## 3 Results and Discussion  
### Bracket Selection  
Quenched Steel 45 was selected as the material of the bracket due to its high stiffness. Its physical properties were: Young's modulus = 210 GPa, Poisson's ratio = 0.3, shear modulus = 80 GPa, and density = 7800 kg/m\({}^{3}\)[22]. The modal analysis of the housing was performed in ANSYS for bracket dimensions of 80 \(\times\) 24 \(\times\) 1 mm, and the extrude was introduced as 12 \(\times\) 12 mm. The mesh statistics are shown in Table 2.  
The modal analysis of the bracket was performed in ANSYS, and the eigenvalues were 925.98 Hz, 1995.8 Hz, 3681.8 Hz, 4156 Hz, 9412.4 Hz, and 11,828 Hz (Figure 5). These are the first five-mode shapes of the bracket. For modal analysis, the bracket is fixed on the base and at the contact surface region with a bolt. Furthermore, the modal analysis was performed for the system components consisting of the bearing, housing, bolt, and bracket. The frictional connection was defined between the bearing races and housing (0.4), rollers and bearing races (0.21), and bolts and bracket (0.23). The active mode shape for the bracket in the system was 1363.58 Hz, as shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Bracket** & **Components (Bearing, Housing, Bracket, and Bolt)** \\ \hline Nodes & 4831 & 57,284 \\ Element & 2182 & 21,317 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mesh statistics.  
Figure 4: The meshed system.  
The radial load applied was obtained from the sum of the components: flywheel (392 N), drum (196 N), shaft (7.84 N), blower/fan (39.2 N), and the pull force from the belt drive (11.637 N). Belt pull is the force which is employed on the shaft which relies on drive power, rotation speed driven, pitch diameter of the driving pulley and driving factor. The pull force from belt drive can be calculated as [23]:  
\[\text{Belt Pull}=(126000\times\text{HP}\times\text{f})/(\text{RPM}\times\text{PD} )=2.615\text{ lbs.}=11.637\text{ N} \tag{1}\]  
where HP is the drive power to the threshing (16.5 KW), f is the driving factor based on the synchronous belt drive (1.3) [24], RPM is the rotation speed of the small sprocket (1180 min\({}^{-1}\)), and PD is the pitch diameter of the small sprocket (29.97 mm).  
The total radial load on the bearing was calculated as 646.677 N. The bearing load is applied to the inner race of the bearing. The motion pattern of a system oscillation at its natural frequency by forced vibration in harmonic response analysis for the bracket  
Figure 5: Eigenvalues and eigenvector of the bracket.  
Figure 6: Mode shape of the bracket in the system modal analysis.  
maximum displacement was found at 936 Hz of 9.322 mm displacement. Thus, frequencies near 936 Hz need to be avoided for other components to avoid resonance in the system. Figure 7 represents the displacement of a bracket in forced vibration using harmonic response analysis.  
Similarly, from the modal and harmonic response analysis of bearing housing, the maximum displacement of 0.00062 mm was obtained at 3748.5 Hz (Figure 7) for the radial load applied to the housing. In addition, bearing defect frequencies were calculated [3; 25]. The calculated bearing defect frequency of the outer ring (f-RPI) was 118 Hz, the inner ring (f-RPV) was 175 Hz, and the rollers defect (f-RDD) was 45 Hz. Since the eigenvalues of the associated components vary, the steel 45 material and the dimensions were considered for the manufacture of the bracket for vibration analysis.