## 3 Calibration of Contact Parameters between Lily Bulb and Q235 Steel
### Rolling Friction Factor  
The rolling friction coefficient is a vital contact parameter between the lily bulb and Q235 steel. The inclined rolling test is mainly performed to calibrate the rolling friction coefficient between the lily bulb and Q235 steel. This test is illustrated in Figure 7[27]. This test was conducted by placing the lily bulb on an inclined surface with an inclination angle of \(\varphi_{2}\) = 40\({}^{\circ}\), at a fixed height S\({}_{1}\) = 300 mm. Hence, the lily bulb rolls down the inclined surface with an initial speed of 0. The horizontal rolling distance of the lily bulb was measured when it rolled down and was completely still on the horizontal surface. The bench test was repeated 5 times to acquire the average value. The measured value of the horizontal rolling distance was S\({}_{2}\) = 149.8 mm.  
The collision recovery coefficient between lily bulbs (X\({}_{1}\)), static friction (X\({}_{2}\)), and rolling friction (X\({}_{3}\)) had no effect on the horizontal rolling distance. In the EDEM simulation test, the values of X\({}_{1}\), X\({}_{2}\), and X\({}_{3}\) were all set to 0 to avoid interference. The calibrated parameters were used in this research. The coefficient of recovery from the collision between lily bulb and Q235 steel was x\({}_{1}\) = 0.301 while the value of static friction was x\({}_{2}\) = 0.423. After the pre-simulation test, the rolling friction coefficient between lily bulb and Q235 steel x\({}_{3}\) was in the range of 0.04-0.09, with a step length of 0.01. Moreover, 6 sets of the simulation were conducted with each set of experiments repeated 5 times to take the average value. The experimental design plan and results are provided in Table 5, where y\({}_{3}\) represents the simulation value of the horizontal rolling distance.  
The curve fitting was performed on the test data in Table 5 to obtain the relationship between the rolling friction factor and the horizontal rolling distance of the lily bulb and  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Rolling Friction Coefficient x\({}_{3}\)**} & **Horizontal Scroll Distance Value** \\  & & **Simulation Value y\({}_{3}\)/mm** \\ \hline
1 & 0.04 & 189.51 \\
2 & 0.05 & 167.31 \\
3 & 0.06 & 155.74 \\
4 & 0.07 & 139.22 \\
5 & 0.08 & 129.73 \\
6 & 0.09 & 116.35 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental scheme and results of rolling friction coefficient simulation experiment.  
Figure 7: Calibration experiment of rolling friction coefficient. (**a**) Physical experiment; (**b**) Simulation test. 1. Horizontal plane; 2. Inclined plane; 3. Lily bulb; 4. Right angle ruler.  
Q235 steel in the simulation test. The second-order polynomial fitting curve was obtained, as illustrated in Figure 8. The curve equation (Equation (6)) y3 is:  
\[\text{y}_{3}=9360.7\text{x}_{3}{}^{2}-2631.3\text{x}_{3}+278.4 \tag{6}\]  
The coefficient of determination of Equation (6) was R2 = 0.9948, which was close to 1, indicating the high fitting reliability of the equation. By substituting the actual measured value of the horizontal rolling distance of 149.8 mm into Equation (6), x3 = 0.063 was obtained. This value was further entered into EDEM for verification. The test was repeated 5 times to obtain the average values. The simulated value of the horizontal rolling distance measured by the simulation test was 142.3 mm, with a measured relative error value of 5.3%, suggesting that the calibration simulation results are basically consistent with the bench test. In the EDEM simulation test, the coefficient of rolling friction between the lily bulb and Q235 steel was determined to be x3 = 0.063.