## 4 Discussion  
It is well known that the different components of the tractor are rigidly connected, and the engine is the main vibration source of the tractor. The major components in the vibration transmission route of the tractor, such as the front axle, engine, gearbox, differential box, and rear axle, are all rigidly connected and fixed to the main frame structure. Meanwhile, the tractor has an approximately symmetrical structure, so the left and right vibration characteristics of the front and rear axles should be similar when the tractor is under idling conditions. Based on the test results, it could be seen that the left and right sides of the tractor had good symmetry in the main vibration direction.  
The engine of the tractor is a compression ignition engine, which generates the main force in the Z direction. The main force is also the driving force that drives the tractor. Moreover, the reciprocating motion components of the engine can also generate forces in the Y direction. Based on the structure of the tractor, the front axle is closer to the engine than the rear axle and the front axle bears more engine weight than the rear axle. Furthermore, the pneumatic tires, have a damping effect that helps reduce the vibration intensity in the Z direction [13; 29]. Consequently, the fluctuation of the air pressure inside the tires due to vibration can increase the Y direction vibration of the front axle of the tractor, as can be seen in Figures 8 and 9. The vibration generated by the tractor engine is transmitted along the vibration transmission route 2 shown in Figure 3. The engine, transmission, differential, and rear axle are rigidly connected and the cab situated over the rear axle is also rigidly connected to the frame. This will limit the transmission of tractor vibration along transmission route 2. Hence, the vibration intensity of the rear axle test locations will be reduced, especially in the X and Y directions [30]. The vibration intensity of the rear axle test points in the X and Y directions was significantly lower than that of the front axle test points in the X and Y directions. The main vibration direction of the rear axle test point was the Z direction. Therefore, the main vibration directions of the front and rear axle test points of the tractor were inconsistent, as can be seen from Figures 8 and 9.  
When the tractor was at high idle speed or low idle speed, respectively, the main vibration direction for the front and rear axle test points remained constant. However, the vibration intensity of the tractor at an idle speed of 1000 r/min was lower than that at an idle speed of 800 r/min, as shown in Figure 8. This reduction in vibration intensity may be attributed to the working principle of the compression ignition engine of the tractor, which can encounter issues such as unstable engine operation and inadequate combustion at lower speeds. Unnecessary vibration will be caused.  
Combined with the test results, it can be seen that the proposed wireless vibration testing method can be utilized to effectively and accurately assess the vibration characteristics of the tractor in the idle state. The proposed wireless vibration testing method can be used to accurately determine the main direction of vibration generated by the tractor under idle conditions. In turn, it can be used to detect any faults or assembly defects in the tractor.