Co-optimization method for composite profile gear pump with installation size constraints

Abstract

The application discloses a composite profile gear pump optimization method under installation size constraints, and relates to the field of gear pump design and optimization. The method adopts an optimization algorithm to iteratively optimize target variables of a gear pump with the minimum target function value as the optimization target. In the iteration process, the following steps are performed for each candidate parameter combination composed of the target variables: determining whether the candidate composite profile generated by the candidate parameter combination can be geometrically effectively closed through a tooth profile closure verification mechanism; if yes, calculating the target function value corresponding to the candidate parameter combination through a first target function; and if no, calculating the target function value corresponding to the candidate parameter combination through a second target function. The method aims to solve the problems of geometric false solution, size false optimization and performance evaluation model distortion in the existing composite profile gear pump optimization design method.

Description

Technical Field

[0001] This application relates to the field of gear pump design and optimization, and in particular to a collaborative optimization method for a composite gear pump with installation dimensions constrained. Background Technology

[0002] Existing collaborative optimization methods for composite gear pumps typically use parameters such as normal module, pressure angle, and tooth width directly as optimization variables, and often directly employ spur gears or simplified end-face models to evaluate flow pulsation. These methods have the following drawbacks: For applications with a small number of teeth, while some optimization results may appear superior at the objective function level, issues such as involute segments not being tangent to circular arc segments, tooth profile self-intersection, or unsolvable nonlinear equations can occur. This renders the resulting parameter combinations unusable for actual machining, preventing the assembly into a gear pump with a sealed working cavity—meaning the gear shape fails to achieve geometric closure. Furthermore, traditional methods often prioritize increasing displacement, assuming that a larger module or tooth width directly translates to higher displacement, without applying installation boundary constraints consistent with the actual housing dimensions. This can lead the optimizer to approximate along the upper limit of parameters, resulting in pseudo-optimization results dependent on size enlargement. Consequently, the gear dimensions may exceed the physical limitations of the gear pump housing's internal cavity, causing assembly interference. Such results fail to reflect the engineering value of increased displacement per unit installation volume within a confined space. For flow pulsation assessment, the axial overlap caused by the helix angle and its impact on pulsation attenuation are not included in the evaluation, leading to a discrepancy between the objective function and actual operating conditions, making effective synergistic optimization of displacement and pulsation difficult. Summary of the Invention

[0003] The purpose of this application is to provide a collaborative optimization method for composite gear pumps constrained by installation dimensions, aiming to solve the problems of geometric pseudo-solution, dimensional pseudo-optimization, and performance evaluation model distortion in existing composite gear pump optimization design methods. This provides a method that can accurately and robustly collaboratively optimize the flow rate and pulsation of composite gear pumps under strict installation dimensions and manufacturability constraints.

[0004] To achieve the above objectives, this application provides the following solution: In the first aspect, this application provides a collaborative optimization method for a composite gear pump constrained by installation dimensions, which uses an optimization algorithm to iteratively optimize the target variables of the gear pump with the goal of minimizing the objective function value; During the iteration process, the following steps are performed for each candidate parameter combination consisting of the target variable: The tooth profile closure verification mechanism is used to determine whether the candidate composite tooth profile generated by the combination of the candidate parameters can be geometrically and effectively closed. If so, the objective function value corresponding to the candidate parameter combination is calculated through the first objective function. The first objective function includes a performance evaluation term and a size penalty term. The performance evaluation term is used to calculate the performance index of the candidate composite tooth profile under the premise of considering the filtering effect of the helix angle on the flow pulsation. The size penalty term is used to apply a penalty when the tooth tip circle diameter of the candidate composite tooth profile is greater than the maximum allowable tooth tip circle diameter determined by the pump casing. If not, the objective function value corresponding to the candidate parameter combination is calculated by the second objective function, which includes a geometric penalty term and a size penalty term. The geometric penalty term is used to apply a penalty when the candidate compound tooth profile fails to close geometrically effectively.

[0005] In a second aspect, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the composite gear pump co-optimization method constrained by installation dimensions as described above.

[0006] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described composite gear pump co-optimization method constrained by installation dimensions.

[0007] Fourthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described composite gear pump co-optimization method constrained by installation dimensions.

