# Analysis of Interference-Fit Joints
## 3 Results of Numerical Calculations and Experimental Studies
### Numerical Simulation of the Pressing Process
The results from Table 4 are presented in Figure 11.  
Figure 11 shows graphs of the dependence of load-bearing force of the joint from the interference value for a constant diameter of the hub opening of o 8 mm with a joint length of 15 mm. The results of the numerical simulation were approximated by the graph of a third-degree curve described by the following function: \(0.575x^{3}-41.21x^{2}+946.1x-906.8\). Analyzing results presented in Figure 10, obtained from the numerical analysis, it can be noted that with larger interferences between the shaft and the hub, which result \begin{table}
\begin{tabular}{c c c} \hline \hline
**Joint** & **Surface Pressure,** & **Maximum Plastic Strain,** \\
**Symbol** & **MPa** & **mm/mm** \\ \hline J1 & 81 & 0 \\ J2 & 122 & 0 \\ J3 & 162 & \(9.05\times 10^{-4}\) \\ J4 & 202 & \(4.95\times 10^{-3}\) \\ J5 & 240 & \(1.09\times 10^{-2}\) \\ J6 & 236 & \(1.71\times 10^{-2}\) \\ J7 & 253 & \(2.34\times 10^{-2}\) \\ J8 & 263 & \(2.97\times 10^{-2}\) \\ J9 & 272 & \(3.62\times 10^{-2}\) \\ J10 & 277 & \(4.22\times 10^{-2}\) \\ J11 & 277 & \(4.91\times 10^{-2}\) \\ J12 & 270 & \(5.26\times 10^{-2}\) \\ J13 & 274 & \(5.77\times 10^{-2}\) \\ J14 & 283 & \(6.05\times 10^{-2}\) \\ J15 & 293 & \(6.39\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Surface pressures and plastic strains were obtained from the FEM analysis. Figure 9: Values of total strains. in plasticization of contact surfaces in the pressing process, calculating the load capacity according to the formulas resulting from [PERSON]'s elastic analogy is pointless. As can be seen from Figure 10, starting with an interference value of 16 \(\upmu\)m, the value of the joint breaking force is set at a constant level and does not depend on the dimension of interference. For these joints, plasticization occurs along the entire length of the contact zone and progresses deeper into the joined elements with increasing dimensional interferences. Numerical analysis performed for the joints considered in the work showed that the breaking force value was inconsistent with the values obtained from [PERSON]'s formulas, even in the range of interferences less than 16 \(\upmu\)m. Therefore, it can be concluded that the joint load capacity determined according to these formulas leads to errors. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Joint** \\ **Symbol** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Interference** \\ **\(\Delta\), mm** \\ \end{tabular} } & \multicolumn{2}{c}{**FEM Analysis**} & \multicolumn{2}{c}{**Lame’s Formula**} \\ \cline{3-6}  & & **Assembly Force** & **Breaking Force** & **Acc. (1 and 2), N** & **Breaking Force** \\ \hline J1 & 0.004 & 2293 & 2092 & 1663 & 599 \\ J2 & 0.006 & 3438 & 3137 & 2494 & 1430 \\ J3 & 0.008 & 4516 & 4220 & 3325 & 2261 \\ J4 & 0.010 & 5549 & 5125 & 4156 & 3092 \\ J5 & 0.012 & 6437 & 5801 & 4988 & 3924 \\ J6 & 0.014 & 7714 & 6006 & 5819 & 4755 \\ J7 & 0.016 & 7784 & 6004 & 6650 & 5586 \\ J8 & 0.018 & 8285 & 6010 & 7481 & 6417 \\ J9 & 0.020 & 8682 & 6010 & 8313 & 7249 \\ J10 & 0.022 & 8986 & 6002 & 9144 & 8080 \\ J11 & 0.024 & 9209 & 5999 & 9975 & 8911 \\ J12 & 0.026 & 9373 & 6001 & 10,806 & 9742 \\ J13 & 0.028 & 9474 & 5999 & 11,638 & 10,574 \\ J14 & 0.030 & 9560 & 5960 & 12,469 & 11,405 \\ J15 & 0.032 & 9632 & 5974 & 13,300 & 12,236 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of assembly forces and breaking forces for each joint. Figure 10: Graphs of assembly forces with marked breaking forces of the J1, J5, J10, and J15 joint.