Influence Analysis of Design Parameters of Elastic Valve Plate and Structural Types of Guide Flow Disc on the Performance of Relief Valve

Abstract

The elastic valve plate and guide flow disc are key components that influence parameters such as opening and pressure difference of pilot-relief valve, which are also the core components enabling continuous damping adjustment in valve-controlled continuously variable dampers. Based on deformation characteristics of elastic valve plate and various structural types of guide flow disc, this paper reveals the impact of structural types of guide flow disc and design parameters of elastic valve plate on the performance of pilot-relief valve and obtains the relationship curves between opening pressure, pressure difference and opening of relief valve versus structural types and the angle, width and the number of arc plates of elastic valve plate. It shows that the pressure difference of the relief valve reaches maximum with min angle, max width, most arc plates and irregular-shaped type, and the opening reaches maximum with max angle, min width, fewest plates and round hole type. By adjusting structural types of guide flow disc and design parameters of elastic valve plate, the pressure difference and opening of the relief valve can be precisely controlled, providing theoretical support for the precise design of pilot-relief valve and the optimization of damping characteristics.

1. Introduction

Pilot-relief valve provides continuous adjustability of damper damping force through flow and pressure. The special poppet structure and appropriate spring stiffness provide excellent steady-state position retention and fast dynamic response. However, it is complicated to analyze the performance of the relief valve under the influence of the elastic valve plate and guide flow disc, especially when it involves the complex poppet structure and the change of the flow field, and it is exceptionally difficult to analytically calculate the liquid force through the momentum equation. Therefore, based on the deformation theory of the elastic valve plate, it is crucial to study the influence of key design parameters of the elastic valve plate on the relief valve opening and investigate the effect of the structural types of the guide flow disc on the pressure difference-opening relationship of the relief valve, to optimize the design of pilot-relief valve.

At present, the computational fluid dynamics method is the mainstream method for solving the dynamic stroke of complex valve bodies. Zhang [1], Song [2], and Beune [3] established a transient flow model of a pressure valve based on the transient computational fluid dynamics method, investigated the internal flow characteristics of the pressure valve at different stages of the opening process, and revealed the influence of the key parameters of the relevant valve system on the liquid flow. Roberto [4] and others established a three-dimensional pilot-relief valve geometric model and carried out numerical simulation and experimental study on the pressure-flow characteristics of the relief valve with flow compensation. All the above scholars used a three-dimensional model for calculation, which is a complicated calculation process and consumes a long calculation time. The simplified two-dimensional model can save computational resources, which provides a reference for efficiently identifying the operating characteristics of the pilot-relief valve.

Yuan et al. [5,6] established a nonlinear column coordinate control equation by establishing equivalence between concentrated forces and localized distributed forces. Through finite element analysis, they investigated the transient characteristics of relief valve opening dynamics, providing a solution framework for the nonlinear thin plate equation. Zhang [7] proposed a differential quadrature method based on the Fourier expansion and numerically analyzed the nonlinear bending deformation of an axially symmetric thin plate analysis. Hedayati et al. [8] investigated the free vibration of embedded annular sector plates based on three-dimensional elasticity theory. Tornabene [9] analyzed the deformation of an annular thin plate of medium thickness using first-order shear deformation theory and discretized it using a generalized differential quadrature method. Xu [10] et al. used a hybrid method of large deflection and beam deflection to develop a shock absorber elastic valve plate mathematical model of deformation. To address the deformation characteristics of the radial and circumferential boundaries of the valve plate, Bao [11] and others established a nonlinear mathematical model based on the principle of arithmetic and analyzed the effects of the damping holes and the damping valve plate structural parameters on the dynamic characteristics of the relief valve. Yin et al. [12] investigated the influence of dynamic pressure feedback holes on valve transient characteristics through frequency-domain analysis. By optimizing the geometry of the guided valve plate, they significantly improved the stability of a hydraulically piloted safety valve system.

The problem of deformation at the radial and circumferential edges of thin plates under the special case settings of fixed and free ends has not been resolved in the above studies. In this regard, the bending deformation of a circular elastic valve has been analyzed by this group [13] using the variational approximation method, with the addition of torque. At the same time, the effect of the thickness of the elastic valve on their performance has been considered, providing proof of the deformation behavior of the circular elastic valve.

