Multi-objective optimization design of low-power-driven, large-flux, and fast-response three-stage valve

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Scientific Reports volume 14, Article number: 21575 (2024 ) Cite this article pvc slide valve

Intrinsically safe solenoids drive solenoid valves in coal mining equipment. The low power consumption of these solenoids limits the response time of the solenoid valves. Additionally, the low viscosity and high susceptibility to dust contamination of the emulsion fluid often lead to leakage and sticking of hydraulic valves. This study proposes a low-power-driven, large-flux, fast-response three-stage valve structure with an internal displacement feedback device to address these issues. The critical parameters of the valve were optimized using a novel multi-objective optimization algorithm. A prototype was manufactured based on the obtained parameters and subjected to simulation and experimental verification. The results demonstrate that the valve has an opening time of 21 ms, a closing time of 12 ms, and a maximum flow rate of approximately 225 L/min. The driving power of this structure is less than 1.2 W. By utilizing this valve for hydraulic cylinder control, a positioning accuracy of ± 0.15 mm was achieved. The comparative test results show that the proposed structural control error fluctuation is smaller than that of the 3/4 proportional valve.

High-pressure water-based hydraulic valves are widely used in coal mining equipment. However, the water-based transmission medium in the hydraulic system of comprehensive mining faces is highly susceptible to dust contamination, leading to common issues such as valve components jamming and leaking during operation1,2. Therefore, enhancing the pollution resistance of valves and reducing internal leakage have become urgent issues to address3. The failure of hydraulic valves can result in numerous malfunctions of controlled equipment, directly threatening the safety of coal miners, damaging mechanical equipment in the work area, increasing maintenance workload, and severely affecting production efficiency on the work surface4.

The working medium of the hydraulic valves in the fully mechanized mining face is a high water-based fluid with 5% oil and 95% water, forming an oil-in-water (O/W) emulsion, which has low viscosity and operates at high pressures, typically around 32 MPa5. Under the exact clearance and pressure drop, the leakage loss of high-pressure water-based hydraulic valves of the same specifications is tens of times that of oil pressure control valves, requiring a tight matching in their structure6. Additionally, internal leakage must be almost zero when the spool is closed, necessitating the avoidance of slide-valve structures7. To meet these performance indicators, it is necessary to consider the sole physicochemical properties of water-based medium comprehensively, improve the structure and design parameters of hydraulic valves, or develop entirely new designs.

In addition to the issues of clutch and leakage, the driving solenoid power of control valves in coal mining equipment should be less than 1.2 W8. To meet the system's mass flow rate requirements, existing research often adopts a two-stage or three-stage valve structure9,10. In addition to the high flow rate, the hydraulic system in the fully mechanized mining face imposes stricter demands on response time than conventional hydraulic systems. However, due to factors such as large flux, spool mass, and large stroke, a conflict exists between large flux and fast response, making the design of such control valves challenging11.

High-speed on–off valves (HSV), belonging to a type of digital hydraulic component, are always in either fully open or fully closed states. They can convert discrete control signals into discrete flow rates, offering advantages such as fast response, simple structure, high reliability, and insensitivity to hydraulic fluid contamination12. However, due to their inability to provide significant flow rates during rapid responses, multiple actuators are often employed for small-scale equipment or pilot valves13. To address this limitation, without altering the structure and type of high-speed valves, multiple high-speed valves are typically connected in parallel to form a Digital Flow Control Unit (DFCU) to expand flow rate gain and resolve the contradiction mentioned above14.

Previous research on high-flow and fast-response valves has primarily focused on proportional/servo or HSV15,16,17. In recent years, there has also been significant progress in pilot valves for HSV18,19. However, it is almost inevitable to have spool structures when controlling flow direction in hydraulic systems using proportional/servo valves20. Some HSVs, driven by armature coils with permanent magnet structures in on–off valves, can generate significant flow rates, but they operate at low pressures and have internal piston-type structures21,22. On the other hand, standard high-flow cartridge valves cannot meet the demand due to their lack of fast response23.

Multi-objective optimization algorithms are commonly employed in the optimization design of valve structures24,25,26. The proposed three-stage valve (TSV) exhibits strong coupling relationships among its stages, making its critical design parameters difficult to determine. With multiple design parameters and mutual constraints, obtaining the optimal solution by optimizing a single parameter is highly challenging. The optimization design problem of the TSV is a multi-objective optimization problem, with advanced solutions achieved through optimization algorithms. Among them, metaheuristic methods find extensive engineering applications. Metaheuristic algorithms refer to an algorithmic framework independent of specific problems, where heuristic methods are inspired by natural phenomena, biological behaviors, or even mathematical principles27. Metaheuristic methods possess advantages such as randomness, ease of implementation, and consideration of black-box scenarios, making them adept at tackling complex engineering problems28.

