## 2 Strength and Stiffness of the Frame
### Stiffness of Welded Frame  
The dimension of frame and load capacity is huge, so that defining the stiffness of the component is difficult through testing. Thus, this parameter was assessed by finite element analysis. The finite element model of frame established by software HYPERMESH (Altair, Boston, MA, USA) is shown in Figure 1. The frame was meshed with triangular and quadrilateral shell elements. There were 165,985 elements and 159,450 nodes. Before estimating stiffness of the frame at intervals, the finite element model was testified. The stress due to dynamic loading in five measurement points at full load at the speed of 30 km/h on the mine road was measured, Figure 2. The strain gauge rosette was cemented in the selected zones of the frame, Figure 3[20]. Both the results from the simulation and the road test are listed in Table 3[20]. For point 4, the high relative error was caused by neglecting the loads at this region, because these masses from cooling system and cab were supposed to have little effect on bearing state. This high \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & **Maximum Force** & **Width of** & **Thickness of** & **Ultimate Tensile** \\  & **(kN)** & **Specimen (mm)** & **Specimen (mm)** & **Strength (MPa)** \\ \hline
1 & 22.14 & 6.13 & 5.97 & 604.98 \\
2 & 18.05 & 6.22 & 5.81 & 499.47 \\
3 & 24.15 & 6.05 & 6.10 & 654.38 \\
4 & 27.12 & 5.89 & 6.04 & 762.32 \\
5 & 16.66 & 6.00 & 5.89 & 471.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Monotonic experimental data and results. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **1** & **2** & **3** & **123** & **124** & **125** \\ \hline Tensile & & & & & & \\ strength & 439.11 & 443.44 & 445.57 & 777.97 & 781.78 & 792.52 \\ (MPa) & 1.000 & 0.992 & 0.984 & 0.024 & 0.016 & 0.008 \\ Credibility & 1.000 & 0.992 & 0.984 & 0.024 & 0.016 & 0.008 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of ultimate tensile strength and credibility obtained by means of the blind numbers theory. Figure 1: Finite element model of frame. stress level could be produced by geometric mutation. The relative error of remaining measurement points all stayed within 10%, which showed that the simulated results agreed well with tested ones. The bending stiffness of frame at interval could be estimated as follows:  
\[\left[\underline{C_{b}},\overline{C_{b}}\right]=\frac{\left[\underline{F_{b}}, \overline{F_{b}}\right]\left[\underline{a_{b}}^{3},\overline{a_{b}}^{3}\right] }{48\left[\underline{f_{b}},\overline{f_{b}}\right]} \tag{8}\]  
where \(\left[\underline{F_{b}},\overline{F_{b}}\right]\) expresses the interval concentrated bending load applied to the center of gravity of the goods, \(\left[\underline{a_{b}},\overline{a_{b}}\right]\) is wheelbase of this truck at interval, and \(\left[\underline{f_{b}},\overline{f_{b}}\right]\) is maximum deformation of frame in force center at interval [19]. Five finite element models and concentrated loading of frame on bending from the component project were determined. The degrees of freedom at suspensions were constrained. Then, the deformation of the frame under bending could be calculated, as listed in Table 4.  
Figure 3: The strain gauge rosette on the component. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Road Test Data (MPa)**} & \multicolumn{2}{c}{**Simulated Results**} & \multirow{2}{*}{**Relative Error (\%)**} \\  & & **(MPa)** & \\ \hline
1 & 125 & 121 & 3.2 \\
2 & 145 & 143 & 1.4 \\
3 & 196 & 177 & 9.7 \\
4 & 169 & 7 & 95.6 \\
5 & 179 & 181 & 1.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of simulated results and experimental data. Figure 2: Diagram of the five measurement points.