To summarize the above, both domestic and international research on the relief valve has primarily concentrated on the calculation and analysis of three-dimensional flow field models. However, there has been a notable lack of research on the mapping relationship between the design parameters of the elastic valve plate and the opening characteristics of the pilot-relief valve. Furthermore, the influence of the structural types of guide flow disc on the operating characteristics of the relief valve has been less considered, resulting in deviations in predicting the operating characteristics of the pilot relief valve. To address these shortcomings, the six-degree-of-freedom two-dimensional flow field model has been established in this paper. It is demonstrated that changes in the opening of the pilot valve directly affect the operating characteristics of the relief valve. Additionally, based on the deformation theory of elastic plate, the influence of key design parameters of the elastic valve plate on the pressure difference of the pilot-relief valve has been studied. The opening characteristics of the pilot-relief valve have been obtained under different structural types of guide flow disc, as well as the different arc plate angle, arc plate width, and the number of arc plates of elastic valve plate. The pressure difference-opening mathematical model has been developed to provide theoretical support for the optimal design of the pilot-relief valve.

2. Influence Analysis of Design Parameters of Elastic Valve Plate on the Operating Characteristics of the Pilot-Relief Valve

As illustrated in Figure 1a, the structure of the pilot-relief valve consists of a two-stage valve, with the upper part functioning as an electromagnetic pilot valve and the lower part serving as the relief valve. These two components work in unison. The operating characteristics of the pilot-relief valve are characterized by the opening and pressure difference of the relief valve, which illustrates their effects on the regulation of flow and pressure within the hydraulic system.

As shown in Figure 1b, since the pilot-relief valve under study is a symmetrical structure, the three-dimensional model is split into two-thirds of the three-dimensional model, the cross section of the two-thirds of the three-dimensional model is extracted, and finally the cross section is simplified into two-thirds of the two-dimensional model. The fluid domain is represented by the light blue region.

The direction of liquid flow is indicated by the light blue arrow in Figure 1a. When the pilot-relief valve is in the closed state, the pilot valve poppet is in close contact with the piston seat due to the pressure of the return spring, and the relief valve poppet is in the closed state due to the spring force of the series spring system composed of the elastic valve plate and the main spring, and the opening of the pilot valve and the relief valve are both zero. When the relief valve opening reaches a certain value, the solenoid valve is energized, causing the armature to move downward due to electromagnetic force. This movement separates the pilot valve poppet from the piston valve seat, creating the opening of the pilot valve. As the pilot increases, the pressure in the relief valve chamber decreases, which causes the relief valve poppet to move upward. When the pressure in the relief valve chamber falls to a certain level, the solenoid valve is de-energized, and the armature is restored to its initial position by the action of the reset washer. This completes the working stroke of the pilot-relief valve.

2.1. Deformation Model of the Elastic Valve Plate

As shown in Figure 2 [13], the four connecting regions of the elastic valve plate are designated as arc plates n (where n = 1, 2, 3, 4). A parallel relationship is established among the four segments of the arc plate, and the deformation of each segment is assumed to be independent of the others. Furthermore, the size, shape, and deformation characteristics of each segment are considered identical. Consequently, the deformation of each segment can be approximated as the deformation of the elastic valve plate.

Considering the torque generated by the external load at the free end of the arc plate, in order to more fully describe the deformation characteristics of the arc plate, introducing the torque T, and the deformation control differential equation of the arc plate is established as,

$${\displaystyle \frac{T}{r^2}}{\displaystyle \frac{\partial }{\partial r}}\left(r^2{\displaystyle \frac{{\partial }^{3}w}{\partial r^3}}\right)-{\displaystyle \frac{1}{r}}{\displaystyle \frac{\partial }{\partial r}}\left({\displaystyle \frac{1}{r}}{\displaystyle \frac{\partial w}{\partial r}}\right)-K^2{\omega }^{2}w=0$$

(1)

where, $K=\sqrt{24\rho h/Eb{h}^3}$, $\omega =\sqrt{c{\pi }^2/b^2\rho }$, K and ω are both dimensionless quantities, r is the distance from the inner diameter to the outer diameter of the arc plate, and its value range is r ∈ [r₁, r₂], r₁ is the inner diameter of the arc plate, r₂ is the outer diameter of the arc plate; w is the deformation of the arc plate, ρ is the density of the elastic valve plate, h is the thickness of the valve plate, D is the flexural rigidity, E is the elastic modulus, b is the width of the arc plate, θ is the angle of the arc plate, and c is the shear modulus, Torque T can be represented as,

$$T=FL=2F{r}_0\sin \left({\displaystyle \frac{90\theta }{\pi }}\right)$$

(2)

In the formula, F is the action force of the circular elastic valve plate, and its action position is shown in the red area of Figure 2, and the direction is perpendicular to the surface of the valve plate, r₀ is the mid-diameter of the arc plate, and L is the chord length at the position of the arc plate’s mid-diameter.

