Alternatively, if we assume that there is no rope slippage over the pulley surface, the pulley instead tends to rotate about its axle.

As shown in Figure 9.2: Pulley with Axle Surface Bearing Friction, the radiuses of the pulley sheave and axle are not the same (). In this case, without considering the inertia force on the pulley, the total reaction force and moment about the axle center should be null, for example

(9–6)

where is the average bearing friction coefficient of the pulley axle.

Figure 9.2: Pulley with Axle Surface Bearing Friction

If the tension ratio is defined as an input pulley property when the equivalent average bearing friction coefficient can be determined by

(9–7)

The reaction force and pulley line end tensions on a pulley system may then be evaluated from the given attachment points and pulley axle center location at the current time step or iteration stage.