In the field of valve remote control systems, particularly within the marine industry, the selection of an appropriate actuator for butterfly and ball valves is critical. Various types exist, including electric, pneumatic, hydraulic, and electro-hydraulic actuators, each with distinct advantages and limitations. Electric actuators offer versatile communication modes and rapid response but become structurally complex and bulky when designed for fail-safe (single-acting) operation, especially in submerged environments. Pneumatic actuators, utilizing compressed air, are simple in design but limited by the compressibility of air, typically operating within 0.2 to 0.8 MPa pressure ranges, which constrains their torque output and results in larger sizes, poorer stability, and slower response. Helical hydraulic actuators employ double-stage involute spiral mechanisms, requiring complex manufacturing processes, high precision, and higher costs; when configured for single-acting functionality, their elongated height poses installation challenges. Electro-hydraulic actuators combine the benefits of electric and hydraulic systems, enabling precise valve positioning with fast, stable control, but the inclusion of an individual power source per unit increases overall costs significantly. In response to these challenges, I have developed a single-acting hydraulic actuator based on a rack and pinion gear mechanism, utilizing disc springs for energy storage. This design ensures automatic valve closure upon loss of hydraulic power, offering advantages such as simplified manufacturing, lower processing precision requirements, cost-effectiveness, compact dimensions, and high torque output. Its low-profile design allows installation along pipeline lengths, saving space in marine ventilation systems, making the rack and pinion gear configuration widely applicable in this sector.
The working principle of the single-acting rack and pinion hydraulic actuator involves converting the linear motion of a rack into the rotary motion of a pinion gear. When an electric motor drives a gear pump to rotate at high speed, hydraulic oil is directed through specific circuits into the piston’s sealed chamber of the actuator. This pressurized oil forces the piston to move toward the disc spring chamber, compressing the disc springs until a limit switch in the valve position indicator triggers, signaling the control system that the valve is fully open and stopping the motor. Upon receiving a close signal, the control system de-energizes a two-position, two-way solenoid valve, returning it to its normally open position. The compressed disc springs then release their stored potential energy, displacing hydraulic oil from the piston chamber back to the tank and driving the piston to return to the closed position. This rack and pinion mechanism ensures reliable operation and fail-safe closure, which is essential for safety-critical applications.
The structural configuration of the single-acting rack and pinion hydraulic actuator comprises several key components, including a base body, rack, pinion shaft, cylinder barrel, end covers, piston, disc spring chamber, limit bolts, and sealing elements. The base body features a cross-shaped internal cavity to house the rack and pinion gear assembly. The cylinder barrels are threaded into the base body, forming sealed chamber A with the piston, cylinder barrel, closed limit bolt, and seals. Chamber B, formed by the disc spring set and the single-acting cylinder barrel, stores the potential energy from spring compression. The piston is equipped with wear rings, U-seals, and Glyd rings, allowing smooth movement within the cylinder barrel, with travel limits set by the limit bolts. Hydraulic oil entering chamber A via a compression fitting pushes the rack linearly, rotating the pinion shaft counterclockwise to open the valve while compressing the disc springs. In the event of power loss, the disc springs expand, moving the rack in the opposite direction to close the valve via clockwise pinion rotation. This rack and pinion design is central to the actuator’s functionality, providing efficient motion conversion and robust performance.
To determine the mechanical parameters of the rack and pinion gear, I established a mathematical model targeting an initial output torque of 160 N·m at the 0° position. The gear and rack must withstand shear stresses and exhibit high wear resistance at the tooth roots. I selected 45 steel for the pinion, treated with QPQ salt bath to enhance surface hardness and wear resistance, and 40Cr for the rack, subjected to quenching and tempering for improved durability. The mechanical strength was verified based on tooth root bending strength, using the following formula for the module calculation:
$$ m \geq \sqrt[3]{\frac{2KT’}{\phi_d Z_1^2} \left( \frac{Y_{Fa} Y_{Sa}}{[\sigma_F]} \right)} = 2.97 $$
where \( K \) is the load factor, \( T’ \) is the design output torque in N·m, \( \phi_d \) is the face width coefficient, \( Z_1 \) is the number of teeth, \( [\sigma_F] \) is the allowable bending fatigue strength in MPa, \( Y_{Fa} \) is the form factor, and \( Y_{Sa} \) is the stress correction factor. Based on this, I finalized the parameters with a module \( m = 3 \) and teeth number \( Z = 18 \). The material properties are summarized in the table below:
| Component | Material | Tensile Strength σb (MPa) | Yield Strength σs (MPa) |
|---|---|---|---|
| Pinion Gear | 45 Steel | 650 | 360 |
| Rack | 40Cr | 700 | 500 |
For the disc spring selection and calculation, I considered the torque requirements at initial and fully open positions. At 0° position, the output torque \( T_1 = 160 \, \text{N·m} \), and the force on the rack is calculated as follows, with the pitch radius \( R \):