[0008] According to the specific embodiments provided in this application, the following technical effects are disclosed: 1. This invention ensures the manufacturability and feasibility of the optimized results. By embedding a tooth profile closure verification mechanism based on nonlinear solution within the optimization algorithm, this invention fundamentally eliminates the generation of distorted tooth profiles (i.e., geometric pseudo-solutions). This mechanism ensures that any output optimization result corresponds to a physically continuous, smooth, and self-intersecting manufacturable gear, thereby guaranteeing the meshing smoothness and volumetric sealing of the gear pump.

[0009] 2. This invention achieves lightweight design and high power density in gear pumps. By using the maximum permissible addendum circle diameter as a hard constraint and introducing a dimensional penalty term positively correlated with exceeding the limit, the optimization process is forced to seek performance maximization within a given, constrained pump casing space, rather than relying on simply enlarging dimensions to obtain pseudo-optimization results. This allows the optimization results to achieve a higher displacement per unit installation volume under the same external dimensions, thereby achieving high power density and lightweight structure in the gear pump.

[0010] 3. Realistic and collaborative performance optimization is achieved. This invention introduces an attenuation term representing the effect of helix angle filtering into the flow pulsation model, making the performance evaluation model closer to the actual physical conditions of the helical gear pump, thus solving the problem of optimization target deviation caused by model distortion.

[0011] 4. Significantly enhanced robustness and convergence of the algorithm. This invention effectively solves the problem of algorithm non-convergence caused by the narrow geometric feasible region under extreme conditions such as a small number of teeth by adopting a collaborative mechanism of "feasible initial seed pre-scanning" and "error-based continuous geometric penalty guidance". Pre-scanning ensures that the algorithm has a good starting point, while the continuous penalty term can be effectively guided back to the correct path when the algorithm "goes astray" into the infeasible region during the exploration process, thereby ensuring the stability of obtaining the global optimal solution. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating a collaborative optimization method for a composite gear pump with installation size constraints according to an embodiment of this application. Figure 2 This is a flowchart illustrating a collaborative optimization method for a composite gear pump with installation size constraints according to an embodiment of this application. Figure 3 This is a two-dimensional end face view of the optimized composite tooth profile in one embodiment of this application; Figure 4 This is a three-dimensional solid model of the optimized composite tooth profile in one embodiment of this application; Figure 5 Assembly of the optimized composite tooth profile in one embodiment of this application Figure 1 ; Figure 6 Assembly of the optimized composite tooth profile in one embodiment of this application Figure 2 ; Figure 7 This is a geometrical analytical diagram of a circular arc-involute composite tooth profile in one embodiment of this application. Detailed Implementation

[0014] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] The collaborative optimization method for composite gear pumps with installation size constraints in this application embodiment is executed by a computer device, which can be a terminal computing device or a server. The terminal computing device can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, and IoT devices. The server can be a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0017] In one embodiment of this application, the collaborative optimization method for a composite gear pump constrained by installation dimensions specifically includes: using an optimization algorithm to iteratively optimize the target variables of the gear pump with the goal of minimizing the objective function value. The optimization engine iteratively optimizes a series of target variables of the gear pump, with the ultimate goal of finding a set of parameter combinations that minimizes the preset comprehensive objective function value. Throughout the iterative optimization cycle, the optimization engine continuously generates new candidate parameter combinations and passes these combinations to subsequent functional modules for evaluation.

[0018] During the iteration process, for each combination of candidate parameters consisting of the target variable, the following steps are performed: Step S110 involves using a tooth profile closure verification mechanism to determine whether the candidate composite tooth profile generated from the candidate parameter combination can be geometrically effectively closed. This step aims to address the common geometric pseudo-solution problem in the background art. In traditional optimization methods, the algorithm may produce a parameter combination that performs well mathematically on the objective function but cannot physically form a continuous, smooth tooth profile. This embodiment, by setting a tooth profile closure verification mechanism, can quickly identify these invalid solutions that lack manufacturability before calculating complex performance indicators, thereby greatly improving optimization efficiency and the reliability of the results.

[0019] If so, then proceed to step S120, calculate the objective function value corresponding to the candidate parameter combination through the first objective function. The first objective function includes a performance evaluation term and a size penalty term. The performance evaluation term is used to calculate the performance index of the candidate composite tooth profile under the premise of considering the filtering effect of the helix angle on the flow pulsation. The size penalty term is used to apply a penalty when the tooth tip circle diameter of the candidate composite tooth profile is greater than the maximum allowable tooth tip circle diameter determined by the pump casing.

