Optimization design method for pilot-operated overflow valve system

Abstract

According to the optimization design method for the pilot-operated overflow valve system, firstly, a flow continuity equation and a force balance equation of a pilot-operated overflow valve are established, then, a pressure and flow relation equation and a state equation are established, and finally, the state equation is solved. In the step of optimizing the mathematical model, three sub-targets of the maximum overshoot, the steady-state error and the root-mean-square error of the system pressure value of the pilot-operated overflow valve system are firstly established, then a multi-target function is established according to the sub-targets, then design variables are selected, constraint conditions are established, and finally the mathematical model is optimized and solved. According to the optimization design method for the pilot-operated type overflow valve system, the diameter of the damping hole of the main valve, the coefficient of the valve port of the main valve and the maximum overshoot of the pressure of the pilot valve in the pilot-operated type overflow valve system are all optimized, and the comprehensive performance of the pilot-operated type overflow valve system is improved.

Description

Technical Field

[0001] The present invention relates to a pilot-operated overflow valve, and more specifically, to an optimization design method for a pilot-operated overflow valve system. Background Art

[0002] The pilot-operated relief valve is composed of a main valve and a pilot valve. When the oil pressure at the oil inlet is less than the opening pressure of the pilot valve, the pilot valve is in a closed state and the main valve does not open; when the oil pressure reaches or exceeds the opening pressure of the pilot valve, the main valve opens to achieve oil overflow. Therefore, the pilot-operated relief valve has the function of maintaining a constant oil pipeline pressure. Compared with the direct-acting relief valve, the pilot-operated relief valve is equivalent to adding a pilot valve, and the structure is more complicated, which also leads to the corresponding speed and sensitivity of the pilot-operated relief valve being lower than that of the direct-acting relief valve. The pilot-operated relief valve is suitable for use in high-pressure and high-flow situations.

[0003] In the design process of the pilot relief valve system, in order to increase its response speed as much as possible and ensure that the sensitivity of the pilot relief valve meets the requirements, it is necessary to optimize the design of its structural parameters. Since the pilot relief valve has many design parameters, if all parameters are selected as optimization design variables, the design process will be complicated and not conducive to the implementation of the optimization design method. Therefore, it is necessary to establish a mathematical model of the pilot relief valve system and select appropriate design parameters for its optimization design; this paper gives a specific optimization design method for the pilot relief valve system. Summary of the invention

[0004] In order to overcome the disadvantages of the above technical problems, the present invention provides a method for optimizing the design of a pilot-operated overflow valve system.

[0005] The pilot-operated overflow valve system optimization design method of the present invention comprises a pilot-operated overflow valve composed of a main valve and a pilot valve, wherein a main valve core and a main valve spring are arranged in the main valve, a pilot valve core and a pilot valve spring are arranged in the pilot valve, the lower end of the main valve core forms a main valve front cavity, the right end of the pilot valve core forms a pilot valve front cavity, an oil inlet and an oil return port are provided on the main valve, a main valve damping hole is provided on the main valve core, a pilot valve damping hole communicating with the main valve damping hole is provided on the pilot valve, and a pilot valve return port is provided on the pilot valve; the pilot-operated overflow valve system optimization design method comprises a mathematical model establishment step, a mathematical model optimization step, and a result analysis and improvement step, and is characterized in that: The method of the mathematical model establishment steps is: first establish the flow continuity equation and force balance equation of the pilot-operated relief valve, then establish the pressure and flow relationship equation and the state equation, and finally solve the state equation; the method of the mathematical model optimization steps is: first establish three sub-goals of the maximum overshoot, steady-state error and root mean square error of the system pressure value of the pilot-operated relief valve system, then establish a multi-objective function based on the sub-goals, then select the design variables and establish constraints, and finally optimize the mathematical model and solve it; the method of the result analysis and improvement steps is: introduce the pressure of the pilot valve into the multi-objective function for solution.

