## 5 Simulation Test of the Grouser Effect
### Coupling Analysis of Multiple Factors  
After a reliable mathematical model had been created and its statistical significance had been confirmed, the effect of each input parameter on the traction force was estimated [26]. Figure 16 indicates the linear dependence of the traction force on all input parameters. The significance of \(h\times h\), \(h\times l\) and \(\lambda\times h\) suggests a quadratic relation among the traction force but with smaller effects (3.41753, 2.93124 and 2.41996, respectively). Regarding the impact of individual factors, the grouser's height \(h\) has the strongest influence on the traction force (22.7396), the grouser's pitch \(l\) and the ratio of the grouser's thickness to the length of the track shoe \(\lambda\) have less influence on the traction force, which are 5.18175 and 2.26022, respectively. Figure 15: Scatterplot of the residuals vs. responses. (**a**) Scatterplot of the residuals vs. \(h\); (**b**) scatterplot of the residuals vs. \(l\); (**c**) scatterplot of the residuals vs. \(\lambda\). Figure 17 shows the effects of the interaction between the grouser's height and the track shoe's pitch on the traction force. When the grouser's height remained constant, the traction force gradually decreased with an increase in the track shoe's pitch. When the track shoe's pitch remained constant, the traction force gradually increased with an increase in the grouser's height. When the grouser's height and the track shoe's pitch changed at the same time, the growth rate of the traction force also showed a great change. When the track shoe's pitch was small, the traction force increased faster with an increase in the grouser's height. When the track shoe's pitch was large, the traction force increased slowly with an increase in the grouser's height. When the grouser's height was low, the traction force increased at a slower rate as the track shoe's pitch decreased. When the height of the grouser was large, the traction force increased faster with a decrease in the track shoe's pitch. It can be seen that the interaction between the grouser's height and the track shoe's pitch was more significant. The \(p\)-values of \(\lambda\)\(\times\)\(l\) were 0.24089, which is greater than 0.05, indicating that the parameter was not significant. Figure 18 shows the effects of the interaction between the ratio of the thickness of the grouser to the length of the track shoe \(\lambda\) and the pitch of the track shoe on the traction force. When \(\lambda\) was kept constant, the traction force gradually increased with a decrease in the track shoe's pitch. When the track shoe's pitch was kept constant, the traction force first gradually decreased and then increased as \(\lambda\) decreased. Figure 16: Pareto chart of standardized factor effects. Figure 17: Effects of \(h\) and \(l\) on traction. When \(\lambda\) and the track shoe's pitch changed simultaneously, the change in the traction force was similar to the case of considering one response alone, and the change in traction force as a whole was not large. Therefore, it is verified that the interaction between the ratio \(\lambda\) of the thickness of the grouser to the length of the track shoe and the pitch of the track shoe was not significant. Figure 19 shows the effects of the interaction between the ratio of the thickness of the grouser to the length of the track shoe \(\lambda\) and the height of the grouser on the traction. When \(\lambda\) remained constant, the traction force gradually increased with an increase in the grouser's height. When the grouser's height \(h\) remained constant, the traction force gradually increased with a decrease in \(\lambda\). When \(\lambda\) and the grouser's height \(h\) changed at the same time, the growth rate of the traction force changed greatly. When \(\lambda\) was small, the traction force increased faster as the grouser's height \(h\) increased. When \(\lambda\) was large, the traction force increased slowly with an increase in the grouser's height.