$$ R = \frac{m \times Z}{2} = 0.027 \, \text{m} $$
$$ F_1 = \frac{T_1}{R} = 5926 \, \text{N} $$
where \( F_1 \) is the spring force at initial position. When the actuator rotates 90°, the rack displacement \( S \) is:
$$ S = \frac{\pi \times m \times Z \times 90^\circ}{360^\circ} = 42.39 \, \text{mm} $$
Under a hydraulic pressure of 13 MPa and cylinder diameter \( D = 50 \, \text{mm} \), the output torque \( T’_2 \) overcoming the minimum spring compression force \( F_2 \) is:
$$ T’_2 = p \times \frac{\pi \times D^2}{4} \times \frac{m \times Z}{2} \times \eta = 586 \, \text{N·m} $$
$$ F_2 = \frac{T’_2}{R} = 21703 \, \text{N} $$
where \( \eta \) is the mechanical efficiency. Thus, the disc spring must exert less than 21,703 N at maximum compression. I selected disc spring model 180060 in a series combination, with parameters and force-displacement characteristics as below:
| Parameter | Value |
|---|---|
| Outer Diameter D (mm) | 60 |
| Inner Diameter d (mm) | 20.5 |
| Thickness t (mm) | 3 |
| Free Height H0 (mm) | 5.2 |
| h0/t | 0.733 |
| h0 (mm) | 2.2 |
From the force-displacement curve, the force at minimum compression is 12,892 N, well below 21,703 N, meeting the design requirement. Using the single-piece compression, I determined 54 disc spring pieces. The actual torque at minimum compression \( T_3 \) is:
$$ T_3 = F’_2 \times R = 348 \, \text{N·m} $$
Thus, the output torque at full open position (90°) under 13 MPa is:
$$ T_2 = T’_2 – T_3 = 238 \, \text{N·m} $$
For the cylinder barrel wall thickness calculation and verification, I used material 45# steel with tensile strength \( \sigma_b = 600 \, \text{MPa} \). Assuming a safety factor of 5, the allowable stress \( \sigma_p \) is:
$$ \sigma_p = \frac{\sigma_b}{n} = 120 \, \text{MPa} $$
The minimum wall thickness \( \delta \) is calculated as:
$$ \delta = \delta_0 + C_1 + C_2 $$
where \( C_1 \) is the outer diameter tolerance, \( C_2 \) is the corrosion allowance, and \( \delta_0 \) is the minimum thickness based on material strength:
$$ \delta_0 \geq \frac{p_{\text{max}} \times D}{2.3 \sigma_P – 3 p_{\text{max}}} $$
with \( p_{\text{max}} = 20 \, \text{MPa} \) and \( D = 50 \, \text{mm} \). For a cylinder with inner diameter 50 mm and wall thickness 5 mm, the permissible plastic deformation pressure is verified using:
$$ p_N \leq 0.35 \times \sigma_s \times \frac{D_1^2 – D^2}{D_1^2} $$
where \( \sigma_s = 355 \, \text{MPa} \), \( D_1 \) is the outer diameter. The bottom thickness \( \delta_1 \) of the cylinder is calculated as:
$$ \delta_1 \geq 0.433 \times D_2 \times \sqrt{\frac{p}{\sigma_P}} $$
where \( D_2 \) is the cylinder outer diameter. The results are summarized in the tables:
| Parameter | Value |
|---|---|
| Cylinder Bore Inner Diameter (mm) | 50 |
| Minimum Wall Thickness (mm) | 4.6 |
| Parameter | Value |
|---|---|
| Cylinder Bore (mm) | 50 |
| Wall Thickness (mm) | 5 |
| Outer Diameter (mm) | 60 |
| Verification Value (MPa) | 38 |
| 0.35 Fully Plastic Deformation (MPa) | 23 |
| 0.42 Fully Plastic Deformation (MPa) | 27 |
| Parameter | Value |
|---|---|
| Cylinder Bore Inner Diameter (mm) | 50 |
| Bottom Thickness (mm) | 8.8 |
The working volume of hydraulic oil required for a full stroke from closed to open position is determined by the rack displacement \( S = 42.39 \, \text{mm} \) and cylinder diameter \( D = 50 \, \text{mm} \):
$$ V_1 = \frac{\pi \times D^2}{4} \times S \times 10^{-3} = 83 \, \text{mL} $$
This volume is essential for sizing the hydraulic pump and reservoir in the system.
To validate the theoretical models, I manufactured a prototype HSQ160 single-acting rack and pinion hydraulic actuator based on the design drawings and conducted performance tests. The torque test involved connecting the actuator to a hydraulic power pack and a torque test bench. Measurements at initial position showed an output torque consistent with the theoretical 160 N·m, while at full open position under spring compression, the torque aligned with calculated values. By adjusting the relief valve pressures, I recorded output torques at various input pressures and compared them with theoretical predictions, as summarized in the table below:
| Input Pressure (MPa) | Theoretical Torque (N·m) | Actual Torque (N·m) |
|---|---|---|
| 5 | 225 | 218 |
| 8 | 360 | 352 |
| 10 | 450 | 442 |
| 13 | 585 | 578 |
The results demonstrate close agreement between theoretical and actual values, confirming the accuracy of the rack and pinion gear design and disc spring selection. For impact pressure resistance and sealing tests, I set the hydraulic power pack relief valve to 19.5 MPa and maintained the pressure for 5 minutes. The actuator components showed no damage or permanent deformation, and no hydraulic oil leakage was observed from the seals, verifying the structural integrity and sealing effectiveness under high-pressure conditions.
In conclusion, the development of the single-acting rack and pinion hydraulic actuator involved detailed mathematical modeling of the rack and pinion gear parameters, disc spring selection, cylinder strength verification, and volumetric calculations. The prototype testing validated the design, showing that the output torque, pressure resistance, and leakage performance meet the requirements. This work provides a reliable foundation for scaling the design to other torque ranges and applications, leveraging the benefits of the rack and pinion mechanism for compact, efficient, and cost-effective hydraulic actuation in marine and other industries. The successful integration of disc springs ensures fail-safe operation, while the rack and pinion gear system offers a robust solution for converting linear motion to rotary torque with high efficiency and reliability.