[0020] If not, proceed to step S130, calculate the objective function value corresponding to the candidate parameter combination through the second objective function. The second objective function includes a geometric penalty term and a size penalty term. The geometric penalty term is used to apply a penalty when the candidate compound tooth profile fails to close geometrically effectively.

[0021] Specifically, based on the judgment result of the tooth profile closure verification mechanism, the subsequent calculation of the objective function value will adopt different paths. If the judgment result is "yes," meaning that the current candidate parameter combination can generate a geometrically effective closed candidate composite tooth profile, the system will activate the first objective function to calculate its corresponding objective function value. This first objective function is a comprehensive evaluation system, which not only includes performance evaluation items for evaluating the working performance of the gear pump, but also a key size penalty item. The ingenuity of the performance evaluation items lies in their full consideration of the natural filtering effect of the helix angle of the helical gear on the pulsation when evaluating flow pulsation, making the performance evaluation results closer to the actual physical working conditions of the gear pump and solving the problem of performance model distortion in the background technology. At the same time, the size penalty item is designed to solve the problem of size pseudo-optimization. It monitors the addendum circle diameter of the gear generated by the current parameters. Once this diameter exceeds the maximum allowable addendum circle diameter determined by the actual internal cavity size of the pump housing, the penalty item will be activated, imposing a significant penalty on the objective function, thereby preventing the optimization process from evolving in the direction of unreasonable size increase.

[0022] Conversely, if the tooth closure verification mechanism determines "no," meaning the current candidate parameter combination cannot generate a geometrically valid closed tooth profile, the system will use a second objective function to calculate its objective function value. It no longer calculates complex performance metrics, because discussing performance is meaningless for a geometrically invalid gear. Instead, it primarily consists of a geometric penalty term and the aforementioned dimensional penalty term. The geometric penalty term calculates a continuous penalty value based on the geometric deviation information provided by the tooth closure verification mechanism. This penalty value acts like a gradient, telling the optimization engine the specific problem with the current invalid solution and in which direction the parameters should be modified to make it feasible (i.e., return to the geometrically valid region). This mechanism avoids simply discarding invalid solutions but uses the information it provides to guide the search, greatly enhancing the robustness of this embodiment under complex constraints.

[0023] Finally, the optimization engine adjusts its internal state based on the received objective function value (for example, updating the velocity and position of particles in the particle swarm optimization algorithm), and starts a new round of iterations until the preset convergence conditions are met, ultimately outputting an optimal combination of parameters that satisfies all physical constraints.

[0024] In this embodiment, the target variables include normal module, normal pressure angle, and tooth width. Normal module is a fundamental parameter determining gear size and strength; normal pressure angle primarily affects tooth profile shape, contact ratio, and load-bearing capacity; tooth width directly relates to the gear's axial contact length and displacement. Using these three parameters as optimization targets allows the optimization process to directly impact the core of gear design, enabling a more effective trade-off between geometric constraints and performance indicators.

[0025] It should be noted that before optimization begins, an effective search space for the normal module, normal pressure angle, and tooth width can be given, thereby improving optimization efficiency.

[0026] In this embodiment, the tooth profile closure verification mechanism specifically includes: for any theoretically sequentially connected first arc segment, involute segment, and second arc segment on the candidate compound tooth profile, based on the candidate parameter combination and by solving the arc equation, the endpoint of the first arc segment and the starting point of the second arc segment are determined. The endpoint of the first arc segment and the starting point of the second arc segment are respectively used as the boundary approximation targets of the involute segment. The starting roll angle and the ending roll angle of the involute segment are solved by a nonlinear equation solving algorithm. If the solution error of the endpoint of the first arc segment and the starting point of the second arc segment are both less than the threshold, and the starting roll angle of the involute segment is greater than the ending roll angle and the two satisfy the preset directional relationship, it is determined that the candidate compound tooth profile can be geometrically effectively closed; otherwise, it is determined that the candidate compound tooth profile has failed to be geometrically effectively closed.

[0027] This verification method, based on underlying geometric analysis and nonlinear solutions, has higher accuracy and reliability compared to traditional judgments based on empirical rules, fundamentally guaranteeing the physical feasibility of the optimization results.

[0028] The following example illustrates the specific calculation process of the tooth-shaped closure verification mechanism.