Among various metaheuristic algorithms, the Electric Eel Foraging Algorithm (EEFO) has recently gained significant attention in the literature. This algorithm mathematically models four key foraging behaviors of electric eel groups: “Interacting, Resting, Hunting, and Migrating.” It provides exploration and exploitation during the optimization process. An energy factor is developed to manage the transition from global to local search and balance exploration and exploitation in the search space. Test results have shown that EEFO exhibits excellent performance in exploitation, balancing exploration and exploitation, and avoiding local optima29.

Structural adjustments are made to the poppet valve to avoid using a slide-valve structure. In this study, the displacement-flow feedback principle is utilized, where the piston in the lift valve structure is replaced with a pressure control chamber. Four displacement feedback orifices are installed on the valve spool to control the valve opening based on the pressure control chamber's pressure.

The displacement-flow feedback principle, also known as the “Valvistor” valve control principle, was proposed by ANDERSSON from Linköping University in Sweden in the 1980s. It has advantages such as a simple structure and gratifying dynamic and static characteristics and has been widely applied30,31. By replacing the slide structure in the poppet valve with a pressure control chamber, a TSV structure, as shown in Fig. 1, is proposed in this research. The three-stage poppet valve comprises a pilot HSV, a secondary stage, and a main valve. The two pilot valves are a bidirectional poppet valve and an HSV. The modified poppet valve still has a slide-valve structure, which means there may be leakage. However, the sealing of this valve does not rely on the piston structure. The leakage flow from the piston structure towards the C port is reliably blocked by the poppet valve in the previous stage, together with the flow passing through the feedback orifice32. Therefore, the novel TSV structure does not have leakage issues. Since there is no requirement for the sealing performance of the piston structure and a displacement feedback orifice is present on the mating surface, the spool will not experience clutch phenomena.

Working principle of the three-stage valve and structure of the spool.

The flow controlled by the secondary stage should be sufficiently large to achieve a fast step response at the main stage. Therefore, the size and flow capacity of the secondary valve are always more extensive than those of conventional high-flow directional valves and HSVs. As a result, the HSV's electromagnetic driving force is insufficient to drive the secondary valve directly without a pilot valve. Adding a pilot stage to the secondary stage drives the secondary stage by pressure instead of magnetic force. Since the steady-state hydrodynamic force acting on the hydraulic lift valve is much weaker than the pressure, hydrodynamic forces' influence on the spool motion is neglected28. At the same time, the pilot valve's size and the electromagnetic valve's driving force are reduced, resulting in a shorter response time for the pilot stage. Due to these advantages, the valve adopts a three-stage structure. The secondary stage and the main valve are poppet valves with displacement feedback structures that connect ports A and C. Due to the larger area of the top end of the poppet valve compared to the bottom end, the poppet valve can reliably close under static pressure. At the same time, the internal leakage between the spool and the sleeve can be shielded by the pilot stage. The oil supply port P is connected to high-pressure oil, and the oil return port T is connected to the load.

The working principle of the TSV is as follows. When a control signal is input, the pilot HSV opens, causing a pressure decrease at port C2. As a result, the secondary stage opens, leading to a pressure decrease at port C1, and the main valve opens. The closing process is the same as the opening process, and after the pilot HSV is closed, the secondary and main valves close sequentially. This valve has a proportional throttling function in the A-B direction and a check valve cutoff function in the other direction.

The hydraulic system discussed in this article is depicted in Fig. 2. As shown, the position of the inertial load is driven by an asymmetric single-rod hydraulic cylinder, actuated by four TSVs (Throttle Servo Valves). The flow input of the TSVs is adjusted via the control signal u. When u > 0, valves (a) and (d) are open, and valves (b) and (c) are closed. High-pressure fluid from the oil pump flows through valve (a) into the rodless chamber of the hydraulic cylinder, causing it to extend under the pressure differential. Conversely, when u < 0, valves (b) and (c) are open, and valves (a) and (d) are closed. High-pressure fluid from the pump flows through valve (c) into the rod chamber of the hydraulic cylinder, causing it to retract due to the pressure differential. Ps = 7 MPa, Pt = 0 MPa, and each TSV’s flow rate should exceed 100 L/min (Q01 > 100 L/min, Q02 > 100 L/min). The response time should be minimized while meeting the required flow rates.

