 Original Article
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Effect of Dynamic Pressure Feedback Orifice on Stability of CartridgeType Hydraulic PilotOperated Relief Valve
Chinese Journal of Mechanical Engineering volume 36, Article number: 85 (2023)
Abstract
Current research on pilotoperated relief valve stability is primarily conducted from the perspective of system dynamics or stability criteria, and most of the existing conclusions focus on the spool shape, damping hole size, and pulsation frequency of the pump. However, the essential factors pertaining to the unstable vibration of relief valves remain ambiguous. In this study, the dynamic behavior of a pilotoperated relief valve is investigated using the frequencydomain method. The result suggests that the dynamic pressure feedback orifice is vital to the dynamic characteristics of the valve. A large orifice has a low flow resistance. In this case, the fluid in the main spring chamber flows freely, which is not conducive to the stability of the relief valve. However, a small orifice may create significant flow resistance, thus restricting fluid flow. In this case, the oil inside the main valve spring chamber is equivalent to a highstiffness liquid spring. The main mass–spring vibration system has a natural frequency that differs significantly from the operating frequency of the relief valve, which is conducive to the stability of the relief valve. Good agreement is obtained between the theoretical analysis and experiments. The results indicate that designing a dynamic pressure feedback orifice of an appropriate size is beneficial to improving the stability of hydraulic pilotoperated relief valves. In addition, the dynamic pressure feedback orifice reduces the response speed of the relief valve. This study comprehensively considers the stability, rapidity, and immunity of relief valves and expands current investigations into the dynamic characteristics of relief valves from the perspective of classical control theory, thus revealing the importance of different parameters.
1 Introduction
To guarantee a smooth and accurate performance of the actuator, hydraulic systems are typically designed to operate within a specified pressure range. Relief valves are frequently used in hydraulic systems to limit the maximum pressure in a system or to prevent hydraulic circuits from overloading [1]. In general, relief valves can be categorized into direct and pilot types. The pilot type is a twostage structure invented by Vickers in 1931 [2]. Owing to their effective pressure control properties, pilotoperated relief valves are used extensively in hydraulic control systems featuring high pressures and large flows. However, during operation, relief valves occasionally vibrate, thus causing system pressure fluctuations and severely reducing the safety, stability, and reliability of the hydraulic system [3].
Several analyses from various perspectives have been performed to clarify the instability and vibration of relief valves. One approach is to conduct various studies to determine the causes of instability. Hayashi investigated the stability of singlestage poppet valves, and the results indicated that various factors, such as the effects of the valve poppet and seat, and the hysteresis of the transient hydrodynamic force, might cause the poppet valve to destabilize vibrations [4]. Additionally, some studies indicate that the stability of relief valves can be affected by the precompression shrinkage of springs [5], half cone angle [6], damping orifice size [7], flow rate in valve chambers [8], spool damping coefficient [9], valve orifice diameter [10], upstream and downstream pipelines [11, 12], cavitation [13,14,15,16], impact between the spool and seat [17], and valve chamber volume [18]. In addition, some scholars established a fluid–structure interaction model of the relief valve and investigated its stability [19, 20]. Meanwhile, some scholars investigated the effects of various parameters on the stability of the valve via theoretical analysis and simulations [21,22,23], whereas others have experimentally obtained the conditions for the steady operation of the relief valve [24].
Numerous strategies have been proposed to increase the stability of relief valves. Merrit placed a fixed office between a pressurecontrolled chamber and valve port and discovered that reasonably matching the fixed office with the sensitive chamber volume can increase the relief valve stability [25]. Moreover, designing a buffer structure at the end of the valve poppet can enhance its stability [26].
Although the stability of relief valves has been investigated extensively, quantitative agreement between predicted and measured stabilities has not been achieved because parameters such as damping and friction coefficients cannot be easily calculated accurately; therefore, the orifice size can only be confirmed through extensive experiments. However, because hydraulic technology is developing toward miniaturization, intelligence, and high performance, the relevant theories must be supplemented urgently.