[0006] The pilot-operated relief valve system optimization design method of the present invention, the step of establishing the mathematical model is specifically implemented by the following steps:

[0007] a-1). Establish the flow continuity equation; First, according to the continuity of the pressure oil flowing in the pilot relief valve, establish the flow continuity equation shown in formula (1) to formula (3):

[0008] q1+q4+q c1 =q(1)

[0009] q2+q y2 +q c2 =q4(2)

[0010] q3+q y1 =q4(3)

[0011] Where:

[0012] q is the flow rate of the oil inlet;

[0013] q1 and q2 are the flow rates flowing out of the valve ports of the main valve and pilot valve respectively;

[0014] q3 and q4 are the flows into the damping hole of the main valve and the damping hole of the pilot valve respectively;

[0015] q y1 ,q y2 They are the dynamic flows caused by the main valve core displacement y1 and the pilot valve core displacement y2 respectively;

[0016] qc1 ,q c2 They are respectively the liquid compression flow rates of the main valve front chamber V1 and the pilot valve front chamber V2;

[0017] a-2). Establish a force balance equation; then, according to the force balance of the pressure oil flowing in the pilot relief valve, establish the force balance equations shown in formulas (4) to (6):

[0018]

[0019]

[0020] p1-(p2+p3+p4)=0 (6)

[0021] Where:

[0022] p1 is the pressure at the oil inlet;

[0023] m1 and m2 are the masses of the main valve core and the pilot valve core respectively;

[0024] y1 and y2 are the opening amounts of the main valve and pilot valve respectively;

[0025] b1 and b2 are the viscous damping coefficients of the main valve and pilot valve respectively;

[0026] k1 and k2 are the stiffness of the main valve spring and the pilot valve spring respectively;

[0027] p2 is the pilot valve pressure;

[0028] p3 and p4 are the pressure difference at both ends of the main valve damping hole and the pressure difference at both ends of the pilot valve damping hole respectively;

[0029] A1 and A2 are the effective areas of the main valve and pilot valve respectively;

[0030] F1 and F2 are the steady-state hydraulic forces of the main valve and pilot valve respectively, where:

[0031]

[0032] r1 and r2 are the opening structural coefficients of the main valve and the pilot valve respectively;

[0033] a-3). Establish the pressure and flow relationship equation; According to the structure of the pilot relief valve, establish the pressure and flow relationship equation shown in formula (9) to formula (14):

[0034]

[0035]

[0036] Where:

[0037] d1 and d2 are the diameters of the main valve and pilot valve openings respectively;

[0038] d3 and d4 are the diameters of the main valve damping hole and the pilot valve damping hole respectively;

[0039] α1 and α2 are the opening slope angles of the main valve and pilot valve respectively;

[0040] C d1 , C d2 are the opening flow coefficients of the main valve and the pilot valve respectively;

[0041] C d3 , C d4 are the flow coefficients of the main valve damping hole and the pilot valve damping hole respectively;

[0042] C i The flow coefficient depends on the opening and damping hole structure, which is obtained by formula (15) and formula (16):

[0043]

[0044] A3 and A4 are the cross-sectional areas of the main valve damping hole and the pilot valve damping hole, respectively, namely:

[0045]

[0046] V1 and V2 are the volumes of the main valve front chamber and the pilot valve front chamber respectively;

[0047] E is the bulk elastic modulus of the oil;

[0048] R e is the Reynolds number;

[0049] ρ is the oil density;

[0050] a-4) Establish the state equation; select six states y1, y2, u1, u1, u2, p1, p2, where u1 = y1, u2 = y2, combine equations (1) to (17), and obtain the following state equation:

[0051]

[0052]

[0053] The state equation is written in vector form as follows:

[0054]

[0055] Wherein the state variable X=(y1,y2,u1,u2,p1,p2);

[0056] Since q4 is not a state variable, q4 needs to be eliminated from the equation as follows:

[0057]

[0058] After sorting:

[0059]

[0060] Where:

[0061]

[0062] a-5). Solve the state equation; Use the Euler and Runge-Kutta method to solve the state equations (18) to (24), and choose a suitable step size to get a satisfactory result; take the initial value X(0) = X0, that is, the initial working point is u0 = (p 10 ,q0), and let Solving the nonlinear equations given by formula (27), we get the specific results:

[0063]

[0064] The optimization design method of the pilot-operated relief valve system of the present invention, the optimization step of the mathematical model is specifically implemented by the following steps:

[0065] b-1). Determine the sub-targets; First, the maximum overshoot δ1 and steady-state error e of the pilot-operated relief valve system are established by formula (28), formula (29) and formula (30) f And the root mean square error σ of the system pressure value:

[0066] δ1=(p1) max -p 10 (28)

[0067]

[0068] Where: (p1) max is the maximum value of the oil inlet pressure p1, p 10 is the initial value of the oil inlet pressure p1; (p1) av is t1~t f The average value of p1 during the sampling period, N1, N2, ..., N f The sampling time period is t1~t f The number of sequences within p1, p 1i is the corresponding sampling value;

[0069] b-2) Establish a multi-objective function; Establish a multi-objective function F1 as shown in formula (31):

