AQ sealing element structure parameter optimization method based on whale optimization algorithm

Abstract

The invention provides an AQ sealing element structure parameter optimization method based on a whale optimization algorithm, and the method comprises the following steps: (1) selecting a fitness function of AQ sealing element structure parameters; (2) initializing basic parameters of the whale optimization algorithm; (3) initializing individuals in a matrix of an optimized whale group P; and (5) taking the whale position vector with the minimum current fitness function value as seven adjustable parameters x1, x2, x3, x4, x5, x6 and x7 of the AQ sealing element, substituting the seven adjustable parameters into the regression equation established in the step (1), and solving the predicted leakage rate and the service life of the finally optimized AQ sealing element. Based on the structure parameter library, the structure of the AQ sealing element is optimized, the steps of experimental operation and manual parameter simulation and debugging are replaced, and the time cost is saved.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to an AQ seal structural parameter optimization method based on a whale optimization algorithm. Background Art

[0002] The AQ seal is a combined sealing element, typically consisting of a polytetrafluoroethylene (F-PTFE)-filled sealing ring, an O-ring, and a quad-ring made of rubber (nitrile rubber (NBR) or fluororubber (FKM)). It includes a Turcon sealing ring, a quad-ring, and an O-ring acting as a force-applying element. The Turcon sealing ring and quad-ring together provide dynamic sealing, while the O-ring provides static sealing. It offers excellent liquid / gas separation sealing, a very low coefficient of friction, and a simple groove design. It is interchangeable with Turcon Glyd Rings, and exhibits excellent sliding performance with no "slippage." Available in diameters ranging from 15 to 700 mm, it is suitable for a wide range of operating conditions. It is widely used in construction machinery, machine tools, presses, piston accumulators, heavy-duty suspension cylinders, offshore valves, jacks, forklifts, and other fields.

[0003] AQ seals are complex structures with numerous parameters. For a long time, researchers have typically optimized their structures based on experimental results and the impact of parameters measured in actual use on performance, which is time-consuming, labor-intensive, and wasteful of materials. Summary of the Invention

[0004] The technical problem solved by the present invention is to provide an AQ seal structural parameter optimization method based on the whale optimization algorithm to solve the problems raised in the above background technology.

[0005] The technical problem solved by the present invention is achieved by adopting the following technical solution: A method for optimizing the structural parameters of an AQ seal based on a whale optimization algorithm, comprising the following steps:

[0006] Step (1). Selection of AQ seal structural parameter fitness function:

[0007] Step (2). Initialize the basic parameters of the whale optimization algorithm: Initialize the population size of the whale group P, that is, the number of optimized individuals is N; initialize the spatial dimension D. Since the position vector of each whale group is composed of 7 structural parameters of the AQ seal, the spatial dimension D = 7; set the value range of the separator structural parameters (x1, x2, x3, x4, x5, x6 and x7); set the maximum number of iterations Max_iter. The matrix expression of the whale group P is as follows:

[0008]

[0009] Step (3). Initialize the individuals in the matrix of the optimal whale group P, substitute the initialized individuals into the fitness function to calculate the fitness function value of each whale individual, and record the optimal individual position X*(0) in this iteration step. Update the individual position of the whale based on the initialization matrix, obtain the updated X(1) and calculate the fitness value;

[0010] Step (4). Iterate the optimization process and determine whether the current step has reached the maximum number of iterations. If the number of iterations is greater than the maximum number of iterations, the optimization iteration process ends; otherwise, the optimization iteration continues.

[0011] Step (5). The whale position vector with the minimum current fitness function value is used as the seven adjustable parameters x1, x2, x3, x4, x5, x6 and x7 of the AQ seal, and substituted into the regression equation established in step 1 to obtain the predicted leakage rate and life of the AQ seal obtained by the final optimization.

[0012] In the step (1), the AQ seal uses two O-rings as energy storage elements, plus a star ring on the other side. The structural parameters that affect the performance of the AQ seal include: 1. cylinder diameter D, 2. groove bottom diameter d1, 3. O-ring cross-sectional diameter d2, 4. O-ring inner diameter D2, 5. star ring height h1, 6. star ring inner diameter D1, 7. plastic sealing ring thickness h, where x1, x2, x3, x4, x5, x6 and x7 represent the above seven parameters respectively.