At the same time, the boundary conditions are

$${\displaystyle \frac{\partial w}{\partial r}}{|}_{r=0}=0,w{|}_{r=0}=0,T{|}_{r=0}=0$$

(3)

Associating Equations (1) and (2), the actual control equations for the deformation amount of the arc plate are obtained as follows,

$$2F{r}^3{r}_0\sin \left({\displaystyle \frac{90\theta }{\pi }}\right){\displaystyle \frac{{\partial }^{4}w}{\partial r^4}}+4F{r}^2{r}_0\sin \left({\displaystyle \frac{90\theta }{\pi }}\right){\displaystyle \frac{{\partial }^{3}w}{\partial r^3}}-r{\displaystyle \frac{{\partial }^{2}w}{\partial r^2}}+{\displaystyle \frac{\partial w}{\partial r}}-24{\displaystyle \frac{\rho {\pi }^{2}c{r}^3}{E{b}^3{h}^2\rho }}w=0$$

(4)

2.2. Influence Analysis of Key Design Parameters of the Elastic Valve Plate on the Pressure Difference-Opening Characteristics of the Relief Valve

The key design parameters of the elastic valve plate mainly include arc plate angle (θ), arc plate width (b), and the number of arc plates (n), which affect the size of the stiffness of the elastic valve plate and further lead to the change of the stiffness of the spring system controlling the relief poppet, and ultimately affect the pressure difference, opening, and flow characteristics of the pilot-relief valve. Based on the elastic valve plate’s deformation characteristics and structural features, this paper sets θ as π/18rad–π/6rad, b as 0.3–0.7 mm, and n as 2, 3, and 4 for the case to be studied.

The stiffness of the elastic valve plate was analyzed based on the deformation model described above. By applying different displacement values to the main spring force contact area, as shown in Figure 2, the elastic force generated by the elastic valve plate with different arc plate angle θ, arc plate width b, and the number of arc plates n is obtained, and then the corresponding stiffness values of the elastic valve plate are obtained, as shown in

Table 1. Relationship between key design parameters and the stiffness of the elastic valve plate.

θ/(Rad)	Stiffness of Elastic Valve Plate/(N·mm−1)	b/(mm)	Stiffness of Elastic Valve Plate/(N·mm−1)	n	Stiffness of Elastic Valve Plate/(N·mm−1)
π/18	8.2	0.2	3.7	2	1.1
π/12	6.2	0.3	3.8
π/9	5.1	0.4	4.1	3	2.2
5π/36	3.9	0.5	6.9	4	3.7
π/6	3.7	0.6	7.3

.

The opening of the relief valve in the pilot-relief valve is primarily regulated by the movement of the relief poppet, which is also affected by the opening (d) of the pilot valve to a certain extent.

The opening d of the pilot valve range is set to 0–0.25 mm; set A = [d θ b n], and the opening-pressure difference characteristic of the relief valve is analyzed with the example as A = [0.25 π/18rad 0.3 4].

2.2.1. Pressure Difference Analysis of Relief Valve Based on Key Design Parameters of the Elastic Valve Plate

• Influence analysis of arc plate angle θ on pressure difference.

As shown in Figure 3, in just passing into the oil, due to the oil in the valve port there is a build-up phenomenon, increasing the slope of the curve. The pressure difference increased rapidly, and when the relief valve began to overflow, the valve system pressure difference gradually decreased, and the valve port pressure difference increased as the oil continued to flow. When the relief valve begins to open, the pressure difference with the valve system gradually decreases, while the pressure difference at the valve opening increases as oil continues to flow.

As seen in Figure 3a,b, when the pilot valve opening d remains constant, increasing the arc plate angle θ reduces the elastic valve plate’s stiffness. This stiffness reduction propagates through the series-connected spring system that governs the relief valve poppet movement, ultimately lowering the inlet pressure at the relief valve opening. The diminished inlet pressure attenuates oil accumulation at the valve opening, thereby decreasing the opening resistance. These coupled effects lead to a progressive reduction in the pressure difference across the relief valve opening with increasing θ values.

• Influence analysis of arc plate width b on pressure difference.