In this study, the stability of a cartridgetype pilotoperated relief valve is investigated via frequencydomain analysis. In addition, a Bode diagram is used to assess elements that are different between the original and contrast models. Finally, theoretical conclusions are presented based on numerical simulation and experimental results.
2 Mathematical Model of Pilotoperated Relief Valve
2.1 Description of Pilotoperated Relief Valve
Generally, a pilotoperated relief valve comprises a main valve and a pilot valve. Figure 1 shows the structural diagram of a cartridgetype antivibration pilotoperated relief valve, and its schematic diagram is illustrated in Figure 2. The system pressure p_{s} is transmitted to the sensitive chamber C through the sharpedged orifice R_{1} and then transmitted to the pressuresensing chamber B through the dynamic pressure feedback orifice R_{2}, which is sensed by the pilot valve. If p_{s} does not exceed the cracking pressure, then the pilot valve is closed by the preload spring force. Based on Pascal’s law, p_{s} = p_{b} = p_{c}; thus, the main poppet is hydraulically balanced. However, it is also maintained in the seat by a preloaded spring force. Any positive deviation from the reference value causes the pilot port to open and flow, thus causing the main poppet to be unbalanced due to the pressure difference Δp between chambers A and B. Consequently, the main poppet is lifted and relieves the system flow from chamber A to the tank.
The following assumptions were introduced to derive a mathematical model for the relief valve:

1.
The bulk modulus of the fluid is constant.

2.
The valve outlet pressure is equal to the tank pressure.

3.
Perturbations are minimal, which allows the mathematical model to be linearized at the rated operating point.

4.
Leakage around the main poppet is negligible.
2.2 Static Characteristics
Under steady state, the physical model of the pilotoperated relief valve is described as follows:
The steady flow passing through the relief valve is expressed as
where Q_{p} is the supply flow rate, Q_{L} the flow rate to the load, Q_{x} the flow rate at the pilot port, and Q_{y} the flow rate at the main port.
The mechanical equilibrium equation of the main poppet is
where A_{1} is the crosssectional area of the main poppet; p_{s} is the pressure in chamber A; p_{b} is the pressure in chamber B; k_{1} is the main spring stiffness; y is the main valve displacement; and y_{0} is the constant precompression of the main spring. Meanwhile, F_{s1} is the steady flow force of the main valve, expressed as \(F_{{{\text{s}}1}} = \rho Q_{y} v_{y} \cos \alpha = C_{{{\text{d}}1}} C_{{{\text{v}}1}} {\uppi }d_{{1}} \sin \left( {2\alpha } \right)yp_{{\text{s}}}\), where ρ is the fluid density, v_{y} the main port flow velocity, α the halfangle of the main valve, C_{d1} and C_{v1} are the discharge and velocity coefficients of the main exit port, respectively, and d_{1} the diameter of the main exit port.
The flow rate passing through the main exit port can be represented by the following wellestablished relationship:
where A_{y} denotes the crosssectional area of the main port. Here, \(A_{y} = {\uppi }d_{1} y\sin \alpha \left( {1  \frac{y}{{2d_{1} }}\sin 2\alpha } \right)\), and because y << d_{1}, A_{y} can be approximated as \(A_{y} = {\uppi }d_{1} y\sin \alpha\).
The flow rate passing through the sharpedged orifice R_{1} is expressed as
where C_{r1} is the discharge coefficient of orifice R_{1}, d_{r1} the diameter of orifice R_{1}, and p_{c} the pressure in chamber C.
The mechanical equilibrium equation of the pilot poppet is
where A_{2} is the crosssectional area of the pilot poppet, k_{2} the pilot spring stiffness, x the pilot valve displacement, and x_{0} the precompression constant of the pilot spring. F_{s2} is the steady flow force of pilot valve, expressed as \(F_{{{\text{s2}}}} = \rho Q_{x} v_{x} \cos \beta = C_{{{\text{d2}}}} C_{{{\text{v2}}}} {\uppi }d_{2} \sin \left( {2\beta } \right)xp_{{\text{b}}}\), where v_{x} is the pilot port flow velocity, β the halfangle of the pilot poppet, C_{d2} and C_{v2} are the discharge coefficient and velocity coefficient of pilot port, respectively, and d_{2} is the diameter of the pilot port.
