## 2 Materials and Methods
### Electro-Hydraulic Integrated Sowing Depth Measurement and Control System Design
#### 2.4.1 Hardware Design  
(a) Integrated Pressure-Reducing Cylinder (IPRC)  
In order to facilitate the multi-row expansion and reduce the wiring and improve the system response speed, the electro-hydraulic IPRC is designed adaptively, which consists of a cartridge-type pressure-reducing valve and a single piston cylinder. As shown in Figure 6, the cylinder rod cavity is directly connected to the return path B, and the piston cavity is directly connected to the proportional pressure-reducing valve and connected  
Figure 5: Diagram of the force of the sowing depth adjustment mechanism: (1) sowing depth adjustment handle, (2) frame, (3) gauge wheel arm, (4) depth-limiting block, (5) axle pin sensing, (6) axle pin fixing support, (7) depth-limiting stopper. to the inlet path A and the overflow path T. In the multi-row connection, each cylinder is interconnected with the oil port in the form of A-A1, B-B1 and C-C1 (Figure 6), eliminating the need for wiring between rows of valve groups and improving the integration of the system. When the IPRC is working, the coil YA0 is energized, and the left position of the solenoid valve is pressurized; when the power is lost, the right position is decompressed, and the spool is dynamically balanced, so that the hydraulic force is stabilized near the target value. In Section 2.3.1, the theoretical hydraulic force value of at least 10.3 kN needs to be applied at the four-bar linkage. Taking into account the no-till sowing environment, seed and fertilizer consumption and other factors, the design is carried out according to the maximum thrust limit \(Pn\) of the cylinder which is 16 kN and the pressure drop \(\Delta F_{Y}\) which is 12\(\sim\)16 kN within the range of the mechanical adjustment of the sowing depth. According to the safe stroke \(S_{safe}\) of the cylinder which is 55 mm, the permissible stroke of the cylinder is determined as 60 mm and the installation distance is 30 cm. After consulting the work manual of the tractor, the oil supply pressure p of the tractor is selected as 16 MPa and the rated flow rate is 40 L\(\cdot\)min\({}^{-1}\). The cylinder speed ratio is the area ratio of the rodless chamber to the rod chamber. Generally speaking, when the cylinder stroke is long and subject to thrust (piston rod extension when there is force), in order to improve the piston rod pressure stability, one should choose a higher cylinder speed ratio. We take the speed ratio factor of 1.38 commonly used in agricultural machinery. According to the design criteria of the hydraulic cylinder [42], the formula for calculating the hydraulic cylinder bore \(D\) is  
\[D\ =\ \sqrt{\frac{4P_{n}\varphi}{\pi p}} \tag{11}\]  
where \(D\) is the hydraulic cylinder inner diameter, m; \(Pn\) is the hydraulic cylinder theoretical thrust, take 16 kN; \(p\) is the system oil supply pressure, take 16 MPa; and \(\varphi\) is the speed ratio coefficient, take 1.38. The calculation can be obtained \(D\approx\) 0.0419 m, according to the hydraulic cylinder design manual, and the preliminary determination of the hydraulic cylinder bore \(D\) is 40 mm. From the speed ratio formula,  
\[\varphi=\frac{D^{2}}{D^{2}-d^{2}} \tag{12}\]  
Figure 6: (**a**) Diagram of the IPRC, (**b**) IPRC schematic: (1) valve block, (2) return pipe, (3) piston rod, (4) cylinder, (5) cartridge-type pressure-reducing valve. where \(D\) is the hydraulic cylinder inner diameter, take 0.04 m; \(d\) is the hydraulic cylinder piston rod diameter, m; and \(\varphi\) is the speed ratio coefficient, take 1.38. The calculation can be obtained \(d\) = 20.1 mm, according to the design manual of the hydraulic cylinder piston rod, and the diameter of the piston rod \(d\) is 20 mm. According to [PERSON]'s principle, the pressure-reducing range of the cylinder is  
\[\Delta P=\frac{\Delta F_{Y}}{\pi\left(\frac{D}{2}\right)^{2}} \tag{13}\]  
The theoretical downforce drop \(\Delta F_{Y}\) is 4 kN, and the theoretical pressure reduction range is 3.184 MPa by substituting into Equation (13).