# Susceptibility Modeling of a Rubber Track for Lightweight Mobile Robots
## 6 Discussion  
### Relative Errors Comparison of Modeling Methods  
Three methods of track modeling simulation were compared in terms of relative error for the mean value of the experimental results. The error values of simulation-determined parameters are presented in Table 8. The height's Hd and logarithmic decrement were stiffness and damping parameters adjusting criteria. Other parameters indicated the compatibility level of the results. The track deformation width errors Ws and Wd did not change significantly depending on the adopted simulation methods and variants. They amounted to no more than 2%.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Simulation** &
\begin{tabular}{c} **Cr** \\ **(N-mm,s)** \\ **end** & **Hs [mm]** & **Ws [mm]** & **Hd [mm]** & **Wd [mm]** & **T [s]** & \(\mathbf{\Lambda}\) \\ \hline E38 & 360 & 329 & 1057 & 225 & 1078 & 0.76 & 0.69 \\ E56 & 500 & 323 & 1070 & 223 & 1093 & 0.77 & 0.78 \\ E76 & 700 & 322 & 1065 & 225 & 1101 & 0.74 & 0.76 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Simulations results from variable stiffness constraint model (III) in variants E38, E56, E76.  
Figure 11: The track oscillations plots comparison: experimental measurement and simulation results from variable stiffness constraint model in variants E38, E56 and E76.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation Variant** & \
\begin{tabular}{c} **Rotation Angle Range in** \\ **Constraint A \(\zeta_{\text{Z1}}\)**[\({}^{\circ}\)]** \\ \end{tabular} &
\begin{tabular}{c} **Rotation Angle Range in** \\ **Constraint C \(\zeta_{\text{Z1}}\)**[\({}^{\circ}\)]** \\ \end{tabular} \\ \hline E38 & 0..2 & \(-37\ldots-34\) \\ E56 & 0..3 & \(-25\ldots-23\) \\ E76 & 0..2 & \(-19\ldots-17\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ranges of rotation angle in selected constraint s of the track belt (Figure 4) in variable stiffness model in variants E38, E56 and E76.  
The first method of the simulations (I) was the one most burdened with the time period error. The use of bivalent stiffness (II) reduced the time period relative error ten times and the height Hd relative error four times compared with the first simulation method (I). The use of the variable stiffness method (III) allowed for the most accurate model of susceptibility tests. The largest error in this case (apart from the criteria parameters) concerns the time period, which amounted to 4%. There were no significant differences between the three simulation variants. By selecting the correct values of the damping and stiffness coefficients, it was possible to obtain almost the same plots of oscillation for a track composed of longer and shorter links.  
The use of method I, which is characterized by model simplicity and low calculation time, allows achieving satisfactory results only in static tests. It may be appropriate for vehicle static stability tests. The use of the second method slightly complicates the computational model but significantly improves the accuracy of dynamic test results. This method can be a good compromise between complex track stiffness characteristics and its constant value assumption. In this method of simulation (II), it might be possible to observe reliable track deflection and its oscillations while driving. The use of the third method (III) will extend the model calculation time, but it allows the most accurate prediction of both static and dynamic track performance. It can be useful for accurately determining the parameters of track deformation or energy dissipation in rubber track running gear simulations. However, accurate stiffness characteristics will only be valid for a specific construction and type of track belt, so they will not be universal.