## 3 Results  
Based on the vibration test procedures and details, wireless vibration sensors were arranged on the tractor axle as shown in Figure 4. The vibration waves at the left and right test points of the front and rear axles of the tractor at different idle speeds are shown in Figures 6 and 7. During the test, the vibration collection time was 400 ms.  
The vibration test data collected from model LX2204 tractor at idle speeds of 800 r/min and 1000 r/min were converted and processed using Equation (1). The vibration intensity at different test positions of the tractor was calculated. Figure 8 shows the results of repeated vibration tests of the tractor at different idle speeds, providing a visual representation of vibration intensity at each test location.  
Figure 5: The procedure for the vibration test.  
Figure 8: Vibration test results of tractor in idle state.  
Figure 6: Vibration waves on the left and right sides of the front axle when idling at 800 rpm.  
Figure 7: Vibration waves on the left and right sides of the front axle when idling at 1000 rpm.  
As can be seen from Figure 8, the difference in vibration intensity between the left and right sides of the front and rear axles of the tractor in the idle state was small. The total vibration intensity of the front axle of the tractor at an idle speed of 800 r/min was greater than that of the front axle of the tractor at an idle speed of 1000 r/min, and the vibration intensity of the front axle in the X and Y directions was greater than that of the rear axle in the X and Y directions. The vibration intensity of the front axle in the Z direction was greater than that of the rear axle in the Z direction, although the difference between the vibration intensity of the front axle and the rear axle in the Z direction was relatively small. Furthermore, when the idle speed of the tractor was set at 800 r/min, the vibration intensity of the left side of the front axle in the X, Y, and Z directions was greater than that of the right side of the front axle in the X, Y, and Z directions. These results are crucial for understanding the vibration distribution of the tractor's frame and can be instrumental in diagnosing any potential mechanical issues.  
When the idling speed of the tractor was 1000 r/min, the vibration intensity of the left side of the front and rear axles of the tractor in the X and Y directions was greater than the vibration intensity of the right side of the front and rear axles in the X and Y directions. This was opposite to the change in vibration intensity of the left and right sides of the front axle in the Z direction.  
Based on the test results shown in Figure 8, the main vibration direction of the tractor in the idle state was determined based on the vibration intensity in different directions at different idle speeds. The results are shown in Figure 9. It can be seen that regardless of the idle speed of the tractor engine setting at 800 r/min or 1000 r/min, the main vibration direction on both sides of the front axle was in the Y direction, and the main vibration direction on the rear axle was in the Z direction.  
Figure 9: The proportion of vibration intensity in different directions at idle speeds.