## 2 Materials and Methods
### Field Vibration Data Collection and Analysis
The experiment was conducted in two sets: first, the seed drill operated at a low speed of 0.56 m/s; second, it operated at a higher speed of 0.83 m/s. Each test lasted 20 min to satisfy the requirements for the subsequent spectral analysis of the signal length. During the tests, the vibration test system was powered up and the DAQami data collection and analysis software, which pairs with the E-1608 data acquisition card, was launched on a portable computer. The software was set up to connect to the wireless router network, and the sampling frequency was adjusted to 2000 Hz. After subjecting the raw vibration signals to appropriate and rational mathematical treatment, we found that the minimum acceleration was \(-9.83944\) m/s\({}^{2}\) and the maximum acceleration was \(35.2845\) m/s\({}^{2}\) in low-speed conditions, as seen in Figure 2. In high-speed conditions, the minimum acceleration was \(-9.04467\) m/s\({}^{2}\) and the maximum acceleration was \(79.26817\) m/s\({}^{2}\). It is clear that the vibration intensity of the seed drill was significantly greater at high speeds than at low speeds. When installing the accelerometer, the vertically downward direction was designated as negative and the vertically upward as positive. As the seed drill performed shallow tilling and stubble removal, the blades cutting downward into the soil produced an upward reactionary force. This caused the seed drill to move upwards, resulting in an upward acceleration. Conversely, when gravity affected the seed drill on its descent, it experienced a downward acceleration. Due to the substantial rotational inertia of the rotary tiller blades at high speeds, the downward acceleration should be between 0 and \(-9.8\) m/s\({}^{2}\), as evident in Figure 2.  
The vibration signals from the seed drill in the rice stubble field exhibit numerous discrete peaks. These are likely due to the rotary tiller blades encountering the tough rice stubble roots during rotary tillage for stubble removal, generating considerable reactionary forces when cutting through them. This phenomenon is particularly notable when the seed drill operates at high speeds. The vibrations of the seed drill on the rice stubble field were significant and markedly increased with the operational speed of the seed drill. Figure 2: Time domain signal diagram for the vibration acceleration of the seed drill at different speed. To process the acceleration signals gathered during the test, a frequency domain integration was performed. The formula for the numerical computation of the second integration in the frequency domain is as follows [18; 19]:  
\[y(r)=\sum_{K=0}^{N-1}-\frac{1}{\left(2\pi\kappa\Delta f\right)^{2}}H(k)X(k)e^{i2 \pi\hbar\tau/N} \tag{1}\]  
Matlab 2018 was employed to carry out a Fourier transform on the vibration data, from which trend terms were removed [20]. The data underwent second-order integration in the frequency domain, and an inverse Fourier transform was then applied to obtain the vibration displacement as a function of time. The selected lower and upper cutoff frequencies were 2 Hz and 200 Hz, respectively. As shown in Figure 3, the seed drill's maximum vibration amplitude reached 2.49 mm at low operational speeds; at high operational speeds, the maximum amplitude increased to 7.78 mm, indicating that the vibration amplitude escalated with the seed drill's working speed. There were sporadic sharp rises in the vibration amplitude of the seed drill within the first 15 s. This occurred because the 2 BYG-220 type rapeseed combined seed drill performed rotary tillage for stubble removal. It shattered parts of the rice stubble that were embedded in the soil--roots and stalks--and were more robust than the soil itself. When the rotary filler blades encountered difficulty in breaking the stubble smoothly, the vibrations from the tillage process increased abruptly. Hence, the seed drill experienced random surges in vibration amplitude. The vibration pattern of the seed drill in the rice stubble field is fundamentally composed of sinusoidal signals.