The flow rate passing through the dynamic pressure feedback orifice R_{2} is expressed as
where d_{r2} and l_{r2} are the diameter and length of orifice R_{2}, respectively; μ is the dynamic viscosity of the fluid; and p_{b} = p_{c} in steady state.
The flow rate passing through the pilot port is expressed as
where A_{x} is the crosssectional area of the pilot port. Here, \(A_{x} = {\uppi }d_{2} x\sin \beta \left( {1  \frac{x}{{2d_{2} }}\sin 2\beta } \right)\), and because x << d_{2}, A_{x} can be approximated as \(A_{x} = {\uppi }d_{2} x\sin \beta\).
2.3 Dynamic Mathematical Model
In the transient state, the mathematical model of the pilotoperated relief valve is as follows:
As shown in Figure 2, the continuity equation applied to chamber A of volume V_{A} yields
where E is the bulk stiffness of the fluid.
The mechanical equilibrium equation of the main poppet is
where m_{1} is the effective main poppet mass (including 1/3 of the spring mass); and f_{1} is the viscous damping coefficient of the main poppet, which is expressed as
where, f_{m1} and f_{t1} are expressed as
where, A_{m} is the equivalent wetting area of the main poppet; δ_{1} the clearance between the main poppet and valve body; and l_{1} the damping length of the main poppet.
The flow continuity equation applied to chamber B of volume V_{B} can be written as
The continuity equation applied to chamber C of volume V_{C} yields
The mechanical equilibrium equation of the pilot poppet is
where m_{2} is the effective pilot poppet mass (including 1/3 of the spring mass); and f_{2} is the viscous damping coefficient of the pilot poppet, which is expressed as
where f_{m2} and f_{t2} are expressed as
where, A_{p} is the equivalent wetting area of the pilot poppet, δ_{2} the clearance between the pilot poppet and valve body, and l_{2} the damping length of the pilot poppet.
2.4 Linearization Analysis
Directly analyzing a higherorder complex system using classical control theory is challenging. Linearization is a widely used mathematical approach in mechanical engineering. Consider a slight perturbation near the rated operating point. Subsequently, using the Laplace transform of Eqs. (3), (4), (6)–(9), and (13)–(15), the following mathematical model can be obtained:
where, y_{x} and x_{x} are the main and pilot valve displacements under the rated operating point, respectively; and p_{sx} and p_{cx} are the pressures in chambers A and C under the rated operating point, respectively.
The physical meanings and expressions of K_{n} are shown in Table 1.
4 Theoretical Analysis
4.1 System Block Diagram
In this section, the effect of the dynamic pressure feedback orifice is analyzed using the frequencydomain method. Using the flow rate at inlet Q_{p}Q_{L} as the input and the pressure of chamber A, p_{s}, as the output, the system block diagrams of the original and contrast models are developed, as shown in Figures 5 and 6, respectively.
The physical meanings and expressions of ω_{n} are presented in Table 2. A comparison of Figures 5 and 6 reveals the discrepancies between the original and contrast models. Circuits 1 and 3 contain the same components, which indicate the transfer function of the main valve mass–spring vibration system. Circuit 2 depicts the transfer function of pilot valve pressure control chamber C. Circuits 1, 2, and 3 of the original model have one more firstorder inertial element than those of the contrast model. According to the classical control theory, for a system comprising a firstorder inertial element and an oscillation element, the dynamic characteristics are primarily dominated by the firstorder inertial element if the break frequency of the firstorder inertial element is much lower than that of the oscillation element. The hysteresis of the firstorder inertial element can counterbalance the lead effect of the oscillation element, thereby improving the stability of the subsystems. This may be beneficial to the global stability of the pilotoperated relief valve.