[0013] In step (1), a regression equation for leakage rate r1 and life r2 of a series of AQ seals is established based on the Box-Behnken response surface method:

[0014] Leakage r1 = -26.886889110926 + 23.865140902708x1 - 24.571261175359x2

[0015] -47.893458142879x3+2.0867943976867x4+7.0278750476864x5-1.294986148047x5

[0016] -30.692710532323x7+0.018693215604869x1*x2-0.030129683826105x1*x3-0.026183455264081x1*x4-0.0 091597993591525x1*x5+0.0075653748019506x1*x6-0.021661381432067x1*x7-0.0028129935049371x2*x3

[0017] Lifespan r2 = -34.121817945827 + 12.520367635402x1 - 11.12805541913x2

[0018] -22.406941226753x3-0.44281404163016x4-20.015612452324x5-0.85392 373019601x6+3.3066006944933x7+0.0034599030491033x1*x2+0.15803687 079884x1*x3-0.0070162968104624x1*x4+0.058976132365478x1*x5+0.004 1744948330964x1*x6-0.070927264760154x1*x7-0.21139587013368x2*x3.

[0019] In step (3), the global optimal individual position at this time is further updated. If there is an individual in X(1) that is smaller than X*(0), this individual is marked as the global optimal position X*(1) of the current iteration step; if there is no individual in X(1) that is smaller than X*(0), the global optimal position X*(1) of the current iteration step is X*(0).

[0020] In step (3), the individual positions of the whales are then updated. The new individual positions of the whale group are based on the current X(t), surround the global optimal individual X*(t) in the current iteration step, and are updated to position X(t+1), where t is the current update number.

[0021] Compared with the prior art, the present invention has the following beneficial effects: the present invention optimizes the AQ seal structure based on the structural parameter library, replaces the experimental operation and manual simulation parameter debugging steps, and saves time and cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic diagram of the process of the present invention.

[0023] Figure 2 Schematic diagram of the AQ seal structure of the present invention. DETAILED DESCRIPTION

[0024] In order to make the technical means for realizing the present invention, the creative features, the purpose and the effect easily understood, the present invention is further described below with reference to specific diagrams. In the description of the present invention, it should be noted that, unless otherwise clearly stipulated and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection. It can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be internal communication between two components.

[0025] like Figure 1 、 Figure 2 As shown, a method for optimizing the structural parameters of an AQ seal based on a whale optimization algorithm comprises the following steps:

[0026] Step (1). Using DOE (Design of Experiments), randomly select initial sampling points, i.e., a series of AQ seal structural parameters and the corresponding leakage rate and life under a specific working condition.

[0027] Step (2). Based on the Box-Behnken response surface method, a regression equation for the leakage rate r1 and life r2 of a series of AQ seals is established:

[0028] Leakage:

[0029] r1=26.886889110926+23.865140902708x124.571261175359x2-47.893458142879x3+2.08 67943976867x4+7.0278750476864x5-1.294986148047x5-30.692710532323x7+0.01869321 5604869x1*x2-0.030129683826105x1*x3-0.026183455264081x1*x4-0.009159799359152 5x1*x5+0.0075653748019506x1*x6-0.021661381432067x1*x7-0.0028129935049371x2*x3

[0030] life:

[0031] r2=-34.121817945827+12.520367635402x1-11.12805541913x2-22.406941226753x3-0.44 281404163016x4-20.015612452324x5-0.85392373019601x6+3.3066006944933x7+0.00345 99030491033x1*x2+0.15803687079884x1*x3-0.0070162968104624x1*x4+0.058976132365 478x1*x5+0.0041744948330964x1*x6-0.070927264760154x1*x7-0.21139587013368x2*x3.

[0032] Step (3). Initialize the basic parameters of the whale optimization algorithm: Initialize the population size of the optimal whale group P, the number of optimal individuals N, and the initial spatial dimension D. As mentioned above, this study considers the seven structural parameters of the AQ seal during optimization, so the spatial dimension D = 7. The matrix expression of the optimal whale group P is as follows:

[0033]

[0034] Step (4). Initialize the individuals in the matrix of the optimal whale group P, substitute the initialized individuals into the fitness function to calculate the fitness function value of each whale individual, and record the optimal individual position X*(0) in this iteration step. Update the individual position of the whale based on the initialization matrix to obtain the updated X(1) and calculate the fitness value. Further update the global optimal individual position at this time. If there is an individual smaller than X*(0) in X(1), mark this individual as the global optimal position X*(1) of the current iteration step; if there is no individual smaller than X*(0) in X(1), the global optimal position X*(1) of the current iteration step is X*(0). Then update the individual position of the whale. The new individual position of the whale group is based on the current X(t), surrounds the global optimal individual X*(t) of the current iteration step and updates to the position X(t+1), where t is the current update number.