As can be seen from Figure 4, when the oil is initially passed, the accumulation of oil at the valve opening causes an increase in the slope of the curve, leading to a rapid rise in the pressure difference. When the relief valve begins to open, the pressure difference gradually decreases, but it continues to increase as oil flows further into the valve.

As seen in Figure 4a,b, when the opening d of the pilot valve is fixed, the stiffness of the elastic valve plate increases as the arc plate width b increases, which leads to an increase in the stiffness of the series spring system controlling the movement of the relief valve poppet. This in turn enhances the accumulation of oil at the valve opening, increasing the opening resistance of the relief valve. Therefore, as b increases, the pressure difference of the relief valve increases. When b is unchanged, the flow area increases with the increase in the opening d of the pilot valve, making it easier for oil to flow. The pilot flow rate increases and the relief flow rate decreases, which reduces the pressure in the relief valve chamber, causing a corresponding decrease in the pressure difference of the valve system.

• Influence analysis of the number of arc plates n on pressure difference.

From Figure 5, when oil is initially passed, the accumulation of oil at the valve opening causes localized high pressure, which increases the slope of the curve and leads to a rapid rise in the pressure difference. As the relief valve begins to open and release pressure, the pressure difference gradually decreases. However, as oil continues to flow in, the pressure difference at the valve opening increases once again.

From Figure 5a,b, maintaining a constant pilot valve opening d while increasing the number of arc plates n enhances the elastic valve plate’s stiffness. This stiffness augmentation directly strengthens the series spring system controlling the relief valve poppet movement. The heightened system stiffness triggers intensified oil accumulation at the valve port, consequently amplifying the opening resistance. These cumulative effects systematically elevate the pressure difference across the relief valve with increasing n values.

When n is held constant, an increase in the opening d of the pilot valve leads to an increase in the flow area, facilitating the flow of oil. This results in an increase in the pilot flow rate and a decrease in the relief flow rate, which lowers the pressure within the relief valve chamber. Consequently, the pressure difference across the valve system decreases.

2.2.2. Opening Analysis of the Relief Valve Based on Key Design Parameters of the Elastic Valve Plate

• Influence analysis of arc plate angle θ on the opening;

As seen from Figure 6, at time 0 s, the relief valve is closed, with an opening of 0 mm. As oil flows into the system, the relief valve opens once the opening pressure is reached. At this point, the pressure difference across the valve port increases dramatically, causing the slope of the curve to steepen. The rate of valve opening also increases, exhibiting a nonlinear change. As the relief valve briefly relieves pressure, slope of the curve becomes less steep, and the rate of increase in valve opening slows. Since the relief valve is a velocity-type inlet, the oil flow rate increases proportionally with time, causing the curve’s slope to stabilize. Subsequently, the rate of increase in valve opening continues, albeit at a slower pace.

From Figure 6a,b, it can be observed that, for a constant the opening d of the pilot valve, as the stiffness of the elastic valve plate decreases with an increase in the arc plate angle θ of the elastic valve plate, the stiffness of the tandem spring system controlling the movement of the relief valve poppet also decreases. As a result, the pressure at the valve port decreases, and the accumulation of oil at the valve port becomes less pronounced. This leads to a reduction in the valve system’s pressure difference, causing the resistance to valve opening to diminish. Consequently, the opening of the relief valve increases as the arc angle θ of the elastic valve plate increases.

When θ is held constant, the increase in the opening d of the pilot valve increases the pilot flow, which lowers the pressure within the relief valve chamber. This reduction in pressure difference across the relief valve orifice weakens the resistance to valve opening, thus increasing the relief valve opening.

• Influence analysis of the arc plate width b on the opening;

As illustrated in Figure 7, the relief valve starts in a closed position. As oil flows in, the valve opens once the pressure reaches the valve-opening threshold. The rate at which the valve opens increases in a nonlinear manner. After a brief period of pressure relief, the slope of the opening curve begins to decrease, leading to a slower rate of increase in the valve opening. Since the relief valve is equipped with a velocity-type inlet, the flow of oil increases proportionally over time. At this stage, the slope of the curve stabilizes and the relief valve opening continues to expand.

As seen in Figure 7a,b, when the opening d of the pilot valve remains constant, the stiffness of the elastic valve plate increases as the arc plate width b of the arc plate increases. This enhancement in stiffness of the series spring system regulates the movement of the relief valve poppet. Consequently, the inlet pressure at the valve port increases, leading to an increase in the system’s pressure difference. As a result, the resistance to valve opening increases, causing a decrease in the relief valve opening as b increases.