The complete list of parameters used in the investigation is presented in Table 3.
Solving Eqs. (1)–(7) allows one to determine the steadystate operating point of the relief valve at a flow rate of 90 L/min, as listed in Table 4.
4.2 Dynamic Characteristics of Pilot Valve Subsystem
For the original model, the system transfer function of the pilot valve subsystem can be expressed as
where K_{m2} is the equivalent mechanical spring stiffness of the main valve and K_{m2} = k_{2}+K_{G}p_{cx}. Because V_{B} >> V_{C}, ω_{4} >> ω_{7}, Eq. (28) can be approximated using Eq. (29).
where ω_{a} is the break frequency of the firstorder inertial element related to orifice R_{2} as well as chambers B and C in the original model.
For the contrast model, the system transfer function of the pilot valve subsystem can be expressed as follows:
Based on comparison, G_{piloto}(s) has one more highfrequency firstorder differential element than G_{pilotc}(s). However, the value of ω_{7} is high; therefore, the effect of the firstorder differential on the stability and rapidity of G_{piloto}(s) is negligible. The Bode diagrams of the pilot valve subsystem are shown in Figure 7.
4.2.1 Stability, Rapidity, and Immunity of Pilot Valve Subsystem
As shown in Figure 7, G_{piloto}(s) and G_{pilotc}(s) do not differ significantly within the operating frequency range of the relief valve unless the value of ω_{a} is sufficiently small that the delay of the firstorder inertial element can significantly improve the stability of the pilot valve.
Similar to the stability analysis above, the rapidity of G_{piloto}(s) or G_{pilotc}(s) does not differ significantly in the operating frequency range of the relief valve. However, if ω_{a} is sufficiently small, then the delay in the firstorder inertial element may reduce the rapidity of the pilot valve.
As shown in Figure 7, G_{piloto}(s) has one more highfrequency firstorder differential element than G_{pilotc}(s), which implies that the immunity of G_{piloto}(s) is lower than that of G_{pilotc}(s). Additionally, similar to the observation that ω_{7} decreases with the size of orifice R_{2}, the immunity of G_{piloto}(s) decreases with the size of R_{2} as well.
4.3 Dynamic Characteristics of Main Valve Subsystem
In the original model, the system transfer function of the main valve subsystem is expressed as follows:
where K_{m1} is the equivalent mechanical spring stiffness of the main valve, expressed as K_{m1} = k_{1}+K_{D}p_{sx}; and ω_{c} is the equivalent break frequency produced by the dynamic pressure feedback orifice R_{2} and main spring.
For the contrast model, the system transfer function of the main valve subsystem can be expressed as follows:
Figure 8 shows the Bode diagrams of the main valve subsystem. As shown in Figure 8, the dynamic characteristics of G_{maino}(s) differ from those of G_{mainc}(s). G_{maino}(s) is more stable than G_{mainc}(s). By contrast, G_{mainc}(s) is more rapid than G_{maino}(s). In addition, the stability of G_{maino}(s) illustrates different states, depending on the orifice R_{2} aperture value. For further analysis, dimensional normalization was performed.
4.3.1 Normalization Analysis
By disregarding the minor effect of ζ_{1}, the denominator term in Eq. (32) can be approximated using Eq. (35).
Subsequently, Eq. (35) is converted into the product of two linear terms and a quadratic term, as shown in Eq. (36).
where ω_{α} is the break frequency of the firstorder inertia element; and ω_{β} and ζ_{β} are the resonance frequency and damping ratio of the oscillation element, respectively. However, the values of ω_{α}, ω_{β,} and ζ_{β} cannot be obtained easily using a simple analytical method; hence, dimensional normalization was performed.