[0035] Step (5). Iterate the optimization process and determine whether the current step has reached the maximum number of iterations. If the number of iterations is greater than the maximum number of iterations, the optimization iteration process ends; otherwise, return to step 4 and continue the optimization iteration.

[0036] Step (6). Use the whale position vector with the minimum current fitness function value as the seven adjustable parameters x1, x2, x3, x4, x5, x6 and x7 of the AQ seal, substitute them into the regression equation established in step 1, and calculate the predicted leakage rate and life of the AQ seal obtained by the final optimization.

[0037] The present invention introduces an intelligent control algorithm when designing the AQ seal structure, replacing experimental operations and manual simulation parameter debugging steps, saving time and cost, and improving the efficiency of optimizing the AQ seal structure parameters.

[0038] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for optimizing the structural parameters of an AQ seal based on a whale optimization algorithm, characterized by: The following steps are involved: Step (1). Selection of AQ seal structural parameter fitness function: Step (2). Initialize the basic parameters of the whale optimization algorithm: initialize the population size of the whale group P, that is, the number of optimal individuals is N; initialize the spatial dimension D. Since the position vector of each whale group is composed of 7 structural parameters of the AQ seal, the spatial dimension D = 7; set the value range of the separator structure parameters (x1, x2, x3, x4, x5, x6 and x7); set the maximum number of iterations Max_iter, then the matrix expression of the whale group P is as follows: Step (3). Initialize the individuals in the matrix of the optimal whale group P, substitute the initialized individuals into the fitness function to calculate the fitness function value of each whale individual, and record the optimal individual position X*(0) in this iteration step. Update the individual position of the whale based on the initialization matrix, obtain the updated X(1) and calculate the fitness value; Step (4). Iterate the optimization process and determine whether the current step has reached the maximum number of iterations. If the number of iterations is greater than the maximum number of iterations, the optimization iteration process ends; otherwise, the optimization iteration continues. Step (5). The whale position vector with the minimum current fitness function value is used as the seven adjustable parameters x1, x2, x3, x4, x5, x6 and x7 of the AQ seal, and substituted into the regression equation established in step 1 to obtain the predicted leakage rate and life of the AQ seal obtained by the final optimization.

2. The AQ seal structural parameter optimization method based on the whale optimization algorithm according to claim 1, characterized in that: In the step (1), the AQ seal uses two O-rings as energy storage elements, plus a star ring on the other side. The structural parameters that affect the performance of the AQ seal include:

1. cylinder diameter D, 2. groove bottom diameter d1, 3. O-ring cross-sectional diameter d2, 4. O-ring inner diameter D2, 5. star ring height h1, 6. star ring inner diameter D1, 7. plastic sealing ring thickness h, where x1, x2, x3, x4, x5, x6 and x7 represent the above seven parameters respectively.

3. The AQ seal structural parameter optimization method based on the whale optimization algorithm according to claim 1, characterized in that: In step (1), a regression equation for leakage rate r1 and life r2 of a series of AQ seals is established based on the Box-Behnken response surface method: Leakage r1 = -26.886889110926 + 23.865140902708x1 - 24.571261175359x2 -47.893458142879x3+2.0867943976867x4+7.0278750476864x5-1.294986148047x5 -30.692710532323x7+0.018693215604869x1*x2-0.030129683826105x1*x3-0.026183455264081x1*x4-0.0 091597993591525x1*x5+0.0075653748019506x1*x6-0.021661381432067x1*x7-0.0028129935049371x2*x3 Lifespan r2 = -34.121817945827 + 12.520367635402x1 - 11.12805541913x2 -22.406941226753x3-0.44281404163016x4-20.015612452324x5-0.85392 373019601x6+3.3066006944933x7+0.0034599030491033x1*x2+0.15803687 079884x1*x3-0.0070162968104624x1*x4+0.058976132365478x1*x5+0.004 1744948330964x1*x6-0.070927264760154x1*x7-0.21139587013368x2*x3.

4. The AQ seal structural parameter optimization method based on the whale optimization algorithm according to claim 1 is characterized in that: In step (3), the global optimal individual position at this time is further updated. If there is an individual in X(1) that is smaller than X*(0), this individual is marked as the global optimal position X*(1) of the current iteration step; if there is no individual in X(1) that is smaller than X*(0), the global optimal position X*(1) of the current iteration step is X*(0).

5. The AQ seal structural parameter optimization method based on the whale optimization algorithm according to claim 4 is characterized in that: In step (3), the individual positions of the whales are then updated. The new individual positions of the whale group are based on the current X(t), surround the global optimal individual X*(t) in the current iteration step, and are updated to position X(t+1), where t is the current update number.

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