A Sliding bearing makes a contact force between the beam node and the sliding bearing. The shaft is represented circular surface with the centerline polynomial and radius. The sliding bearing is represented a point set with mesh size. The contact force is consisted with spring, damping and friction force under the sliding. Higher order polynomial or multiple piecewise polynomials can be used to represent the centerline of shaft.

Figure 14.217: Polynomial of Shaft Set nodes

First the node distance is examined from the geometry reference frame of sliding bearing.

At least, one of three nodes must be located within sliding guide.

Figure 14.218: Distance between shaft node and sliding bearing

(14–43)

Second, a point of sliding bearing must be located within two beam elements.

Figure 14.219: Candidate node for contact force

(14–44)

Third the contact condition should be satisfied as following equation. This equation will be solved with NR method.

Figure 14.220: Candidate node for contact force

(14–45)

(14–46)

(14–47)

The contact normal force can be calculated as follows.

(14–48)

Two friction forces are calculated as follows.

(14–49)

(14–50)

The total contact force is calculated as follows.

(14–51)