[0070] F1=α1δ1+α2ef +α3σ (31)

[0071] Where: α1, α2, α3 are weighted factors of the multi-objective function, which are determined by the degree of influence of the three sub-objectives on the dynamic performance of the system;

[0072] b-3). Select design variables; Since the main valve damping hole diameter d3 and the main valve port coefficient C1 have the greatest impact on the dynamic performance of the pilot-operated relief valve, the main valve damping hole diameter d3 and the main valve port relative coefficient β are selected as design variables:

[0073]

[0074] In the formula, C 1max The maximum value of the main valve port coefficient C1;

[0075] b-4). Establish constraint conditions; First, establish the boundary constraint conditions shown in formula (33) and formula (34):

[0076] 0.08≤d3 / cm≤0.26 (33)

[0077] 0.1≤β≤1 (34)

[0078] Then the stability constraint condition shown in formula (35) is established:

[0079] max[Re(λ i )]≤0, i=1,2,…,6 (33)

[0080] In the formula, λ i is the eigenvalue of the system, Re is the real part of the eigenvalue;

[0081] b-5). Optimize the mathematical model and solve; solve the main valve damping hole diameter d3 and the main valve port relative coefficient β:

[0082]

[0083] Using the external penalty function method, the nonlinear programming problem with stability constraints is transformed into an unconstrained problem for solution, that is, solving d3 and β:

[0084]

[0085] Among them, M k is the penalty factor;

[0086] The gradient method is used to solve the unconstrained problem of formula (35).

[0087] The pilot-operated relief valve system optimization design method of the present invention includes the following specific methods of result analysis and improvement steps: introducing the pressure p2 of the pilot valve into the multi-objective function, and replacing the objective function F2 in formula (35) with the objective function F3 in formula (36):

[0088] F3=α1δ1+α2e f +α3σ+M k [g(λ i )] 2 +α4δ2(i=1,2,…,6) (36)

[0089] Where:

[0090] δ2 is the maximum overshoot of the pilot valve pressure p2;

[0091] δ2=(p2) max -p 2f

[0092] p 2f is the steady-state pressure of the pilot valve pressure p2;

[0093] (p2) max The maximum pressure of the pilot valve pressure p2;

[0094] α4 is the maximum pressure weighting factor of the pilot valve pressure p2.

[0095] The pilot-operated overflow valve system optimization design method of the present invention, the weighting factors α1, α2, α3, and α4 are: α1=5, α2=10, α3=5, α4=2.375, and the penalty factor M k =10.

[0096] The beneficial effects of the present invention are as follows: the pilot-operated relief valve system optimization design method of the present invention first establishes the flow continuity equation and force balance equation of the pilot-operated relief valve, then establishes the pressure and flow relationship equation and the state equation, and then establishes three sub-goals of the maximum overshoot of the pilot-operated relief valve system, the steady-state error and the root mean square error of the system pressure value, and establishes a multi-objective function according to the sub-goals, then selects the design variables and establishes the constraint conditions, and finally optimizes the mathematical model and solves the problem. In the process of establishing the multi-objective function, the main valve damping hole diameter and the main valve port coefficient that have the greatest influence on the dynamic performance of the pilot-operated relief valve are used as design variables, and the maximum overshoot of the pilot valve pressure is introduced in the result analysis and improvement steps, so that the main valve damping hole diameter, the main valve port coefficient and the maximum overshoot of the pilot valve pressure in the pilot-operated relief valve system are optimized, the comprehensive performance of the pilot-operated relief valve system is improved, and it is conducive to designing a pilot-operated relief valve system whose sensitivity, oil pressure, the maximum overshoot of the main valve oil and the maximum overshoot of the pilot valve oil all meet the requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] Figure 1 It is a structural schematic diagram of the pilot-operated relief valve system of the present invention;

[0098] Figure 2 A simplified model diagram of the pilot-operated relief valve system of the present invention;

[0099] Figure 3 is the dynamic response curve of the oil inlet pressure P1 in the present invention;

[0100] Figure 4 It is an optimization diagram of the gradient method in the present invention;

[0101] Figure 5 is the dynamic response curve of the oil inlet pressure P1 when the starting point is in the stable domain in the present invention;

[0102] Figure 6 is the dynamic response curve of the oil inlet pressure P1 when the starting point is in the unstable region in the present invention;

[0103] Figure 7 is the dynamic response curve of the pilot valve pressure P2 when the starting point is in the stable domain in the present invention;

[0104] Figure 8 is the dynamic response curve of the pilot valve pressure P2 when the starting point is in the unstable region in the present invention;

[0105] Fig. 9 It is the dynamic response curve of the pilot valve pressure P2 after the maximum overshoot of the pilot valve pressure is introduced in the present invention.

