# Development of Vibration Control Structure on Suspended Ceiling Using Pulley Mechanism
## 3 Component Details of the Pulley-Damper System  
### Friction Test of the Pulley Sheaves  
A friction test was conducted to evaluate the friction coefficient of pulley sheaves. A stainless wire-cable comprises 7 \(\times\) 19 strands with 2.75 kN braking force, and 2.0 mm in nominal diameter was selected. The tensile force of the wire-cable during excitations was monitored through strain gauges placed on either side of a copper plate after the calibration in Figure 4. A triple pulley was used in this study as a deviator of wire-cable to smoothly transmit the ceiling displacement to the damper (Figure 5a). The pulley consists of three sets of a sheave of 30 mm in internal diameter, with a ball bearing inside.  
Figure 3: (**a**) Configuration model; (**b**) equivalent truss model.  
The purpose of this test is to discover the friction coefficient per sheave to predict friction force in the following shake table test and simulate it in the following simulation analysis. In this study, the friction coefficient \(\mu\) per sheave was estimated by dividing the mean friction force, \(F_{f}\), by the number of touched sheaves, \(N\), and pre-tension force, \(T\), as follows:  
\[\mu=\frac{F_{f}}{N\times T} \tag{10}\]  
Table 1 summarizes the three test cases for the friction test. The parameter in this friction test is the pre-tension force of the wire-cable and the number of wire-cable loops. Figure 6 shows the specimen view for the friction test. A steel test frame was prepared, and a movable pulley is hung from the top. The generated friction force when the movable pulley went up and down was calculated from the difference of the tensile force between the two strain gauges.  
Figure 7a-c shows the force-displacement loop. The horizontal axis represents the movable pulley displacement, and the vertical axis represents the friction force, which comprises the overall activated sheaves. In all cases, if the number of loops stayed constant, the maximum friction force got larger as the initial tension increased. The friction coefficient was calculated from the displacement range as \(\pm 5\) mm, using Equation (10). As Figure 7d shows the relation of the friction coefficient and the pre-tension force on the wire-cable,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Test Case** &
\begin{tabular}{c} **Number of Loops** \\ **(Activated Sheaves)** \\ \end{tabular} & **Pre-Tension Force** \\ \hline No.1 & 2 (5) & 30 N \\ No.2 & 3 (7) & 40 N \\ No.3 & 4 (9) & 50 N \\ \hline \hline \end{tabular}
\end{table}
Table 1: Information on the friction test.  
Figure 4: (**a**) Installation of the tension measuring plate at the end of the wire in the specimen; (**b**) details of the tension measuring plate.  
Figure 5: (**a**) Overview of the pulley; (**b**) details of the fixture between pulley and ceiling runners.  
the coefficient stays constant and the results of the average friction coefficient in this test were 0.014.  
Figure 6: Test setup for characterizing friction behavior under sinusoidal wave excitation.  
Figure 7: Experimental results of the pulley-friction test: (**a**–**c**) Force–displacement relationship under different number of the wire-cable loop and (**d**) friction coefficient with the average value.