# Research on Adhesive Coefficient of Rubber Wheel Crawler on Wet Tilted Photovoltaic Panel
## 3 Experimental Study  
The logic of this study has the sequence of first including the introduction of the theoretical model. Then, some parameters of this model are obtained through experiment and computational theory. Finally, the relationship between the shore hardness, adhesive coefficient, and the maximum tilted angle of PV is established by simulation studies. A prototype of a rubber wheel crawler is made and equipped with a PV cleaning robot, as shown in Figure 6. The rubber wheel crawler comprises a seamless polyurethane (PU) timing belt with a T10 tooth profile, which runs over two-timing pulleys. The PU timing belt is 75 mm wide, of length 1690 mm, and it has a rubber coating with a cuboidal back-profile to gain the adhesive coefficient of the robot on the slippage surface of PV. The physical parameter of the rubber wheel crawler is designed as shown in Table 1. The PV cleaning robot, which is 80 kg in weight, is designed to move on the tilted angle PV of \(0^{\circ}\div 45^{\circ}\). Figure 5: The displacement (\(\Delta L\)) of rubber track belt. Figure 6: Prototype of PV cleaning robot. To compare the adhesive coefficient of the coating material, there are two types of rubber materials that are utilized to coat the PU timing belt, which are known as red rubber and synthetic rubber. Both types of rubber wheel crawlers are equipped with the PV cleaning robot for working on the same testing conditions. The shore hardness of both types of rubber is verified by a durometer. The tilted angle of the PV panel can vary \(0^{\circ}\div 45^{\circ}\), which is measured by an inclinometer, while it is moistened by the stable water flow supply. The PV cleaning robot is required to move on the PV panel transversely with a travel length of 5 m for every \(5^{\circ}\) increasing the tilted angle PV. The slippage state of the PV cleaning robot on the PV surface is defined as the robot being shifted longitudinally to the PV panel by at least 10 cm, which is measurable by using a laser alignment tool. By conducting experiments on the synthetic rubber track belt with the shore hardness of A35 and the maximum tilted angle of \(25^{\circ}\), the coefficient of friction for the case of using a synthetic coating is determined through Equation (5) as follows:  
\[\mu_{syn}\approx\frac{P\sin\alpha}{P\cos\alpha-K\Delta L}=0.5275 \tag{20}\]  
By recalling Equation (6) and assimilating with Equation (20), the range of \(x\), \(y\) of Equation (6) is determined by referring to the reference [64]:  
\[\left\{ \begin{array}{l}1.1431<y<2.0494\\ -0.0435<x<-0.0176\end{array} \right. \tag{21}\]  
The values of \(x\), \(y\) are approximated as follows:  
\[\mu_{syn}\approx-0.0305S+1.5963 \tag{22}\]  
In the same manner, the coefficient of friction for the case of using a red rubber coating with the shore hardness of A40 and the maximum tilted angle of \(15^{\circ}\) is determined by  
\[\mu_{syn}\approx-0.0315S+1.5578 \tag{23}\]  
For each tilted angle increment and different materials, there exists a certain shore hardness in such a way that can seek the optimal adhesion. Similarly, for each certain shore hardness, there exists a maximum tilted angle value that the cleaning robot can move without slippage. By using Equations (5), (14), (19) and (22) and referring to Table 1, it can be easy to verify the robot slippage through the below equation:  
\[\big{(}P\cos\alpha-\big{(}\int_{0}^{t_{max}}\int_{0}^{u_{max}}\frac{K_{LB}A}{ lw}dwd\big{)}\Delta L\big{)}(-xS+y)-P\sin\alpha\geq 0 \tag{24}\]  
The cleaning robot can move on the PV surfaces without slippage if Equation (24) is satisfied; otherwise, it might be slipped. For a given shore hardness, there exists a maximum tilted angle in such a way that Equation (24) is satisfied. Once the shore hardness is increased, the tilted angle of the PV that the cleaning robot can move without slippage decreases. Figure 7 illustrates the