[0106] In the figure: 1 main valve, 2 pilot valve, 3 main valve core, 4 pilot valve core, 5 oil inlet, 6 oil return port, 7 main valve spring, 8 pilot valve spring, 9 main valve damping hole, 10 pilot valve damping hole, 11 pilot valve oil return port, 12 main valve front chamber, 13 pilot valve front chamber. DETAILED DESCRIPTION

[0107] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0108] like Figure 1 and Figure 2As shown, the structural schematic diagram and simplified model diagram of the pilot relief valve system of the present invention are respectively given. The pilot relief valve shown is composed of a main valve 1 and a pilot valve 2. The main valve 1 is provided with a main valve core 3 and a main valve spring 7. A main valve front chamber 12 is formed between the lower part of the main valve core 3 and the valve body. The main valve 1 is provided with an oil inlet 5 and an oil return port 6 that are connected to the main valve front chamber 12. When the main valve core 3 moves upward, the oil return port 6 is opened. A main valve damping hole 9 is provided on the main valve core 3. The two ends of the main valve damping hole 9 are respectively connected to the main valve front chamber 12 and the main valve rear chamber. The pilot valve 2 is provided with a pilot valve core 4 and a pilot valve spring 8. A pilot valve front chamber 13 is formed between the pilot valve core 4 and the valve body on the right side. A pilot valve damping hole 10 that is connected to the main valve rear chamber is provided on the valve body of the pilot valve 2. The two ends of the pilot valve damping hole 10 are respectively connected to the main valve rear chamber and the pilot valve front chamber 13.

[0109] During operation, the pressurized oil entering through the oil inlet 5 first enters the pilot valve front chamber 12, and enters the main valve rear chamber, the pilot valve damping hole 10 and the pilot valve front chamber 13 through the main valve damping hole 9. When the entering oil pressure is less than the opening pressure of the pilot valve core 4, the pilot valve 2 is in a closed state and the main valve 1 is also in a closed state; when the oil pressure is greater than the opening pressure of the pilot valve 2, the pilot valve 2 opens, and the main valve 1 is opened by relying on the pressure difference at both ends of the main valve core 3, thereby realizing oil overflow.

[0110] The pilot-operated overflow valve system optimization design method of the present invention includes the steps of establishing a mathematical model, optimizing the mathematical model, and analyzing and improving the results. The method of the mathematical model establishment step is: firstly, establishing the flow continuity equation and the force balance equation of the pilot-operated overflow valve, then establishing the pressure and flow relationship equation and the state equation, and finally solving the state equation; the method of the mathematical model optimization step is: firstly, establishing three sub-goals of the maximum overshoot, steady-state error and root mean square error of the system pressure value of the pilot-operated overflow valve system, and then establishing a multi-objective function according to the sub-goals, and then selecting design variables and establishing constraints, and finally optimizing the mathematical model and solving; the method of the result analysis and improvement step is: introducing the pressure of the pilot valve into the multi-objective function for solving; the specific method steps are given below.

[0111] 1. The steps of establishing the mathematical model are specifically implemented through the following steps:

[0112] a-1). Establish the flow continuity equation; First, according to the continuity of the pressure oil flowing in the pilot relief valve, establish the flow continuity equation shown in formula (1) to formula (3):

[0113] q1+q4+q c1 =q (1)

[0114] q2+q y2 +q c2 =q4 (2)

[0115] q3+q y1 =q4 (3)

[0116] Where:

[0117] q is the flow rate of the oil inlet;

[0118] q1 and q2 are the flow rates flowing out of the valve ports of the main valve and pilot valve respectively;

[0119] q3 and q4 are the flows into the damping hole of the main valve and the damping hole of the pilot valve respectively;

[0120] q y1 ,q y2 They are the dynamic flows caused by the main valve core displacement y1 and the pilot valve core displacement y2 respectively;

[0121] q c1 ,q c2 They are respectively the liquid compression flow rates of the main valve front chamber V1 and the pilot valve front chamber V2;

[0122] a-2). Establish a force balance equation; then, according to the force balance of the pressure oil flowing in the pilot relief valve, establish the force balance equations shown in formulas (4) to (6):

[0123]

[0124] p1-(p2+p3+p4)=0 (6)

[0125] Where:

[0126] p1 is the pressure at the oil inlet;

[0127] m1 and m2 are the masses of the main valve core and the pilot valve core respectively;