Before analyzing the system's dynamic characteristics, it is necessary to determine the displacements of the spools in each stage of the TSV at the steady state. This will provide information on the flow rates at each stage and the relationship between the total flow rate and critical design parameters.

The flow through the pilot HSV can be represented as:

The flow through the secondary stage can be represented as:

The flow through the feedback throttling grooves of the secondary stage can be represented as:

The flow through the main stage can be represented as:

The flow through the feedback throttling grooves of the main valve can be represented as:

The total flow equation through the TSV can be represented as:

When the valve is in a steady state, the flow through the feedback throttling grooves of the main stage is equal to the sum of the flows through the secondary stage and the pilot HSV:

The flow through the secondary feedback throttle slot is equal to the flow through the pilot HSV:

In the stable open state of the valve, neglecting the influence of hydrodynamic forces, the force balance equations for the main and secondary spools can be derived:

To obtain the displacement of the main stage spool when the pilot HSV is opened, the following assumptions are made: the flow coefficient of each orifice is the same, the flow inside the pressure control chamber has no effect on the pressure distribution, and the pressure acting on the surfaces of the spool is uniformly distributed, and the force exerted by the spring on each spool is neglected. Firstly, when the spool is at maximum lift, the net force acting on the spool should be zero in the axial direction, and the pressures inside each pressure control chamber are as follows:

Substituting Eqs. (1), and (3) into (8), the displacement of the secondary stage spool is:

Substituting Eqs. (1), (2), and (5) into (7), the displacement of the main valve spool is:

Equations (11), (12), (13), and (14) can be used to solve for the openings of the main and secondary stages. An iterative method can be employed here, starting with a reasonable initial value for Eqs. (9) and (10), then substituting the calculated values of Pc1 and Pc2 into Eqs. (13) and (14), and obtaining x1 and x2. This process is repeated until the interpolated result of two iterations is small enough.

If the influence of the spring force is neglected, by observing Eqs. (13) and (14), it can be concluded that Wt2 affects the opening of the secondary stage spool; increasing x02 or Wt2 will decrease the value of x2. And x2 affects the opening of the main stage; increasing x01, decreasing x2, or increasing Wt1 will decrease the value of x2. Therefore, the design parameters that impact the system flow most are Wt1, Wt2, x01, and x02. To improve the flow capacity of the valve, further optimization design should be carried out.

Even without considering the effects of the circuit, the HSV system is still a third-order system. Since no adjustments are made to the structure of the HSV to simplify calculations, it is assumed that the movement of the secondary stage and the main valve starts after the HSV is fully opened. At this point, the flow through the HSV can be simplified as a function of the control chamber pressure Pc2. The analysis of the dynamic characteristics of the TSV involves the damping analysis of the orifices in the hydraulic control circuit and the force analysis of the poppet valves at each stage, as shown in Fig. 3. It can be observed that the shared control chamber pressure Pci serves as the bridge and link between the stages. There is a strong coupling relationship between each spool, and the interaction between the stages achieves the implementation of the displacement feedback principle and the dynamic and static performance of the hydraulic valve. The dynamic equations for the poppet valve components can be derived based on Newton’s second law:

Force analysis of the moving parts.

When considering dynamics, the instantaneous flow through each orifice no longer has a simple mathematical relationship, and real-time calculations need to be performed based on the dynamic pressures before and after the orifices. The pressure in the pressure control chambers also needs to be integrated using the flow continuity equation. According to the chamber-node method, each control chamber is treated as a flow-node. The dynamic equations for the pressure in each pressure control chamber can be written as follows:

For the general flow Eq. (1) of an orifice, if the flow area A has an analytical relationship with the displacement x of a particular moving component, the flow equation can be linearized near the operating point using a first-order Taylor expansion:

Here, Qω, Aω, Pωin, Pωout, and xω represent the flow, flow area, inlet pressure, outlet pressure, and displacement of the orifice at the operating point, while Pin, Pout, and x represent the incremental changes in inlet pressure, outlet pressure, and displacement near the operating point. kp and kx are the incremental gain factors for the flow-pressure and flow-displacement relationships of the orifice at the operating point. The above equation can be rewritten to express the incremental flow:

Here, δQ represents the incremental flow of the orifice near the operating point. By neglecting the influence of the displacement of the moving component on the dynamic chamber volume, the dynamic Eqs. (16) and (17) for the pressure control chambers can be linearized to obtain their linearized forms:

The coefficients kp1, kp2, kp3, kp4, kx1, and kx2 can be calculated as follows:

The input variables Ps and Pt are proposed, while the incremental displacements x1 and x2 of the spools in the poppet valves are selected as the respective output variables. The incremental displacements x1 and x2 between the second-stage and main spools, their first-order derivatives concerning time \(\dot{x}_{1}\) and \(\dot{x}_{2}\) , and the pressures Pc1 and Pc2 in the control chambers form six state variables. By rearranging Eqs. (15)–(28), the state-space representation of the linearized feedback principle of displacement flow within the TSV near the operating point can be obtained.

where the state variables X are structured as follows:

The input variable U and the output variable Y are structured as follows:

The components of the state matrix A, input matrix B, and output matrix C for the linearized state-space model of the expanded TSV are as follows:

Using the system's state-space model, the unit step response can be obtained, which allows for the analysis of the system’s time response. The step response curve of the system is shown in Fig. 3, where the TSV's response time is considered the adjustment time. Adjusting the input parameters can achieve different system response times. The system's stability can be checked during the computation based on the system’s poles and zeros distribution.

As shown in Table 1, there are six key design parameters determining the TSV system, including Wt1, Wt2, D1, D2, α1, and α2, representing the width of the main valve spool throttle slot, the width of the secondary valve spool throttle slot, the diameter of the main spool, the diameter of the secondary school, the area ratio of the main spool, and the area ratio of the secondary spool, respectively. The initial values and optimization ranges of these parameters are given in Table 1, where the initial values are based on the flow requirements of the valve to meet system stability. The optimization ranges comprehensively consider factors such as the volume of the valve, output flow rate, machining difficulty, etc.

The orifice area of the throttle slot in the TSV should exceed that of the second-stage valve. Hence, Wt1 is set with a minimum value of 2 mm. Increasing Wt1 reduces the opening of the third-stage spool, so a more prominent upper bound is set to allow the optimization algorithm to compute over a broader range. Although choosing a smaller value for Wt2 can achieve a more significant flow amplification coefficient, the throttle slot area should exceed that of the pilot HSV. Considering machining precision and potential liquid contamination during TSV operation, Wt2 should not be set too small. Hence, its minimum is set at 1mm. Furthermore, a conservative upper limit is defined to prevent system instability. The initial values of D1, D2, α1, and α2 are selected based on the flow amplification formula (14), aiming for roughly equal openings of the two relief valves to ensure simultaneous closure of their spools while maintaining system stability.

The preliminary design of the system parameters results in the step response curve of the system shown in Fig. 4. After the control signal input, the system exhibits an overshoot of 73.6% and reaches a steady-state value of 0.557 after three oscillations. The required settling time is 18.17 ms.

Optimization refers to finding the optimal solution or acceptable approximations among numerous solutions for a given problem under certain conditions. Optimization can significantly improve problem-solving efficiency, reduce computational requirements, and save financial resources. The optimization design problem of the novel TSV is a MOO problem. In general, the sub-objectives in an MOO problem are conflicting, and improving one sub-objective may lead to a decrease in the performance of another or several other sub-objectives. It is not possible to simultaneously achieve the optimal values for multiple sub-objectives. Still, coordination and compromise among them are required to achieve the best possible values for each sub-objective33. The essential difference between MOO and single-objective optimization problems is that the solution is not unique but consists of a set of Pareto optimal solutions composed of numerous non-dominated solutions. The decision vectors in the solution set are called non-dominated solutions. The corresponding objective functions to the non-dominated vectors in the Pareto optimal set are represented graphically as the Pareto frontier.

The main parameters that affect the performance of the TSV are Wt1, Wt2, Ac1, Ac2, ɑ1, and ɑ2. When optimizing these parameters, they are interrelated and have trade-offs: increasing the area ratio ɑ1, ɑ2 can enhance the valve spool lift and flux, but it also increases the response time. Increasing the width of the feedback grooves Wt1 and Wt2 can improve the response time of the poppet valves but may reduce the valve lift and result in reduced flow. The fluctuation of each parameter makes it challenging to obtain an optimal solution by optimizing individual parameters.

This study's critical performance indicators for the designed TSV include response time, flow capacity, volume, weight, and manufacturing complexity. Response time denotes how quickly the valve reacts to input signals; a shorter response time enables precise control over fluid or pressure changes, thereby enhancing system controllability. Flow capacity refers to the amount of fluid the valve can process; higher flow output reduces actuator response times and improves system efficiency. Minimizing the valve’s size and weight facilitates easier installation and transportation. However, these parameters are not primary optimization targets due to the inherent conflict between volume/weight and flow capacity in three-way valves. Manufacturing complexity primarily pertains to technical challenges and cost factors during production and assembly, influencing structural dimensions to avoid excessively narrow channels and intricate grooves. Therefore, this study focuses on optimizing two objectives: response time and flow capacity.

