating Shaft and Fixed Bearing

A dry friction journal bearing consists circular bearing surface which supports a rotating or stationary shaft. The support force acts at the single point of tangency of the two circular surfaces. The bearing prevents shaft motion in the radial directions but does not prevent axial motion due to shaft thrust.
Figure 9.6.1 shows a journal bearing supporting a shaft with a vertical load $$P\text{.}$$ Initially the contact point is located directly below the load along its line of action. When a clockwise moment $$M$$ is applied to rotate the shaft, friction between the shaft and bearing causes the surfaces to stick together, and the shaft climbs up the bearing surface until impending motion is reached and slipping occurs. Similarly, when a CCW moment $$M$$ is applied, the contact point will shift to the left.
Free-body diagrams for the shaft in the three cases are shown in Figure 9.6.2. At the contact points we see a normal force $$N$$ and a friction force $$F$$ which can be resolved into a single vertical resultant force $$R\text{.}$$ Normal forces are perpendicular to shaft at the contact point, which makes their lines of action pass through the center of the shaft. When no moment is applied, no friction exists, but in the other two cases, friction creates a moment $$M' = F r_f$$ about the center of the shaft which opposes the applied moment $$M\text{.}$$
The most straightforward process to relate the load, normal and friction forces for a journal bearing is by performing the following steps:
1. Assume that the shaft and bearing opening have the same radius, but draw the shaft a bit smaller to emphasizes the contact point at the point of tangency.
2. Combine the normal and friction forces into a single friction resultant force
\begin{equation*} \vec{R}=\vec{F}+\vec{N} \end{equation*}
.
3. Determine the radius of the friction circle, $$r_f\text{,}$$ which is a circle around the center tangent to the friction resultant $$R\text{.}$$ The friction circle radius is a function of the shaft radius $$r$$ and the friction angle $$\phi_\text{s}\text{.}$$
\begin{equation*} r_f = r \sin \phi_\text{s} =\tan^{-1} F/N. \end{equation*}
4. Finally, draw a free-body diagram of the shaft with all applied loads and the friction resultant $$R\text{,}$$ then solve the equations of equilibrium to find the unknowns.

### Subsection9.6.3Fixed Shaft and Rotating Bearing

Another type of journal bearing is designed with a fixed shaft and a rotating bearing. While the solution process is quite similar to the process covered above, the main difference is that you will draw a free-body diagram of the rotating bearing instead of the shaft.
Figure 9.6.3 shows the diagrams for a journal bearings with a fixed shaft and rotating bearing.