The assumptions introduced are as follows:
Subsequently, the dimensionless transformation of Eqs. (37) to (39) yields
where K_{h1} is the equivalent spring stiffness of the liquid in chamber B, which is expressed as \(K_{{{\text{h1}}}} = \frac{{EA_{1}^{2} }}{{V_{{\text{B}}} }}\). Because V_{B} is small, K_{h1} is large, and \(K_{{{\text{h1}}}} \gg K_{{{\text{m1}}}}\), ω_{h1} is the natural frequency of the mass–spring vibration system formed by the main poppet and the liquid spring of chamber B, which is expressed as \(\omega_{{{\text{h1}}}} = \frac{{K_{{{\text{h1}}}} }}{{m_{1} }}\).
The real root normalization curves of Eqs. (40) and (41) are shown in Figures 9 and 10, respectively. Because \(K_{{{\text{h1}}}} \gg K_{{{\text{m1}}}}\) and \(\frac{{K_{{{\text{h1}}}} }}{{K_{{{\text{m1}}}} }} \gg 1\), the stability of the main valve subsystem exhibits different states as the ratio of \(\frac{{\omega_{{\text{c}}} }}{{\omega_{1} }}\) changes. Next, the following conditions are analyzed:
Condition I: If \(\frac{{\omega_{{\text{c}}} }}{{\omega_{1} }} \ge 0.5\), then
In this case, Eq. (32) can be approximated as follows:
Condition II: If \(\frac{{\omega_{{\text{c}}} }}{{\omega_{1} }} \le 2\sqrt {\frac{{K_{{{\text{h1}}}} }}{{K_{{{\text{m1}}}} }}}\), then
In this case, Eq. (32) can be transformed into
4.3.2 Stability, Rapidity, and Immunity of Main Valve Subsystem Under Condition I
Figure 11 shows the Bode diagrams of the main valve subsystem under Condition I. G_{maino}(s) and G_{mainc}(s) did not differ significantly when the aperture of R_{2} was relatively large, except for the resonant peak of G_{mainc}(s), which was slightly higher than that of G_{maino}(s). Therefore, the damping ratio of G_{maino}(s) was slightly larger than that of G_{mainc}(s). In this case, the stability of the main valve subsystem might not improve significantly. Similarly, the rapidity and immunity of G_{piloto}(s) and G_{pilotc}(s) did not differ significantly.
4.3.3 Stability, Rapidity, and Immunity of Main Valve Subsystem Under Condition II
Figure 12 shows the Bode diagrams of the main valve subsystem under Condition II. Some differences were indicated between the G_{maino}(s) and G_{mainc}(s). First, the resonance frequency of the oscillation element of G_{maino}(s) was much higher than that of G_{mainc}(s). Second, the damping ratio of G_{maino}(s) was larger than that of G_{mainc}(s). In addition, G_{maino}(s) had one more energy storage element (firstorder inertial element) and one more highfrequency firstorder differential element than G_{mainc}(s). Similar to the previous discussion (Section 4.2), the value of ω_{7} was high; therefore, the effect of the firstorder differential on the stability and rapidity of G_{main o}(s) is negligible. As shown in Figure 12, if the break frequency (ω_{c}) of this additional energystorage element is sufficiently small, then its delay can effectively improve the stability of the main valve. Contrary to the stability analysis above, if ω_{c} is sufficiently small, then the delay of the energystorage element may reduce the rapidity of the main valve. Notably, the immunity between G_{maino}(s) and G_{mainc}(s) did not differ significantly because the delay of the energystorage element effectively counteracted the lead of the firstorder differential element. Therefore, G_{maino}(s) and G_{mainc}(s) exhibited similar immunity.
Based on the analysis above, one can conclude that if the diameter of R_{2} is sufficiently small, then a dynamic pressure feedback orifice designed between the main valve and pilot valve may effectively improve the local stability of the hydraulic pilotoperated relief valve, which contributes positively to the global stability of the entire valve. By contrast, the rapidity and immunity of the hydraulic pilotoperated relief valve may be weakened to some extent.
5 Simulation and Experimental Verification
The accuracy of the conclusions inferred the previous section was verified through numerical simulations and measurements.
