# Simulative and Experimental Investigation of Vibration Transfer Path at Gearboxes
## 5 Results and Discussion
### Simulation Results  
Figure 15 shows the simulation and experimental results of the pinion tangential acceleration at 500 rpm and 1000 Nm. The peaks corresponding to the gear mesh frequency, the Outer Race Defect frequency, and their high harmonics can be observed both in the  
Figure 14: Peak-to-mean values of signals after post-processing from rotating sensors at different torques and constant rotational speed. Figure 13: Ratio of peak-to-mean values \(r\) at different rotational speeds and 500 Nm. experiment and in the simulation. The peak at 50 Hz corresponds to the Outer Race Defect frequency and the other three peaks to the gear mesh frequency and their high harmonics. Because of the measurement errors, noise, and effect of the amplitude modulation, there are also more small peaks in the experimental results, and these peaks are difficult to model. Hence, these peaks are not considered in the simulation and, therefore, cannot be observed from the simulation results. Figure 16 shows the radial acceleration of the housing near the pinion shaft. Similar to the result in Figure 15, the important peaks can also be observed. The experiment result shows that the difference between the peaks at the Outer Race Defect frequency and the gear mesh frequency is small. However, the simulation result presents a large difference between the amplitudes of these peaks corresponding to the gear mesh frequency and the Outer Race Defect frequency. The reason for that may be the overestimation of the vibration excitation of the bearings in the simulation. Because of the axial force generated by the helical gear mesh, the right bearing of the pinion shaft and the left bearing of the wheel shaft are loaded in such a way that all rolling elements are always loaded. Hence, the fluctuations in the stiffness of these two bearings are small. The loads on the other two bearings are reduced due to the axial force, and this can lead to a large fluctuation in bearing stiffness, as shown in Figure 17. The larger the fluctuation in the bearing stiffness is, the stronger the vibration excitation of the bearing. This phenomenon can also be observed from the experimental results. Figure 16: Radial acceleration at housing near pinion shaft at 500 rpm and 1000 Nm from experiment and simulation. Figure 15: Tangential acceleration of pinion in axial direction at 500 rpm and 1000 Nm from simulation and rotating sensors. Additionally, the vibration transmission in the transfer path of the gearbox has been investigated through the simulation results. Table 4 presents the amplitude at the gear mesh frequency of the signals from different nodes. As shown in Figure 2, the amplitude of the signal at node 3 shows the vibration intensity of the pinion, the signal at node 6 shows the vibration of the pinion shaft near the right bearing, and the signal at node 14 shows the vibration of the housing part. As presented in Table 4, the amplitude of the vibration with the gear mesh frequency reduces during vibration transmission through the gear, the shaft, and the bearing. By analyzing the differences between the amplitudes at the different nodes in Table 4, it can be observed that the largest reduction in the vibration intensity happens during transmission through the bearings. As a result, the importance of the sensor locations at the rotating components for condition monitoring, such as sensor-integrating gear wheels, can be determined to show the significance and the effect of a different sensor position. Therefore, the simulation shows a good presentation of the vibration frequencies of interest. The simulation shows lower amplitude results at the housing position compared to the measured values, as shown in Figure 16. This is most likely caused by the stiffness model of the housing. At the gear, the amplitudes and frequencies of the simulation show a good comparison to the measurement results, as shown in Figure 15.