[0128] y1 and y2 are the opening amounts of the main valve and pilot valve respectively;

[0129] b1 and b2 are the viscous damping coefficients of the main valve and pilot valve respectively;

[0130] k1 and k2 are the stiffness of the main valve spring and the pilot valve spring respectively;

[0131] p2 is the pilot valve pressure;

[0132] p3 and p4 are the pressure difference at both ends of the main valve damping hole and the pressure difference at both ends of the pilot valve damping hole respectively;

[0133] A1 and A2 are the effective areas of the main valve and pilot valve respectively;

[0134] F1 and F2 are the steady-state hydraulic forces of the main valve and pilot valve respectively, where:

[0135] F1=r1y1p1(7)

[0136] F2=r2y2p2(8)

[0137] r1 and r2 are the opening structural coefficients of the main valve and the pilot valve respectively;

[0138] a-3). Establish the pressure and flow relationship equation; According to the structure of the pilot relief valve, establish the pressure and flow relationship equation shown in formula (9) to formula (14):

[0139]

[0140] Where:

[0141] d1 and d2 are the diameters of the main valve and pilot valve openings respectively;

[0142] d3 and d4 are the diameters of the main valve damping hole and the pilot valve damping hole respectively;

[0143] α1 and α2 are the opening slope angles of the main valve and pilot valve respectively;

[0144] C d1 , C d2 are the opening flow coefficients of the main valve and the pilot valve respectively;

[0145] C d3 , C d4 are the flow coefficients of the main valve damping hole and the pilot valve damping hole respectively;

[0146] C i The flow coefficient depends on the opening and damping hole structure, which is obtained by formula (15) and formula (16):

[0147]

[0148] A3 and A4 are the cross-sectional areas of the main valve damping hole and the pilot valve damping hole, respectively, namely:

[0149]

[0150] V1 and V2 are the volumes of the main valve front chamber and the pilot valve front chamber respectively;

[0151] E is the bulk elastic modulus of the oil;

[0152] R e is the Reynolds number;

[0153] ρ is the oil density;

[0154] a-4) Establish the state equation; select six states y1, y2, u1, u1, u2, p1, p2, where u1 = y1, u2 = y2, combine equations (1) to (17), and obtain the following state equation:

[0155]

[0156] The state equation is written in vector form as follows:

[0157]

[0158] Wherein the state variable X=(y1,y2,u1,u2,p1,p2);

[0159] Since q4 is not a state variable, q4 needs to be eliminated from the equation as follows:

[0160]

[0161] After sorting:

[0162]

[0163] Where:

[0164]

[0165] a-5). Solve the state equation; Use the Euler and Runge-Kutta method to solve the state equations (18) to (24), and choose a suitable step size to get a satisfactory result; take the initial value X(0) = X0, that is, the initial working point is u0 = (p 10 ,q0), and let Solving the nonlinear equations given by formula (27), we get the specific results:

[0166]

[0167] 2. The optimization steps of the mathematical model are specifically implemented through the following steps:

[0168] b-1). Determine the sub-targets; First, the maximum overshoot δ1 and steady-state error e of the pilot-operated relief valve system are established by formula (28), formula (29) and formula (30) f And the root mean square error σ of the system pressure value:

[0169] δ1=(p1) max -p 10 (28)

[0170]

[0171] Where: (p1) maxis the maximum value of the oil inlet pressure p1, p 10 is the initial value of the oil inlet pressure p1; (p1) av is t1~t f The average value of p1 during the sampling period, N1, N2, ..., N f The sampling time period is t1~t f The number of sequences within p1, p 1i is the corresponding sampling value;

[0172] like Figure 3 As shown, the dynamic response curve of the oil inlet pressure P1 in the present invention is given, where the horizontal axis is time, the unit is s, and the vertical axis is the oil inlet pressure value, the unit is Pa. It can be seen that in the initial stage of the system response, the oil inlet pressure P1 fluctuates greatly, with a maximum overshoot δ1, and then gradually tends to be stable, with a steady-state error e f .