5.1 Numerical Simulation Model
A dynamic numerical simulation model of a relief valve was developed using MATLAB, and the nonlinearities were considered using appropriate Simulink blocks. For an accurate computation, solver “ode45” was used as the nonlinear system dynamics simulation mode, where the Runge–Kutta method was used with a fixed time step (1 × 10^{6} s). The parameters used in the simulation were consistent with those listed in Table 3. The supply flow (Q_{p}Q_{L}), which was gradually increased from 0 to 90 L/min, was used as the input signal, whereas the chamber A pressure p_{s}, pilot valve displacement x, and main valve displacement y were the output signals.
5.2 Experimental Model and Test Conditions
5.2.1 Experimental Device
Schematic diagrams of the experimental system and device are shown in Figures 13 and 14, respectively.
In the experimental system, RP3 aerospace kerosene was used as the working medium, and a seamless steel pipe was used as the hydraulic pipeline. An external gear pump (1) driven by an electric motor was used to provide a constant flow of 140 L/min, and the pressure was measured using pressure sensors (13) and (15). The flow rate was measured using a flowmeter (16) (range: 16–160 L/min; accuracy: 0.5%FS). Data were acquired using a synchronous data acquisition instrument (17) at a sampling period of 1.0 ms. The parameters of the tested valve were consistent with those listed in Table 3.
5.2.2 Experimental Scheme
The operational process stability of the relief valve was analyzed. The experimental scheme was formulated as follows: the inlet flow was gradually increased from 0 L/min to the rated flow (90 L/min) while the pressure in chamber A, p_{s}, was monitored. Subsequently, the pressureflow characteristics of the relief valve were analyzed after all experimental data were obtained. During the experiment, the throttle valve (7) was opened to the maximum lift. Subsequently, the data acquisition device (17) was turned on, followed by the pump station, while the throttle valve (8) was adjusted to ensure that the flow rate increased gradually. Finally, the pump station was turned off, and data acquisition was terminated.
5.3 Simulation and Experimental Results
The pressureflow characteristic curves of the original and contrast models obtained via simulation and experiment are shown in Figures 15 and 16, respectively. As shown, the simulation results agreed well with the experimental results.
As shown in Figures 15 and 16, during the entire process, the pressureflow characteristic curves of the original model were smoother or more stable than those of the contrast model. By contrast, the pressureflow characteristic curves of the contrast model exhibited significant fluctuations. The experimental results show that the pressure fluctuation amplitude of the original model near the rated operating point was 0.39 MPa, which was approximately 1.6% of the rated pressure. However, the pressure fluctuation amplitude of the contrast model was approximately 1.64 MPa, which was approximately 6.6% of the rated pressure.
Combining the above with the results presented in Section 4, one can conclude that the contrast model valve is an unstable control system. Additionally, as shown in Figures 15 and 16, the flowpressure characteristics of the valve do not change significantly after the addition of a damping orifice. Thus, designing an orifice between the main and pilot valves is beneficial for improving the stability of the hydraulic pilotoperated relief valve.
5.4 Effect on Valve Response Time
In general, stability and rapidity are contradictory. According to a previous study, an appropriate size of R_{2} may enhance the stability of the relief valve. However, its effect on the valve response time remains unclear. Hence, the pressure response curves of the valve were obtained via numerical simulation, and the supply flow (Q_{p}Q_{L}), which was stepped from 0 to 90 L/min at 50 ms, was used as the input signal, whereas chamber A pressure p_{s}, pilot valve displacement x, and main valve displacement y were specified as the output signals. Figures 17 and 21 present the simulation results for the relief valve response time.
As illustrated in Figures 17, 18, 19, 20 and 21, the response speed of the contrast model was high under stepsignal excitation, and the pressure of the controlled chamber can reach the set value within approximately 9.9 ms (Figure 17). However, the original model with the dynamic pressure feedback orifice required at least 12.5 ms to reach the set value (Figure 18). More importantly, the response time of the relief valve can reach 31.6 ms (Figure 21) when the diameter of orifice R_{2} does not exceed 0.8 mm for a steady pressure output.
