# Research on Adhesive Coefficient of Rubber Wheel Crawler on Wet Tilted Photovoltaic Panel
## 2 Materials and Methods  
The cleaning robot which is used to clean the accumulated dust on the glass surface of the PV panel arrays consists of three modules: two rotating brushes with a water supply and a chassis module equipped with two rubber wheel crawlers that contains an electrical enclosure and battery. The rubber wheel crawler is driven by two primary timing pulleys through a timing belt coated with rubber trackpads. The PU timing belt is supported by auxiliary free wheels that can hump when moving on the misalignment/uneven surface, thanks to the spring tensioners. The rubber wheel crawlers provide the cleaning robot the ability to move on the PV panel surfaces longitudinal to its chassis as well as rotate in place. The usage of the rubber wheel crawler enables a larger area of contact between the cleaning robot and the PV panel surface than the usage of traditional wheels, leading to increased friction force. For the slightly tilted angle of the PV panel (less than 10\({}^{\circ}\)), there is no/rarely slip on the rubber wheel crawler and the PV panel surface; the cleaning robot moves along/orthogonal to the slope of PV panels. However, when there are PV panels with a large tilted angle (over 10\({}^{\circ}\)) in wet conditions, this is a major challenge for researchers to increase the slip resistance between the rubber track and PV panel surface. According to [27, 50, 51, 52, 53, 54], the tilted angle of the PV panel varies 0\({}^{\circ}\div 60^{\circ}\) due to the geographical installation site. The larger tilted angle of PV panels leads to the lower slip resistance at the rubber wheel crawler and PV panels. There are many factors that affect the slip resistance between the rubber wheel crawler and PV panel surfaces: for instance, spring forces, the area of contact, and the weight of the cleaning robot. However, this paper mainly investigates the characteristics of the rubber materials coated on the trackpad of the timing belt to improve the slip resistance by optimizing the reaction force. Assumption:  
* There is no slip on the primary timing pulleys and the PU timing belt;
* The tensions of the PU timing belts on both sides of the cleaning robot are the same;
* The slip resistance is not affected by the direction of rotation of the broom  
Consider the cleaning robot in the stationary state on the PV panel with a tilted angle \(\alpha\) (0\({}^{\circ}\leq\alpha\leq 60^{\circ}\)), as shown in Figure 1. The cleaning robot is applied by the cleaning robot's gravity (\(\overrightarrow{P}\)), the reaction force (\(\overrightarrow{N}\)), the static friction force between the belt and the panel surface (\(\overrightarrow{F_{fr}}\)) [55, 56, 57, 58, 59, 60], and the elastic force of the timing belts (\(\overrightarrow{F_{E}}\)). According to the no-slip condition, the greater the static friction, the larger the slip resistance. On the other hand, the static friction force must be larger than the cleaning robot's gravity to ensure the no-slip condition of the cleaning robot. \[\overrightarrow{F_{fr}}\geq\overrightarrow{P} \tag{1}\]  
Figure 1: Force analysis in the no-slip state and zero acceleration. With the tilted angle \(\alpha\) of the PV panel, the amplitude of the cleaning robot's gravity projected into the shopfloor is calculated by the term of \(P\sin\alpha\). The amplitude of the static friction force is a product of the coefficient of friction (\(\mu\)) and reaction force (\(N\)) [61; 62]. Equation (1) described the adhesive condition between the rubber track and PV panel surface. \[\mu N-P\sin\alpha\geq 0 \tag{2}\]  
It can be seen from Equation (2) that the adhesive condition depends on the reaction force (\(N\)). The larger the reaction force, the higher the slip resistance. It is evident that the reaction force increases as the cleaning robot's weight increases; however, this is impossible because the weight of the cleaning robot should be minimized to avoid the overload of the PV panel. Figure 2 describes the equivalent model of the rubber trackpad coating belt.