## 3 Results  
### Strength Study of the Original Design of the ASC Crossbar  
The strength of the frame was assessed according to the conservative standard for pressure vessels, CSN 69 0010 [35]. The evaluation of the mechanical stress was performed by comparing the mechanical stress of the frame part with the maximum permissible stress for the material used [36]. The calculation of the maximum permissible \(\sigma_{DOV}\) in the structure was drawn out according to the relation (1):  
\[\sigma_{DOV}=\tau\cdot\min\left\{\frac{R_{p\ 0.2}}{n_{T}};\frac{R_{m}}{n_{B}} \right\}\cdot\varphi, \tag{1}\]  
Figure 4: The course of the radial reactions of the ASC wheels when tilting on the tilting platform and 80% unweight of the vehicle wheels. (\(Z_{SCFL}\)—radial reaction of the support front left wheel (N); \(Z_{SCFR}\)—radial reaction of the support front right wheel (N); \(Z_{SCRL}\)—radial reaction of the supporting rear left wheel (N); and \(Z_{SCFR}\)—radial reaction of the supporting rear right wheel). where \(\sigma_{DOV}\) is the permissible mechanical stress (MPa), \(n_{T}\) is the coefficient of safety to yield stress (-), \(\varphi\) is the coefficient of the weld joint, \(R_{p\,0.2}\) (MPa) is the contractual yield stress, \(R_{m}\) is the breaking strength (MPa), and \(n_{b}\) is the coefficient of safety to breaking strength (-). For nonlinear analysis, it is possible to evaluate the reserve against the limit states of the design being examined. In the MNA (materially non-linear) study, the von [PERSON] bilinear model of the material was used and the limit state of plasticity was examined, and in the GMNA study, the limit state of stability loss was investigated. The indicator of this reserve is the so-called Load Factor, which is obtained from the loading characteristics of the selected structural node as the intersection of the tangent to the elastic part and the tangent to the plastic part of the characteristic. The structure will reach its limit if a load equal to the size of the original load, multiplied by the Load Factor, is applied to it. Consequently, if the Load Factor (reduced by the relevant factor of safety according to the Formula (2)) is greater than 1, the design is compliant with the limit state. \[L_{FD}=\min\left\{\frac{L_{FD}}{n_{T}};\frac{L_{Fst}}{n_{u}}\right\}\cdot\varphi, \tag{2}\]  
where \(L_{FD}\) is the permitted Load Factor (-) with a factor of safety, \(L_{FPL}\) is the Load Factor of plasticity (-), \(L_{Fst}\) is the Load Factor of stability (-), \(n_{T}\) is proportionality coefficient (-), and \(n_{u}\) is coefficient of ductility (-). For the manufacturing of the frame, the construction steel S235 JR (with parameters showcased in Table 2) was employed. The ASC frame attachment was realized by limiting the vertical movement applied to the bearing surface, where the car frame sits on the ASC crossbar. The implemented displacement limitation is a suitable simplification prerequisite, but it is well suited to real construction. Another fixture was applied to the split lines on the frame's mounts. From the outer side of the frame mount, the split line simulates the M10 bolt washer with an external diameter of 20 mm DIN 125a. From the inside, the split line covers the entire surface of the mount above the crossbar profile, that is the area that is in contact with the car frame. The condition of full tightening of the bolts was represented by removing all degrees of freedom at the mounting point (Figure 5). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Ultimate tensile strength (MPa) & 360 \\ Yield strength (MPa) & 235 \\ Density (kg.m\({}^{-3}\)) & 7850 \\ Ductility (\%) & 26 \\ Poisson’s ratio (-) & 0.3 \\ Young’s modulus (MPa) & 210,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the material S235 JR [36]. Figure 5: Mounting and loading of the ASC crossbar. The load was defined as the force applied to the wheel units with the caster.