The dynamic pressure feedback orifice results in a longer response time by the relief valve, although it improves the valve stability. Therefore, to satisfy the stability requirements, the diameter of R_{2} should be set as large as possible.
6 Conclusions
In this study, the dynamic characteristics of a cartridgetype hydraulic pilotoperated relief valve were investigated through theoretical analysis and experiments, and the following conclusions were obtained:

(1)
For the case involving a larger dynamic pressure feedback orifice, the stability of the pilotoperated relief valve did not change substantially, except when its damping ratio was increased.

(2)
A smalldiameter orifice resulted in high flow resistance, which was beneficial to the stability of the relief valve. In terms of control engineering, an energystorage element with a lower break frequency was added to the pilotoperated relief valve system, which was beneficial for improving circuit stability. In addition, the oil inside the main spring chamber was equivalent to a liquid spring with an extraordinarily high stiffness, and the resonance frequency of the main valve subsystem increased significantly to a level far exceeding the regulating frequency of the relief valve.

(3)
The dynamic pressure feedback orifice resulted in a longer response time by the relief valve, although it improved the valve stability.

(4)
The simulation and experimental results showed that designing a dynamic pressure feedback orifice with an appropriate size between the main valve and pilot valve is beneficial to the stability of hydraulic pilotoperated relief valves.
References
Y B Yin. Electro hydraulic control theory and its applications under extreme environment. Oxford: Elsevier Inc, 2019: 273–281.
H F Vickers. Liquid relief valve. Patent US2043453, USA, 1931.
K Yonezawa. Flowinduced vibration of a steam control valve. Journal of Fluids and Structures, 2012, 35: 76–88.
S Hayashi. Instability of poppet valve circuit. JSME International Journal, 1995, 38(3): 357–366.
J Lei, J Tao, C Liu, et al. Flow model and dynamic characteristics of a direct spring loaded poppet relief valve. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232(9): 1657–1664.
K Dasgupta, R Karmakar. Dynamic analysis of pilot operated pressure relief valve. Simulation Modelling Practice and Theory, 2001, 10: 35–49.
D N Johnston, K A Edge, M Brunelli. Impedance and stability characteristics of a relief valve. Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering, 2002, 216(5): 371–382.
W Wei, H Jian, Q Yan, et al. Nonlinear modeling and stability analysis of a pilotoperated valvecontrol hydraulic system. Advances in Mechanical Engineering, 2018, 10(11): 1–8.
K Suzukia, E Urataa. Dynamic characteristics of a direct pressure sensing water hydraulic relief valve. Proceedings of the 6th JFPS International Symposium on Fluid Power, Tsukuba, Japan, November 7–10, 2005: 461–466.
Q F Ye, J P Chen. Dynamic analysis of a pilotoperated twostage solenoid valve used in pneumatic system. Simulation Modelling Practice and Theory, 2009, 17: 794–816.
P Moussou. Instability of pressure relief valves in water pipes. Proceedings of the ASME 2009 Pressure Vessels and Piping Division. Prague, Czech Republic, July 26–30, 2009: 1–8.
X T Zhang, W L, Y M Zhang, et al. Experimental investigation and optimization design of multisupport pipeline system. Chinese Journal of Mechanical Engineering, 2021, 34(1): 10.
D Y Yi, L Lu, J Zou, et al. Interactions between poppet vibration and cavitation in relief valve. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2014, 203: 1989–1996.
W Min, H Wang, Z Zheng, et al. Visual experimental investigation on the stability of pressure regulating poppet valve. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2020, 234(4): 2329–2348.
K Kumagai. Investigation of poppet valve vibration with cavitation. International Journal of Fluid Power, 2016, 17(1): 5–24.
S Washio, A R Champneys. Nucleation and subsequent cavitation in a hydraulic oil poppet valve. Mechanical Engineering Science, 2016, 224: 947–958.
