# Analysis of Interference-Fit Joints
## 2 Materials and Methods  
The object of the analysis is a press-fit joint of a 20 mm long shaft with a nominal diameter of \(\omega\) 8 mm with four different fits and a 40 mm long hub with an outer diameter of \(\omega\) 20 mm and an inside diameter of \(\omega\) 8H7 (Figure 2a). The interference fit joint before assembly is shown in Figure 2b.  
After assembly, the set was subjected to tests aimed at verifying the correctness of the numerical model which was built for the analysis of the load-bearing capacity of the joint depending on the interference value.  
The hole in each hub was measured on a coordinate measuring machine at four points on a circle every 90\({}^{\circ}\). The measurement was repeated in three sections at the depth of the hole. The adjacent cylinder with a mean diameter of \(\omega\) 8.0050 \(\pm\) 0.0011 mm was determined from the measurements for each hub [16].  
Measurements of the shaft diameters were performed in the same way as of the holes in the hub obtaining a mean shaft diameter of \(\omega\) 8.0170 \(\pm\) 0.0013 mm. Measurements were carried out on Sheffield discovery III cordax d-28 coordinate measuring machine. The resolution of the machine is 1 \(\upmu\)m. Based on the mean values of the shaft and the hub hole diameters, interference \(\Delta\) of 0.012 mm was calculated. The shaft was pressed into the hub to a depth of 15 mm. Both parts were made of S235 JR steel with a Young's modulus of 200 GPa, the yield point of 225 MPa, and ultimate tensile strength of 360 MPa.  
Four types of joints made for various fits presented in Table 1 were subject to numerical analysis [17].  
The surface pressure value and the value of the maximum force breaking the joint, calculated according to Formulas (1) and (4), are presented in Table 2. In each of the considered types of fit, the joints are assumed to be elastic in nature and the friction coefficient is \(\upmu\) = 0.1 [10]. Calculations in Formula (4) were performed assuming roughness of Ra = 0.4 obtained by finishing turning.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \begin{tabular}{c} **Joint** \\ **Symbol** \\ \end{tabular} & \begin{tabular}{c} **Nominal** \\ **Diameter of** \\ **the Joint** \\ \end{tabular} & **Fit** & \begin{tabular}{c} **Interference** \\ **\(\Delta\), mm** \\ \end{tabular} & **Type of Fit** \\ \hline J1 & & H7/k6 & 0.004 & \\ J2 & & 0.006 & \begin{tabular}{c} Locational transition fit \\ \end{tabular} \\ J3 & & & 0.008 & \\ J4 & & 0.010 & \\ J5 & & H7/p6 & 0.012 & \begin{tabular}{c} Locational interference fit \\ \end{tabular} \\ J6 & & & 0.014 & \\ J7 & & & 0.016 & \\ J8 & \(\omega\) 8 & & 0.018 & \\ J9 & & & 0.020 & \\ J10 & & H7/s6 & 0.022 & \
\begin{tabular}{c} Medium drive fit \\ \end{tabular} \\ J11 & & & 0.024 & \\ J12 & & & 0.026 & \\ J13 & & & 0.028 & \\ J14 & & H7/u6 & 0.030 &
\begin{tabular}{c} Force fit \\ \end{tabular} \\ J15 & & & 0.032 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: A list of joints.  
Figure 2: (a) Technical drawing of the joint, (b) Set before pressing.  
The results presented in Table 2 show that taking into account the roughness of joined surfaces reduces the load-bearing force of the joint.