## 2 Materials and Methods  
The object of the wear tests is the tribological kinematic pair consisting of the shaft and sleeve. As a structural material for each of the elements, C45 steel was used, whose chemical composition is presented in Tables 1 and 2. These tables also present the exemplary mechanical properties of this steel. Steel is most often used in the manufacture of moderately loaded items such as the elements of machinery and equipment. That kind of steel is distinguished by its high strength and ductility. Grinding was used as the finish treatment of both the sleeve hub and shaft axle seat, and that process guaranteed smaller initial surface roughness. The view and dimensions of the tribological kinematic pair under investigation are shown in Figure 1. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Steel** & \multirow{2}{*}{**Concentration**} & \multirow{2}{*}{**C**} & \multirow{2}{*}{**Si**} & \multirow{2}{*}{**Mn**} & \multirow{2}{*}{**P**} & \multirow{2}{*}{**S**} & \multirow{2}{*}{**Cr**} & \multirow{2}{*}{**Cu**} & \multirow{2}{*}{**Mo**} & \multirow{2}{*}{**Ni**} \\
**Grade** & & & & & & & & & & & \\ \hline \multirow{2}{*}{C45} & min. & 0.41 & 0.16 & 0.52 & 0.11 & - & - & - & - & - \\ \cline{2-11}  & max & 0.49 & 0.41 & 0.77 & 0.41 & 0.045 & 0.045 & 0.32 & 0.11 & 0.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of C45 steel [%]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mechanical Property** & \multicolumn{3}{c}{**Value**} \\ \hline \hline Yield strength Re & 310 MPa \\ \hline Young’s modulus & 204 Gpa \\ \hline Maximum bending stresses & 205 Mpa \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mechanical property of C45 steel. The test programme assumed the shaft top layer wear evaluation after fatigue tests and repeated sleeve disassembly. The fatigue tests were divided into three stages. After the first and second stages, the joint was disassembled by pulling the sleeve off the shaft by means of a press. After the third stage, the tribological kinematic pair was prepared for laboratory tests in accordance with the process procedure prepared specially for this purpose. The first stage lasted for 10,000 fatigue cycles, and the remaining two for one thousand cycles each. Each of the tested samples was subjected to the same number of fatigue cycles. The value of the maximum force needed for sleeve disassembly and assembly was recorded each time. Macrographic documentation and surface roughness measurements were also made. The testing programme permitting the assumed objective to be achieved is presented schematically in Figure 2.  
The joint was assembled by pressing the sleeve onto the shaft with the use of the press recording the value of the pressing force. The constant tolerance value was assumed for all the tribological kinematic pairs, and that value was 0.02 mm. For the assumed tolerance value and the initial roughness of the mating surfaces, the average maximum force needed for pressing the sleeve onto the shaft was 3875 N.  
Fatigue tests were conducted for five tribological kinematic pairs, which significantly increased the reliability of the test results obtained. Wear tests were conducted on the fatigue testing machine permitting a rotational bending moment to be obtained. The tribological kinematic pair were loaded symmetrically with a concentrated force, and thus the bending moment pattern shown in Figure 3 was obtained. Wear test parameters are compiled in Table 3.  
In the case of interference joints, the distribution of contact pressure (3D) is uneven. It can be determined by the finite element method, which will be the problem of the next publication. The maximal contact slip amplitude could be evaluated from the solution for a simply supported beam under a concentrated load at the centre. This amplitude value could clarify the type of damage accumulating on the contact interface.