[0173] b-2) Establish a multi-objective function; Establish a multi-objective function F1 as shown in formula (31):

[0174] F1=α1δ1+α2e f +α3σ (31)

[0175] Where: α1, α2, α3 are weighted factors of the multi-objective function, which are determined by the degree of influence of the three sub-objectives on the dynamic performance of the system;

[0176] b-3). Select design variables; Since the main valve damping hole diameter d3 and the main valve port coefficient C1 have the greatest impact on the dynamic performance of the pilot-operated relief valve, the main valve damping hole diameter d3 and the main valve port relative coefficient β are selected as design variables:

[0177]

[0178] In the formula, C 1max The maximum value of the main valve port coefficient C1;

[0179] b-4). Establish constraint conditions; First, establish the boundary constraint conditions shown in formula (33) and formula (34):

[0180] 0.08≤d3 / cm≤0.26 (33)

[0181] 0.1≤β≤1 (34)

[0182] Then the stability constraint condition shown in formula (35) is established:

[0183] max[Re(λ i )]≤0, i=1,2,…,6 (33)

[0184] In the formula, λ i is the eigenvalue of the system, Re is the real part of the eigenvalue;

[0185] b-5). Optimize the mathematical model and solve; solve the main valve damping hole diameter d3 and the main valve port relative coefficient β:

[0186]

[0187] Using the external penalty function method, the nonlinear programming problem with stability constraints is transformed into an unconstrained problem for solution, that is, solving d3 and β:

[0188]

[0189] Among them, M k is the penalty factor;

[0190] The gradient method is used to solve the unconstrained problem of formula (35).

[0191] like Figure 4 As shown, the gradient method optimization diagram of the present invention is given, the horizontal coordinate is the main valve damping hole diameter, the unit is mm, and the vertical coordinate is the ratio of the main valve port coefficient C1 to its maximum value. In the process of solving the unconstrained problem of formula (35) using the gradient method, when one of the boundary constraints is not satisfied, such as point M' (d3>0.26, β=0.5), then set d3=0.26, search to point M (d3>0.26, p=0.5), and find the gradient G(M) of point M. If G(M) points outside the boundary, then continue to search along the boundary until the optimal point M* is reached.

[0192] 3. Figure 5 As shown, the dynamic response curve of the oil inlet pressure P1 when the starting point is in the stable domain in the present invention is given, wherein the horizontal coordinate is time, unit s, and the vertical coordinate is the oil inlet pressure p1, unit pa. Curve 1 is the dynamic characteristic curve before optimization, and curve 2 is the dynamic characteristic curve after optimization according to the objective function formula (35). The weighting factors in the formula are α1=5, α2=10, α3=5, and the penalty factor M k = 10. The starting point of the optimization in the figure is selected in the stable domain, that is, β 0 =0.1.

[0193] Figure 6 The dynamic response curve of the oil inlet pressure P1 when the starting point is in the unstable region in the present invention is given, and the optimized starting point is selected in the unstable region, that is, β 0 =0.8. The curve 1 (before optimization) in the figure shows the characteristic, δ1 0 =0.14, δ 0=0.067, the characteristics of curve 2 (after optimization), δ * =0.016x10 -4 .

[0194] In with Figure 5 and Figure 6 Under exactly the same conditions, we can obtain Figure 7 and Figure 8 The corresponding dynamic response curve of pilot valve pressure p2, Figure 7 The dynamic response curve of the pilot valve pressure P2 when the starting point is in the stable domain in the present invention is given as follows: Figure 8 is the dynamic response curve of the pilot valve pressure P2 when the starting point is in the unstable region in the present invention, through Figures 5 to 8 It can be concluded that:

[0195] (1) Regardless of the starting point, the optimized dynamic response characteristics have been improved to varying degrees, especially when the starting point is selected in the unstable domain, the performance improvement is more obvious.

[0196] (2) Although the dynamic characteristics of the pressure P2 of the pilot valve have been improved to a certain extent after optimization, the peak of the P2 pressure is generated (see Figure 7 Curve 2) is not good. The reason is that the influence of the derivative pressure P2 is not considered in the optimization objective.

[0197] In order to improve and enhance the comprehensive performance of the oil pressure of the pilot-operated relief valve, the following improvement of the objective function is proposed:

[0198] The pressure p2 of the pilot valve is introduced into the multi-objective function, and the objective function F2 in formula (35) is replaced by the objective function F3 in formula (36):

[0199] F3=α1δ1+α2e f +α3σ+M k [g(λ i )] 2 +α4δ2(i=1,2,…,6) (36)

[0200] Where:

[0201] δ2 is the maximum overshoot of the pilot valve pressure p2;

[0202] δ2=(p2) max -p 2f

[0203] p 2f is the steady-state pressure of the pilot valve pressure p2;

[0204] (p2) max The maximum pressure of the pilot valve pressure p2;

[0205] α4 is the maximum pressure weighting factor of the pilot valve pressure p2.

