## 2 Materials and Methods
### Material Parameter Calibration
#### 2.3.4 Determination of the Coefficient of Friction  
The friction coefficient, as a critical parameter characterizing the frictional properties between material surfaces, is primarily determined by key factors including surface topography characteristics, material properties, ambient temperature, and normal load [20]. This study employs the inclined plane method to measure the static friction coefficients of raisins and various foreign objects [21]. Prior to experimentation, a measurement apparatus was constructed using aluminum alloy and positioned on a horizontal plane to ensure ideal horizontal orientation. The static friction coefficient between raisins and 304 stainless steel was measured first. The test sample was placed on the stainless steel surface with one end of the measurement plate secured. The inclination angle was gradually adjusted using an angular regulation device, and the critical angle was recorded immediately upon observing the initiation of sample sliding, as illustrated in Figure 15.  
To determine the frictional characteristics between raisins and foreign objects such as stems, branches, stones, and plastics, test plates were fabricated by securing various heterogeneous materials onto their surfaces using adhesives, with identical experimental conditions maintained during measurements [22]. Each experimental group was replicated ten times, and mean values of static friction coefficients between different materials were obtained through statistical analysis. Static friction angles between raisin particles and stainless steel plates, raisin particles and stems, raisins and branches, raisins and stones, and raisins and plastics were measured. The static friction coefficients between raisins and stainless steel plates/stems/branches/stones/plastics were subsequently calculated using Equations (8) and (9).  
Figure 14: Determination of the coefficient of restitution.  
Figure 15: Experimental determination of friction coefficients.  
\[\left\{\begin{array}{l}F_{1}{=}G\sin\theta\\ F_{2}=G\cos\theta\\ F_{1}-f=0\\ F_{2}-F_{N}=0\\ f=\mu F_{N}\end{array}\right. \tag{8}\]  
\[\mu=\frac{f}{F_{N}}=\frac{F_{1}}{F_{2}}=\frac{G\sin\theta}{G\cos\theta}=\tan\theta \tag{9}\]  
In the equation, \(F_{1}\) represents the component of gravitational force along the inclined plane, \(G\) denotes gravitational force, \(\theta\) is the inclination angle of the plane, \(F_{2}\) corresponds to the applied pressure, \(f\) indicates frictional force, \(F_{N}\) signifies the normal support force, and \(\mu\) is the static friction coefficient.  
The rolling friction coefficient of materials was measured using the inclined plane rolling method [23]. During experiments, materials were placed on a test plate with an inclination angle \(\beta\), where \(\beta\) = 30\({}^{\circ}\) was determined through preliminary trials. To ensure full conversion of gravitational potential energy into work conducted against frictional forces, materials were clamped with tweezers and released from a fixed position (\(L\) = 50 mm) with an initial velocity of 0 m/s. The rolling distance \(D\) along the horizontal direction upon cessation of motion served as the evaluation metric. Ten replicate experiments were conducted, and the rolling friction coefficient \(\eta\) was calculated using Equation (10). The static and rolling friction coefficients obtained from relevant studies [24] and experimental results are presented in Table 6.  
\[GL\sin\beta=G(L\cos\beta+D)\eta \tag{10}\]