This study utilizes an optimizer called EEFO, proposed in reference29, to simulate the foraging behavior of electric eels in a socially intelligent manner. EEFO incorporates four foraging behaviors: interaction, rest, hunting, and migration. It simulates interaction behavior for better exploration and rest, hunting, and migration behaviors for better utilization. The energy factor used in EEFO improves the balance between exploration and exploitation. The algorithm demonstrates excellent performance in development and exploration, balancing growth and exploration, and avoiding local optima. Further details of the EEFO algorithm can be found in reference29.

The computational flowchart for MOO is shown in Fig. 5. Before performing the objective optimization, the system is preliminarily designed, and the following parameters are determined: the lengths of the second-stage valve and the main valve, the stiffness of the reset spring K1 and K2, the pre-opening x01 and x02, and all parameters related to the HSV. The parameters to be optimized are Wt1, Wt2, D1, D2, ɑ1, and ɑ2. Based on the dynamic analysis of the system in “Dynamic modeling” section, the TSV system needs to ensure stability while achieving the most muscular flow capacity in the shortest response time. The optimization design problem of the TSV can be described as follows: under given constraints, select appropriate design variables x to optimize the objective function f(x) to its optimal value. The mathematical model is as follows:

Design flowchart in the present study.

Here, x = (x1, x2, …, x6) represents the design variables, f(x) represents the fitness function, and f(s) means the stability constraint condition, which should be equal to logic 1 when the system is stable. Considering the difficulty of machining, Xmin and Xmax are the lower and upper bounds of the design variables, respectively. The optimization has two fitness functions, representing the valve response time and flow rate. The response time can be calculated based on the adjusting time of the system’s step response. Among them, U(s) is the Laplace transform of the input signal, and H(s) is the system's transfer function. The system's flow rate can be calculated using Eq. (35).

The initial particle swarm is randomly generated and introduced into the main program loop based on the abovementioned constraints and optimization objectives. The particle swarm continues to search for the ideal values. The fitness values for the TSV's output flow rate and response time are calculated. The program can determine the maximum and minimum values of the fitness function and generate a series of Pareto solutions while comparing the distances between the solutions to ensure a certain distance is maintained between each solution and the others. Compared to the previous generations, the current generation's extreme values and positions will be updated. Then, the positions and velocities of the particles are updated, and the next generation of the particle swarm is generated. The loop continues until the specified number of generations. It is worth noting that the solver settings in this research are slightly different from the simulation model analysis in reference29. The solver in this research can simultaneously solve multiple objective functions and generate a Pareto solution set rather than solving the optimal value of a single objective function.

The parameter ranges are set as follows (mm): Wt1 ∈ [2,10], Wt2 ∈ [1,3], D1 ∈ [20,100], D2 ∈ [10,30], ɑ1 ∈ [0.1,1] and ɑ2 ∈ [0.1,1]. The number of iterations for EEFO is set to 500, and the population size is set to 500.

As shown in Fig. 6b, as the iterative calculations progress, the overall trend of the number of obtained solutions shows an increase. From the trend of the solution quantity, it can be observed that at the beginning of the calculation, particles can quickly approach the targets and obtain a significant number of solutions within a relatively short number of iterations. As the iterations proceed, the particles gradually converge near the optimal solution until they finally converge to a specific region, and the number of solutions in the set no longer increases. This indicates that the population and the number of iterations achieve convergence in the calculation. At the same time, a decrease in the number of solutions in the set can be observed. This is because the solutions generated in this iteration dominate one or more solutions in the existing solution set, requiring the removal of dominated solutions. Therefore, a decrease in the total number of solutions in the iteration calculation is expected.

(a) Solutions distribution; (b) changes in the number of solutions.

After the iterative calculations, all non-dominated solutions generated are stored, and completely identical non-dominated solutions are removed. This process results in the Pareto frontier (Fig. 6a), plotted as a two-dimensional scatter plot. From the plot, it can be seen that the obtained solution set does not have any dominance relationships among them and is uniformly distributed along the Pareto frontier. The flow rate is positively correlated with the response time, meaning that as the flow rate increases, the system’s response time also increases. This is because obtaining a larger flow rate requires an increase in the valve spool lift and diameter, which leads to a longer valve action time and increased inertia.