When b is held constant, the increase in the opening of the pilot valve results in a corresponding increase in the pilot flow. This lowers the pressure in the relief valve chamber, reducing the pressure difference across the relief valve. The decreased pressure difference weakens the resistance to the valve opening, thereby causing an increase in the relief valve opening.

• Influence analysis of arc plate number n on the opening;

As shown in Figure 8, at time 0 s, the relief valve is closed with an opening of 0 mm. As oil flows in, the relief valve opens once the valve-opening pressure is reached. At this point, oil rapidly enters the valve body, causing a sharp increase in the pressure difference at the valve port. This results in a steeper curve and a faster valve opening rate, exhibiting nonlinear behavior. As the relief valve briefly relieves pressure, the slope of the curve flattens, and the rate of increase in the valve opening slows. Given that the relief valve operates as a velocity-type inlet, the oil flow increases proportionally with time. Consequently, the slope of the curve stabilizes, and the valve opening continues to increase.

Figure 8a,b illustrate that when the opening d of the pilot valve remains constant, the stiffness of the elastic valve plate increases with the increase in the number of arc plates n, increasing the stiffness of the series spring system that controls the relief valve poppet. The oil buildup at the relief valve is strengthened, the relief valve opening resistance increases, and the opening of all the relief valves decreases with the increase in n.

When the value of n is unchanged, the pilot flow increases with the increase of the opening d of the pilot valve, and the pressure in the relief valve cavity decreases, resulting in a reduction of the pressure difference at the relief valve orifice. Consequently, the resistance to opening of the relief valve is weakened, so the relief valve opening increases accordingly.

3. Influence Analysis of the Structural Types of Guide Flow Disc on the Operating Characteristics of the Pilot-Relief Valve

3.1. Structural Types of the Guide Flow Disc

As a critical component of the valve, the guide flow disc determines the pressure difference, valve opening, flow characteristics, and overall system performance of the relief valve, thereby playing a pivotal role in the valve’s control effectiveness. The primary function of the guide flow disc is to connect the pilot valve chamber to the relief valve chamber while exerting a throttling effect on the oil flowing through its throttling orifice. As depicted in Figure 9, the structural types of the guide flow disc can be categorized into five types based on the shape of the throttling orifice: irregular-shaped, bend-shaped, runway-shaped, arc-shaped, and round hole-shaped. The opening-pressure difference characteristics of the relief valve are analyzed with the opening d of the pilot valve of 0.25 mm as an example.

3.2. Influence Analysis of Structural Types of the Guide Flow Disc on the Opening-Pressure Difference Characteristics of the Relief Valve

3.2.1. Inlet Pressure Analysis of Relief Valve Based on Structural Types of the Guide Flow Disc

The graph in Figure 10 illustrates the relationship between the inlet pressure of the relief valve and time. At 0.15 s, the curve reaches its peak, and the point corresponding to this peak is defined as the opening point of the valve, with the associated pressure referred to as the opening pressure.

As shown in Figure 10, before the valve opening point, oil accumulates at the relief valve, generating localized high pressure, which causes a sharp rise in inlet pressure over time. At this stage, the relief valve remains closed, and fluid enters the valve body solely through the cylindrical valve port. Once the pressure curve reaches the valve opening point, the relief valve opens, and the inlet pressure at this point is defined as the opening pressure. Overflow begins, resulting in a subsequent decrease in inlet pressure. Following a brief period of pressure relief, the inlet pressure continues to rise again as the relief valve poppet slowly moves upward, and the continuous flow of fluid into the valve causes a further increase in inlet pressure.

As depicted in Figure 10a,b, when the opening of the pilot valve is maintained at a constant level, the throttling orifice area of the guide flow disc increases in the following order: irregular-shaped, bend-shaped, racetrack-shaped, arc-shaped, and round hole-shaped. As the orifice area increases, the flow rate of oil passing through the guide flow disc also rises, resulting in a reduction in the flow rate of oil entering the relief valve. Consequently, the pressure within the relief valve chamber decreases, which results in a reduction in both the inlet pressure and the opening pressure. After the valve opens, the inlet pressure continues to decrease.

When the type of guide flow disc is unchanged, the increase in the pilot valve opening leads to an increase in the flow area, thereby facilitating fluid flow. This results in an increase in the pilot flow and a decrease in the overflow flow, which in turn reduces the pressure within the relief valve chamber. Consequently, the opening pressure of the relief valve decreases as the opening of the pilot valve increases.

