# A Model of an Extending Front Loader
## 4 FEM Analyses  
During the design process and FEM numerical analyses, the sensitivity of the structure was assessed due to the material and geometry of extending front loader arms. The possibility of using popular S235 steel was assessed because it is easy to process and welds well. The use of this material reduces the cost of the loader. The geometry of individual components within the structure was also subjected to sensitivity analysis. This approach made it possible to perform an initial optimization of the structure, which was confirmed by the results of the numerical analysis, where the stress and strain values were found to be within the permissible ranges. The initial optimization of the structure made it possible to plan a wide range of visibility from the operator's cabin. Additionally, easy access to the inside of the frame was provided using screwed cover elements. To increase the level of safety, sockets have been designed to manually retract the loader arms in the event of a lack or loss of hydraulic power. The structure elements were subjected to strength analysis using the von [PERSON] reduced stress method using the Autodesk Inventor Professional program. Static tests were performed, paying particular attention to the size of displacements. A triangular mesh shape was chosen for the conducted analyses. Additionally, the mesh density was increased within the holes and at the joints. S235 structural steel was chosen as the loader material with the following parameters: density--7.850 g/cm3; Young's modulus--290 GPa; Poisson's ratio--0.32; yield strength--235 MPa; and tensile strength--360 MPa. The  
Figure 3: Force distribution in bottom position without and with extension [own work]. \begin{table}
\begin{tabular}{l l l} \hline \hline \multirow{2}{*}{**Designation**} & **Fores and Moments** & **Fores and Moments from** \\  & **without Extension** & **the Extension** \\ \hline F\({}_{1}\) & 8300 N & 8300 N \\ \hline F\({}_{2}\) & 8000 N & 8000 N \\ \hline F\({}_{3}\) & 8090 N & 8090 N \\ \hline F\({}_{4}\) & 8390 N & 8  
Figure 8: Detailed view of the most stressed areas of extending loader arm [own work]. Figure 7: [PERSON] stress distribution of extending loader arm (number of mesh elements 52,397, number of nodes 107,068) [own work]. Figure 9: Deflection of the extending loader arm structure [own work]. The stress analysis of the loader arm without extension showed that the maximum stress value occurred in the area where the support cylinder was installed and in the area of the cross-section of the telescopic frame and did not exceed 67 MPa. This value is below 50% of the limit value in the elastic range for S235 steel. For the same load assumptions and input data, an assessment of the deflection of the loader frame without extension was carried out (Figure 6). For the adopted frame beam cross-sections, the maximum deflection of the loader arm without extension does not exceed 1.5 mm. The designated range of deflection of the front loader frame is minimal and does not pose a threat to the operational safety of the loader system. Without extension, the front loader frame is very stiff, which limits the movement resistance of the extension control mechanisms. The stress analysis of the extending loader arm showed that the maximum stress value occurred in the area of the installed frame connector, the actuator controlling the working tool, and the parallel guide long and does not exceed 195.4 MPa. The stress values obtained in the numerical tests are within the permissible range. However, during the detailed evaluation of the kinematic nodes, it may be necessary to locally redesign the arm geometry to distribute the stresses more evenly. Such design optimization can reduce the occurrence of potential damage. The assessment of the deflection of the extending loader frame is shown in Figure 9. The deflection value of the loader frame with the arm extended to the maximum is almost 5 mm (4.934 mm). This deflection is greatest in the area of the end of the sliding frame.