## 3 Calibration of Contact Parameters between Lily Bulb and Q235 Steel
### Collision Recovery Coefficient  
Collision recovery coefficient is a parameter of the ability of an object to recover after contact collision deformation. The collision recovery coefficient between lily bulbs and Q235 steel plate was calibrated by the collision bounce test [25]. With the purpose of ensuring that lily bulbs do not break after being dropped and the bounce height is easy to distinguish, a preliminary test was conducted to reveal that the best height of lily bulbs to fall was 300 mm. As illustrated in Figure 3a, the Q235 steel sheet was placed horizontally, and the lily bulb was freely dropped from the height h\({}_{1}\) of 300 mm. The lily bulb collides with the Q235 steel plate, and the highest bounce height of the lily bulb was recorded by \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Parameter Source** \\ \hline Lily Bulb Poisson’s Ratio & 0.42 & Determination \\ Lily Bulb Shear Modulus/Pa & \(1.85\times 10^{6}\) & Determination \\ Lily Bulb Density/(kg\(\cdot\)m\({}^{-3}\)) & 986 & Determination \\ Q235 steel Poisson’s Ratio & 0.3 & Reference [24] \\ Q235 steel Shear Modulus/Pa & \(8\times 10^{10}\) & Reference [24] \\ Q235 steel Density/(kg\(\cdot\)m\({}^{-3}\)) & 7850 & Reference [24] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation test parameters. Figure 2: The construction process of lily discrete element model. (**a**) Lily Bulb; (**b**) 3D model; (**c**) Discrete Element Model. high-speed video. This was repeated 5 times to obtain the average value (highest bounce height h\({}_{2}\) = 27.5 mm). The static friction factor (x\({}_{2}\)) and rolling friction factor (x\({}_{3}\)) between lily bulbs and Q235 steel, as well as the collision recovery coefficient (X\({}_{1}\)) and static friction factor (X\({}_{2}\)) and rolling friction factor (X\({}_{3}\)) between lily bulbs, have no effect on the bounce height. The values of x\({}_{2}\), x\({}_{3}\), X\({}_{1}\), X\({}_{2}\), and X\({}_{3}\) were all set to 0 to avoid interference in the EDEM simulation test. After pre-simulation tests, the range of the collision recovery coefficient x\({}_{1}\) of the lily bulb and Q235 steel was determined to be 0.20\(\sim\)0.40, and the step length was 0.04. There were 6 sets of simulation tests. Each set of tests were repeated 5 times to obtain the average value. The test design scheme and results are presented in Table 3, in which y\({}_{1}\) denotes the simulation value of the highest bounce height of Q235 steel plate. The curve fitting was performed on the test data in Table 3 to obtain the relationship between the collision recovery coefficient of lily bulb-Q235 steel and lily bulb-clay soil and the maximum bounce height in the simulation test. The second-degree polynomial fitting curve was acquired, as presented in Figure 4. The fitted curve equation (Equation (4)) is:  
\[y_{1}=159.4{\rm x_{1}}^{2}+16.94{\rm x_{1}}+7.811 \tag{4}\]  
Figure 3: Calibration experiment of restitution coefficient. (**a**) Freely dropped height; (**b**) Highest bounce height; (**c**) Simulation test. 1. Lily bulb; 2. Graph paper; 3. Q235 steel. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Collision Recovery Coefficient x\({}_{1}\)** & **Bouncing Height Simulation Value y\({}_{1}\)/mm** \\ \hline
1 & 0.20 & 16.65 \\
2 & 0.24 & 22.81 \\
3 & 0.28 & 24.54 \\
4 & 0.32 & 29.84 \\
5 & 0.36 & 34.16 \\
6 & 0.40 & 40.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental scheme and results of restitution coefficient simulation experiment. The determination system of Equation (4) was R\({}^{2}\) = 0.981, which is close to 1, reflecting the high equation fitting reliability. The actual measured value of 27.5 mm of the lily bulb-Q235 steel plate was substituted into the Equation (4) to obtain x\({}_{1}\) = 0.301, and input into the EDEM software for verification, repeated 5 times. Afterward, the average value was calculated. According to the test, the largest rebound height value was 26.24 mm, with a relative error value of 4.96%.