3.2.2. Pressure Difference Analysis of Relief Valve Based on Structural Types of the Guide Flow Disc

As shown in Figure 11, when oil is first passed through, the accumulation of fluid at the valve port causes the slope of the curve to increase, and the pressure difference rises rapidly. When the relief valve begins to relieve, the pressure difference gradually decreases, and as the fluid continues to flow in, the pressure difference increases accordingly.

From Figure 11a,b, it can be seen that, when the opening of the pilot valve remains constant, after the valve opening point, the inlet pressure of the relief valve decreases in the order of irregular-shaped throttling orifice, bent-shaped throttling orifice, runway-shaped throttling orifice, arc-shaped throttling orifice, and round hole-shaped throttling orifice. This hierarchical pressure decline correlates with diminished fluid accumulation at the valve port, leading to a corresponding decrease in the pressure difference generated by different structural types of guide flow disc.

Furthermore, when maintaining a fixed guide flow disc structure, the increase in the opening of the pilot valve leads to a larger flow area, making it easier for the fluid to flow. As a result, the pilot flow increases, which reduces the overflow flow, and consequently, the opening pressure of the relief valve decreases, causing a corresponding reduction in the pressure difference at the valve port.

3.2.3. Opening Analysis of Relief Valve Port Based on Structural Types of the Guide Flow Disc

As illustrated in Figure 12, at time 0 s, the relief valve is in a closed position with an opening of 0 mm. As fluid begins to flow, the valve opens once the opening pressure is reached. At this moment, the pressure difference across the relief valve rises sharply, causing the slope of the curve to steepen. The resulting nonlinear opening dynamics demonstrate progressively intensifying displacement rates until transient pressure release initiates slope attenuation. Since the valve port is the velocity-type inlet, the fluid flow increases at a constant rate over time. At this point, the slope of the curve stabilizes, and the opening of the relief valve continues to rise.

From Figure 12a,b with an unchanged opening d of the pilot valve, the relief valve opening increases in the following order: irregular-shaped throttling orifice, bent-shaped throttling orifice, runway-shaped throttling orifice, arc-shaped throttling orifice, and round hole-shaped throttling orifice. This phenomenon arises from the sequential mitigation of inlet fluid stagnation through optimized orifice geometries, leading to a corresponding reduction in pressure difference. As a result, the resistance to the opening of the relief valve decreases, and the opening increases gradually.

When the structure of the guide flow disc is fixed, the flow area increases as the opening of the pilot valve increases, increasing pilot flow and causing a corresponding decrease in overflow flow. This leads to a reduction in the pressure difference of the valve port, which weakens the resistance to the relief valve opening. As a result, the opening of the relief valve increases.

4. Conclusions

This paper presents a mathematical model for the deformation of the elastic valve plate. It analyzes the effects of structural types of guide flow disc, as well as the key design parameters of the elastic valve plate, on the inlet pressure, pressure difference, and opening characteristics of the relief valve under different openings of the pilot valve. The conclusions drawn from the analysis are as follows:

(1)

Studies have shown that the opening variation of the pilot valve directly influences both the opening pressure and the opening characteristics of the relief valve. When the opening of the pilot valve increases, pilot flow rises, relief flow decreases, and pressure of the relief valve chamber drops. Meanwhile, the valve port’s opening pressure decreases while the opening of the valve port gradually increases. By precisely adjusting the opening of the pilot valve, the performance of the relief valve can be optimized and accurately controlled;

(2)

The mapping relationship curves between the opening-pressure difference of the relief valve and the key design parameters of the elastic valve plate have been established. It shows that the pressure difference of the relief valve reaches maximum with min angle, max width, most arc plates, and the opening reaches maximum with max angle, min width, fewest plates. By adjusting the arc angle, width, and number of arc plates of the elastic valve plate, the relief valve port’s opening and pressure difference characteristics can be optimized. These findings provide a foundation for the serialization design of the pilot relief valve and their damping compatibility with dampers;

(3)

The study revealed the change rules of the inlet pressure, opening pressure, pressure difference, and opening of the relief valve with the structure of the guide flow disc. When the structure of the guide disc is irregular-shaped type, the inlet pressure and pressure difference of the relief valve reach the maximum; when the structure of the guide disc is round-hole type, the opening of the relief valve reaches maximum. The analysis of pressure difference-opening characteristics of the relief valve provides theoretical support for the precise design of the pilot-relief valve.