G Osama. Modeling of impact of the poppet element on its seat body in pressure relief valves. Proceedings of the Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering, 2020, 235(5): 703–720.
Y B Yin, J Y Yuan, J Y FU. Characteristics of twostage relief valve with a series damping orifice in pilot valve front chamber. Journal of Jilin University(Engineering and Technology Edition), 2017, 47(1): 129–136.
A Misra. Selfexcited vibration of a control valve due to fluidstructure interaction. Journal of Fluids and Structures, 2002, 16(5): 649–665.
W J Ding. SelfExcited Vibration: Theory, Paradigms, and Research Methods. Beijing: Tsinghua University Press, 2011. (in Chinese)
Y J Gong, Z W Wang, J Xu, et al. Simulation and experiments study on water hydraulic pressure relief valve with pilot stage. Chinese Journal of Mechanical Engineering, 2010, 46(24): 136–142.
Q Zhong, H M Bao, Y B Li, et al. Investigation into the independent metering control performance of a twin spools valve with switching technologycontrolled pilot stage. Chinese Journal of Mechanical Engineering, 2021, 34: 91.
Y H Liu, X Guan, P P Lu, et al. Simulation research on dynamic characteristics of hydraulic mount. Chinese Journal of Mechanical Engineering, 2021, 34(1): 49.
W Min, D Wang, Z Zheng. Visualization experiment of vibration and cavitation in poppet valve under low pressure condition. Journal of Mechanical Engineering, 2018, 54(50): 139–144.
H E Merrit. Hydraulic control systems. New York: John Willy & Sons, 1967.
R Shi, C L Wang, T He. Analysis of dynamic characteristics of pressureregulating and pressurelimiting combined relief valve. Physical Problems in Engineering, 2021, 9: 1–13.
Acknowledgements
The authors sincerely thanks to Engineer Jiali Guo and Engineer Sancheng Yu of the Shanghai Aerospace Control Technology Institute for their important assistance in the experiment.
Funding
Supported by National Natural Science Foundation of China (Grant No. 52175059) and National Key Research and Development Program of China (Grant No. 2018YFB2001100).
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YY and JF were in charge of the whole trial; DW wrote the manuscript, and HJ assisted with the sampling and laboratory analyses. All the authors have read and approved the final version of the manuscript.
Authors’ Information
Yaobao Yin born in 1965, is currently a professor at Tongji University, China. He received his Doctor of Engineering Degree in mechanical engineering from Saitama University, Japan, in 1999, after obtaining M.S. degree in engineering from Shanghai Jiao Tong University, China, in 1991, and B.S. degree in mechanical engineering from Shanghai Jiao Tong University, China, in 1988. His research interests include basic theories of fluid power control, hydraulics and pneumatics in extreme environments, aircraft energy and servo mechanisms, highspeed pneumatic control, advanced energy and power control, and the basic theory of ocean wave power generation.
Dong Wang born in 1995, is currently a PhD candidate at Tongji University, China. He received his master degree from Lanzhou University of Technology, China, in 2019. His research interests include basic theory and application of hydraulic components.
Junyong Fu born in 1971, is currently an engineer at Shanghai Aerospace Control Technology Institute, China. He received his master degree from Harbin Institute of Technology, China, in 2005. His research interests include hydraulic transmission technology, fluid transmission, and fluid control.
Hongchao Jian was born in 1989, is currently an engineer at China North Vehicle Research Institute, China. He received his PhD degree from the Beijing Institute of Technology, China, in 2018. His research interests include hydraulic transmission and vehicle engineering.
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Yin, Y., Wang, D., Fu, J. et al. Effect of Dynamic Pressure Feedback Orifice on Stability of CartridgeType Hydraulic PilotOperated Relief Valve. Chin. J. Mech. Eng. 36, 85 (2023). https://doi.org/10.1186/s10033023009225
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DOI: https://doi.org/10.1186/s10033023009225