Directly obtaining usable design parameters from the solutions obtained through the optimization algorithm is still impossible. Here, an Analytical Hierarchy Process (AHP) method is introduced. AHP is a simple method for making decisions on complex and ambiguous problems, especially those that are difficult to analyze quantitatively. It was proposed by Professor T. L. Saaty, an American operations researcher, in the early 1970s as a convenient, flexible, and practical multi-criteria decision-making method34. When determining the weights of factors that influence a specific criterion, these weights are often difficult to quantify. When there are many factors, decision-makers may inconsistently provide data that does not reflect their perceived importance due to incomplete consideration. The pairwise comparison method can establish pairwise comparison judgment matrices for the factors. The comparison judgment matrix for the TSV is shown in Table 3. In the analysis, two additional design parameters, D1 and D2, are included and given relatively low weights. We hope the TSV can have a smaller volume and weight while meeting the optimized performance criteria.

The values in Table 2 indicate the relative importance of the abscissa compared to the ordinate. An immense numerical value implies a greater significance of the parameter corresponding to the abscissa than the parameter corresponding to the ordinate. Therefore, the values on the diagonal are all 1. In this study, the valve's response time (T) is considered the most important performance indicator. Thus, the importance of T is three times that of the flow rate (Qv), five times that of the diameter of the main valve spool (D1), and seven times that of the diameter of the secondary valve spool (D2). Flow rate (Qv) is the second most important performance indicator. The influence of the diameter of the secondary valve spool (D2) on the valve volume is smaller than that of the main valve spool (D1). Hence, it is given a weight lower than that of the main valve spool.

First, the obtained design parameters are normalized, and then the processed data is multiplied by the weights obtained from the AHP method and summed. The results are shown in Fig. 7. Taking into account the machining accuracy and the influence of the AHP analysis results, the final values of the design parameters are obtained as follows.

AHP overall weight percent for solutions on the Pareto front.

The optimized values of each design parameter are shown in Table 3.

A prototype of the valve was manufactured to validate the performance of the proposed TSV, and an experimental setup was constructed based on the calculations from the EEFO algorithm, as shown in Fig. 8.

(a) Secondary stage and main spool, (b) TSV structure.

To test the response time of the HSV, the experimental setup shown in Fig. 9 was utilized for conducting response time tests. A step signal with a duration of 200 ms and a voltage of DC12V was applied as the input to the HSV. The change in current was observed to determine the switching time. The experimental results are shown in Fig. 9. When the step control signal was applied, the electromagnetic coil exhibited inductance, impeding the rise of the current in the coil. The input current was insufficient to overcome the spring’s preloading force, resulting in an increase in current without any movement of the spool. This corresponds to the period from 50 ms to point TA in Fig. 9, during which the HSV had no flow output. In the second phase, the spool began to release, and the reverse cutting of the magnetic flux lines induced a counter-electromotive force, causing the driving current to decrease. This corresponds to the segment from TA to TB in Fig. 9. However, the armature quickly stopped moving, and the driving current continued to rise to its maximum value, corresponding to the portion from point TB to just before the current started to decrease. Similarly, the closing process of the solenoid valve can be divided into two parts: after the control voltage is reduced to zero, due to the combined effect of coil inductance, eddy currents, and residual magnetism in the armature, the armature is still attracted for a certain period, corresponding to the segment from 150 ms to TA′ in Fig. 9. When the current decreases to a level where the armature cannot remain attracted, the armature is pushed out by the resetting spring until it reaches the maximum air gap, corresponding to the segment from TA′ to TB′ in the graph. The opening time of the ball valve is approximately 8 ms, while the closing time is around 9 ms.

Experiment result of dynamic performance.

To test the flow capacity of the TSV, a test setup was designed, as shown in Fig. 10. The output pressure of the hydraulic pump was set to 31.5MPa, and after passing through the TSV, the fluid was connected to a flow meter. The flow meter provided flow signals to a data acquisition device, and fluid flow through the flow transmitter entered the relief valve, which simulated the load. Subsequently, the fluid flowed into the tank. The TSV was controlled by a step signal generated by a signal generator, and the oscilloscope collected the current output from the signal generator. A step signal with a duration of 1s and a voltage of DC12V was applied to the TSV system, and flow data was collected. The selection of experimental components is shown in Table 4.

Simulation model and experimental setup for dynamic performance.