[0206] like Fig. 9 As shown, the dynamic response curve of the pilot valve pressure P2 after the maximum overshoot of the pilot valve pressure is introduced in the present invention is given. By comparing curves 1 and 2 in the figure, it can be seen that the dynamic performance of the pilot valve pressure p2 has been greatly improved. In curve 1, δ2=10.7; in curve 2, δ2=6.45. δ2 is reduced by 38%, but the overshoot δ1 of the system pressure p1 is slightly increased. δ1=6.27 after optimization according to formula (36), and δ1=7.51 after optimization according to formula (6-93), an increase of 19%. Although the performance of p1 has slightly decreased (compared with before optimization, the performance of p1 is still improved), it has been comprehensively improved from the overall comprehensive performance. In summary, a good optimization requires continuous summary, analysis, and continuous improvement of the objective function from the optimization practice, and pays special attention to the reasonable selection of weighting factors and starting points.

Claims

1. A method for optimizing the design of a pilot-operated overflow valve system, wherein the pilot-operated overflow valve is composed of a main valve (1) and a pilot valve (2), wherein a main valve core (3) and a main valve spring (7) are arranged in the main valve, and a pilot valve core (4) and a pilot valve spring (8) are arranged in the pilot valve, wherein the lower end of the main valve core forms a main valve front chamber (12), and the right end of the pilot valve core forms a pilot valve front chamber (13), wherein an oil inlet (5) and an oil return port (6) are provided on the main valve, a main valve damping hole (9) is provided on the main valve core, a pilot valve damping hole (10) communicating with the main valve damping hole is provided on the pilot valve, and a pilot valve return port (11) is provided on the pilot valve; the method for optimizing the design of a pilot-operated overflow valve system comprises a step of establishing a mathematical model, a step of optimizing the mathematical model, and a step of analyzing and improving the results, and is characterized in that: The method of establishing the mathematical model is as follows: firstly, establishing the flow continuity equation and force balance equation of the pilot-operated relief valve, then establishing the pressure and flow relationship equation and the state equation, and finally solving the state equation; The method of the optimization steps of the mathematical model is: first establish three sub-goals of the maximum overshoot of the pilot relief valve system, the steady-state error and the root mean square error of the system pressure value, then establish a multi-objective function based on the sub-goals, then select the design variables and establish constraints, and finally optimize the mathematical model and solve it; the method of the result analysis and improvement steps is: introduce the pressure of the pilot valve into the multi-objective function for solution.

2. The method for optimizing the design of a pilot-operated relief valve system according to claim 1, characterized in that: The steps of establishing the mathematical model are specifically implemented through the following steps: a-1). Establish the flow continuity equation; First, according to the continuity of the pressure oil flowing in the pilot relief valve, establish the flow continuity equation shown in formula (1) to formula (3): q1+q4+q c1 =q(1) q2+q y2 +q c2 =q4(2) q3+q y1 =q4(3) Where: q is the flow rate of the oil inlet; q1 and q2 are the flow rates flowing out of the valve ports of the main valve and pilot valve respectively; q3 and q4 are the flows into the damping hole of the main valve and the damping hole of the pilot valve respectively; q y1 ,q y2 They are the dynamic flows caused by the main valve core displacement y1 and the pilot valve core displacement y2 respectively; q c1 ,q c2 They are respectively the liquid compression flow rates of the main valve front chamber V1 and the pilot valve front chamber V2; a-2). Establish a force balance equation; then, according to the force balance of the pressure oil flowing in the pilot relief valve, establish the force balance equations shown in formulas (4) to (6): p1-(p2+p3+p4)=0 (6) Where: p1 is the pressure at the oil inlet; m1 and m2 are the masses of the main valve core and the pilot valve core respectively; y1 and y2 are the opening amounts of the main valve and pilot valve respectively; b1 and b2 are the viscous damping coefficients of the main valve and pilot valve respectively; k1 and k2 are the stiffness of the main valve spring and the pilot valve spring respectively; p2 is the pilot valve pressure; p3 and p4 are the pressure difference at both ends of the main valve damping hole and the pressure difference at both ends of the pilot valve damping hole respectively; A1 and A2 are the effective areas of the main valve and pilot valve respectively; F1 and F2 are the steady-state hydraulic forces of the main valve and pilot valve respectively, where: F1=r1y1p1(7) F2=r2y2p2(8) r1 and r2 are the opening structural coefficients of the main valve and the pilot valve respectively; a-3). Establish the pressure and flow relationship equation; According to the structure of the pilot relief valve, establish the pressure and flow relationship equation shown in formula (9) to formula (14): Where: d1 and d2 are the diameters of the main valve and pilot valve openings respectively; d3 and d4 are the diameters of the main valve damping hole and the pilot valve damping hole respectively; α1 and α2 are the opening slope angles of the main valve and pilot valve respectively; C d1 , C d2 are the opening flow coefficients of the main valve and the pilot valve respectively; C d3 , C d4 are the flow coefficients of the main valve damping orifice and the pilot valve damping orifice respectively; C i The flow coefficient depends on the opening and damping hole structure, which is obtained by formula (15) and formula (16): A3 and A4 are the cross-sectional areas of the main valve damping hole and the pilot valve damping hole, respectively, namely: V1 and V2 are the volumes of the main valve front chamber and the pilot valve front chamber respectively; E is the bulk elastic modulus of the oil; R e is the Reynolds number; ρ is the oil density; a-4) Establish the state equation; select six states y1, y2, u1, u1, u2, p1, p2, where u1 = y1, u2 = y2, combine equations (1) to (17), and obtain the following state equation: The state equation is written in vector form as follows: Wherein the state variable X=(y1,y2,u1,u2,p1,p2); Since q4 is not a state variable, q4 needs to be eliminated from the equation as follows: After sorting: Where: a-5). Solve the state equation; Use the Euler and Runge-Kutta method to solve the state equations (18) to (24), and choose a suitable step size to get a satisfactory result; take the initial value X(0) = X0, that is, the initial working point is u0 = (p 10 ,q0), and let Solving the nonlinear equations given by formula (27), we get the specific results:

3. The method for optimizing the design of a pilot-operated relief valve system according to claim 2, characterized in that: The optimization step of the mathematical model is specifically implemented through the following steps: b-1). Determine the sub-targets; First, the maximum overshoot δ1 and steady-state error e of the pilot-operated relief valve system are established by formula (28), formula (29) and formula (30) f And the root mean square error σ of the system pressure value: δ1=(p1) max -p 10 (28) Where: (p1) max is the maximum value of the oil inlet pressure p1, p 10 is the initial value of the oil inlet pressure p1; (p1) av is t1~t f The average value of p1 during the sampling period, N1, N2, ..., N f The sampling time period is t1~t f The number of sequences within p1, p 1i is the corresponding sampling value; b-2) Establish a multi-objective function; Establish a multi-objective function F1 as shown in formula (31): F1=α1δ1+α2e f +α3σ (31) Where: α1, α2, α3 are weighted factors of the multi-objective function, which are determined by the degree of influence of the three sub-objectives on the dynamic performance of the system; b-3). Select design variables; Since the main valve damping hole diameter d3 and the main valve port coefficient C1 have the greatest impact on the dynamic performance of the pilot-operated relief valve, the main valve damping hole diameter d3 and the main valve port relative coefficient β are selected as design variables: In the formula, C 1max The maximum value of the main valve port coefficient C1; b-4). Establish constraint conditions; First, establish the boundary constraint conditions shown in formula (33) and formula (34): 0.08≤d3 / cm≤0.26 (33) 0.1≤β≤1 (34) Then the stability constraint condition shown in formula (35) is established: max[Re(λ i )]≤0,i=1,2,…,6 (33) In the formula, λ i is the eigenvalue of the system, Re is the real part of the eigenvalue; b-5). Optimize the mathematical model and solve; solve the main valve damping hole diameter d3 and the main valve port relative coefficient β: Using the external penalty function method, the nonlinear programming problem with stability constraints is transformed into an unconstrained problem for solution, that is, solving d3 and β: Among them, M k is the penalty factor; The gradient method is used to solve the unconstrained problem of formula (35).

4. The method for optimizing the design of a pilot-operated relief valve system according to claim 3, characterized in that: The specific method of result analysis and improvement steps is: introduce the pressure p2 of the pilot valve into the multi-objective function, and replace the objective function F2 in formula (35) with the objective function F3 in formula (36): F3=α1δ1+α2e f +α3σ+M k [g(λ i )] 2 +α4δ2(i=1,2,…,6) (36) Where: δ2 is the maximum overshoot of the pilot valve pressure p2; δ2=(p2) max -p 2f p 2f is the steady-state pressure of the pilot valve pressure p2; (p2) max The maximum pressure of the pilot valve pressure p2; α4 is the maximum pressure weighting factor of the pilot valve pressure p2.

5. The method for optimizing the design of a pilot-operated relief valve system according to claim 4 is characterized in that: The weighting factors α1, α2, α3, and α4 are: α1=5, α2=10, α3=5, and α4=2.375, respectively; the penalty factor M k =10.

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