Due to the unmeasurable valve spool position, as shown in Fig. 11, an AMESim2021.1 dynamic simulation model was developed, and the total flow output of the TSV is shown in Fig. 11. In the simulation, the maximum flow rate was 235 L/min when the pressure drop was 5 MPa. Experimental results indicated an actual output flow rate of approximately 225 L/min, slightly lower than the simulation results. One possible reason for the reduced output flow rate is that the clearance between the poppet valve and the valve sleeve in the manufactured prototype is larger than the value set in the simulation, resulting in an increased flow to the pressure control chamber, causing a decrease in the spool lift. The spool position curve shows that the maximum lift of the main valve is approximately 0.55 mm, the opening of the secondary stage is around 0.21 mm, and the output of the HSV is in terms of flow, with a maximum flow rate of approximately 3.8 L/min. The trend of flow changes is similar to the motion trend of the solenoid coil. When the main valve opens, the startup delay and opening time are 6 ms and 15 ms, respectively. This means that the main valve can fully open within approximately 21 ms. The response time of the main valve is consistent with the response time obtained from the flow changes, indicating that the rapid response of the main valve is crucial for the total flow rate.

Experiment and simulation result of dynamic performance. (a) Flow rate; (b) spool displacement and flow rate of the HSV.

Coal mining machinery requires control valves continuously controlling pressure, flow, and direction. By adjusting the duty cycle of the PWM signal, proportional output of the HSV can be achieved. The proportional control of the TSV can be realized by utilizing the proportional characteristics of the HSV. By inputting a 2 kHz PWM signal to the system and adjusting the duty cycle, the flow output of the HSV can be controlled, thereby controlling the lift of the main spool. Due to the smaller dead zone of the HSV compared to the secondary and main stages, the separate control of the TSV can be achieved by utilizing the dead zone characteristics of each stage.

Figure 12a illustrates the comparison between simulated and experimental flow outputs of the TSV as the system input signal duty cycle increases. Both exhibit similar trends: a significant increase in flow begins around a duty cycle of approximately 0.62 in simulation, whereas in experimentation, this increase starts around a duty cycle of 0.7. Beyond a duty cycle of 0.75, the flow outputs from simulation and experimentation align closely, consistent with the results shown in Fig. 10.

Experiment and simulation result of proportional characteristic, (a) total flow rate; (b) spool displacement.

As shown in Fig. 12b, by observing the displacement of the valve spool in the simulation, it is found that when the PWM ratio is less than 0.56, only the HSV can output flow, with a maximum flow rate of approximately 3 L/min. When the duty cycle increases, the secondary stage starts production flow, with a maximum flow rate of roughly 16 L/min. When the duty cycle reaches 0.62, all stages start to output flow, and the system’s output flow rate increases almost linearly with the increase in the duty cycle.

By comparing Fig. 12a and b, it can be inferred that the difference in output flow is likely due to factors that interfere with the opening of the main valve spool in experiments, which start around a duty cycle of 0.7. These factors may include friction between the valve spool and sleeve, fluctuations in supply hydraulic pressure, and variations in component machining precision.

The performance of the directional valve ultimately hinges on the precision of the positioning of the controlled hydraulic cylinder. To validate its control accuracy, an experimental setup was constructed, as depicted in Fig. 13a. Four sets of TSVs were employed to govern the extension and retraction of the hydraulic cylinder, with a displacement sensor installed inside the cylinder to record displacement data. Figure 13b illustrates the arrangement of a hydraulic cylinder positioning test bench controlled by a 3/4 proportional valve, utilized for comparative purposes with the performance of the TSVs.

Experimental setup for cylinder control performance.

Open-loop control experiments were conducted on the position control system to verify the output characteristics of the TSV. As shown in Fig. 14, the speed and position control of the hydraulic cylinder extension were achieved by adjusting the duty cycle of the input PWM signal. The overall adjustable range of the system’s speed exhibits three regions. When the duty cycle is less than 0.56, the extension speed is proportional to the signal ratio. The growth rate increases from a ratio of 0.56 to 0.62, reaching the maximum speed at a ratio of 0.62. The speed does not increase further with an increase in the duty cycle. The displacement curve of the hydraulic cylinder shows that the TSV allows for a rapid approach to the target and more precise displacement control by reducing the duty cycle when the target is close.

Experiment result of cylinder control.

The experimental results of the hydraulic cylinder displacement tracking controlled by the TSV are shown in Fig. 15. A trapezoidal displacement signal was input, and the hydraulic cylinder could extend and retract following the displacement signal. Based on the system’s tracking error curve, the positioning accuracy of the hydraulic cylinder controlled by the TSV is ± 0.15 mm. In contrast, the displacement tracking accuracy is ± 3 mm, indicating that the system's positioning accuracy is higher than the tracking accuracy. The positioning error curve exhibits continuous fluctuations, and the higher tracking speed of the displacement causes the fluctuation of the error value during displacement tracking. The TSV can only control the flow by continuously switching, resulting in repeated increases and decreases in the error. The error value still fluctuates during positioning but with a smaller amplitude. This may be due to minor leakage in the hydraulic cylinder or deviations introduced by the displacement sensor during signal transmission, affecting the valve opening.

The experiment result of the following control.

To assess the control performance of the TSV, a PI control was applied using a sinusoidal position signal with control parameters kp = 8 and ki = 1. As a performance benchmark, a 3/4 proportional valve control system (depicted in Fig. 16b) was employed, with the TSV system containing an emulsion and the proportional valve control system using hydraulic oil.

Experiment result of cylinder PI control.

The experimental results are illustrated in Fig. 16, where (a) shows the actuator displacement of the proportional valve control system, (b) depicts the actuator displacement error of the proportional system, (c) displays the actuator displacement of the TSV control system, and (d) presents the actuator displacement error of the TSV control system. Due to the PI controller utilized, both systems exhibit some lag error in position tracking. The error profiles of the two control systems are similar, with the TSV system showing smoother error curves and a maximum error magnitude smaller than that of the proportional valve control system.

The entire TSV system is governed by the pilot HSV. Power control experiments were independently conducted on the pilot HSV, and the experimental findings are illustrated in Fig. 17. Panel (a) displays the current within the HSV coil, with the control signal applied at 1 s. A dual-duty cycle control method was utilized to minimize control power consumption: the duty cycle was set to 1 at T = 1 s and reduced to 0.7 after 0.1 s. Panel (b) demonstrates the flow rate of the pilot HSV, achieving an output flow rate of approximately 2.8 L/min. The PWM signal operates at 12 V, indicating that the TSV can be driven by power less than 1.2W.

A novel low-power-driven three-stage poppet valve with an internal feedback structure is proposed in this study based on the displacement feedback principle. The structure utilizes a high-speed on/off valve as the pilot stage, enabling rapid response in high-pressure and water-based environments. It effectively avoids valve leakage and sensitivity to medium contamination, making it a potential replacement for traditional proportional directional valves in coal mining equipment.

Static analysis of the TSV structure was conducted to determine the lift of each stage under steady-state conditions. The state-space equations between the spools and the pressure control chamber system were established, and the step response was analyzed. A MOO design of critical parameters for the secondary and main stages was performed using the electric eel foraging algorithm. The optimization results showed that the solutions obtained by the optimization algorithm could approximate the Pareto front. The design parameters were selected using the analytic hierarchy process.

An experimental setup for the flow characteristics of the TSV was constructed. A prototype was manufactured based on the design parameters and subjected to experimental verification. The results showed that the output flow of the novel TSV was slightly smaller than the theoretical calculation, and the response time was somewhat longer than the theoretical calculation. Proportional control of the TSV was achieved by adjusting the ratio of the PWM control signal. Hydraulic cylinder control experiments were conducted, and a positioning accuracy of ± 0.15 mm was achieved. The TSV system shows smoother error curves and a maximum error magnitude smaller than that of the proportional valve control system.

All data generated or analysed during this study are included in this published article.

Control Chamber Section Area (ACI = π (ru) 2)

Throttle grooves flow area (Ati = Wti(xi+ x0i))

Flow area at the operating point

Friction between the spool and valve sleeve

1 For the main valve, 2 for the secondary stage, 3 for the HSV

Part “i” flow pressure gain

Part “i” flow displacement gain

Main valve moving parts mass

Inlet pressure at the operating point

Outlet pressure at operating point

Inlet pressure increment at the operating point

Outlet pressure increment at the operating point

Inlet pressure at the operating point

Flow rate increment at the operating point

Displacement increment at the operating point

Area ratio of upper and lower end faces of the spool (αi = RL/Ru)

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School of Mechanical and Electrical Engineering, China University of Mining & Technology, Beijing, 100083, China

Aixiang Ma, Heruizhi Xiao, Yue Hao, Xiu Yan & Sihai Zhao

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Aixiang Ma and Heruizhi Xiao authored the main manuscript text, Yue Hao prepared Figs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, Xihao Yan revised the manuscript format, and Sihai Zhao performed content review. All authors have reviewed the manuscript.

The authors declare no competing interests.

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Ma, A., Xiao, H., Hao, Y. et al. Multi-objective optimization design of low-power-driven, large-flux, and fast-response three-stage valve. Sci Rep 14, 21575 (2024). https://doi.org/10.1038/s41598-024-70353-2

DOI: https://doi.org/10.1038/s41598-024-70353-2

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