[0029] Obtain the fixed parameters of the gear pump to be designed, including the number of teeth. z helix angle Rated angular velocity and the maximum permissible installation dimensions of the pump body; wherein the maximum installation dimensions are defined by the maximum permissible tooth tip circle diameter. Da_max This means that the size is directly limited by the radial dimension of the inner cavity of the gear pump housing to ensure that the gear rotor can be smoothly installed into the pump body and form an effective radial sealing gap with the inner wall of the housing.

[0030] normal modulus m n Normal pressure angle and tooth width B Set them as optimization variables and give them their respective search intervals.

[0031] Reference Figure 7 Then, a geometric analytical model of the circular arc-involute composite tooth profile is established.

[0032] Based on normal modulus m n and normal pressure angle A composite tooth profile end face projection geometric model was constructed, and key geometric parameters such as pitch circle radius, base circle radius, tooth tip arc radius, and tooth tip circle radius were obtained.

[0033] Pitch circle radius R for: ; base circle radius R b for: ; Tooth tip radius r for: ; Tooth tip circle radius r a for: ; Establish the parametric equations for the circular arc segment AB: ; in, u α The angle parameter variable is the tooth tip arc AB, and its value range is 0 ≤ u α ≤ u b (rad) u b Let be the angle value at point B.

[0034] Establish the parametric equations for the involute segment BC: ; in, The roll angle of the involute. The phase angle of the involute. .

[0035] Establish the parametric equations for the circular arc segment CD: ; in, u n The angle parameter variable is the tooth root arc CD, and its value range is 0 ≤ u n ≤ u c (rad) u c Let be the angle value at point C.

[0036] Secondly, a tooth profile closure verification mechanism based on nonlinear residual solution is constructed.

[0037] Let B be the endpoint of arc AB, and its coordinates be... The coordinates are derived from the parametric equation of the circular arc segment AB; the starting point of the circular arc CD is C, and its coordinates are... The equations are derived from the parametric equations of the circular arc segment CD. The endpoint B and the starting point C are taken as the boundary approximation targets of the involute segment, and the roll angle of the involute starting point approaching point B is solved using a nonlinear equation solving algorithm. and the final roll angle approaching point C .

[0038] Define E B To find the residual L2 norm (solution error) of the system of equations at point B, E C To find the residual L2 norm of the system of equations at point C, we need to find the solution error if it satisfies E. B <10 -3 And E C <10 -3 And strictly meet > (When the involute curve is generated from the tooth tip to the tooth root and does not self-cross,) and the roll angle satisfies the preset directional relationship, the candidate parameter combination is judged as "geometrically valid closure". For candidate parameter combinations that do not meet the geometric closure conditions, they are marked as geometrically invalid parameter combinations, and the corresponding residual index is output for use in the construction of subsequent penalty terms.

[0039] Accordingly, in this embodiment, the penalty applied by the geometric penalty term is calculated based on the solution error of the end point of the first arc segment and the starting point of the second arc segment (for example, the residual L2 norm in the above example) and the roll angle error (for example, the deviation between the roll angle and the preset direction in the above example).

[0040] When the tooth closure verification fails, the system does not simply return a fixed high penalty value. Instead, it utilizes the byproducts of the verification process—the solution error and the roll angle error. Specifically, the magnitude of the geometric penalty term is calculated comprehensively based on the solution errors at the endpoints of the first and second arc segments, as well as the deviation of the calculated roll angle from the preset direction. For example, the larger the solution error, or the more severe the reverse roll angle, the higher the calculated geometric penalty value. The technical advantage of this design is that it constructs a continuous, differentiable penalty "terrain" for the originally discrete "valid / invalid" binary judgment. The optimization algorithm can descend along the gradient of this "terrain," thus being smoothly guided out of the geometrically infeasible region, rather than oscillating repeatedly at the feasible region boundary, greatly enhancing the algorithm's self-healing ability and convergence efficiency.

[0041] In this embodiment, the performance evaluation term is used to characterize the synergistic relationship between average flow rate and flow pulsation. An attenuation term related to axial overlap is introduced into the calculation of flow pulsation to characterize the filtering effect of the helix angle on flow pulsation.

[0042] Specifically, the axial overlap is calculated based on the helix angle and tooth width in the candidate parameter combination. In the formula for calculating the flow pulsation coefficient, for example, it can be expressed as (1+ This is inversely proportional. Thus, when the helix angle or tooth width increases, leading to increased axial overlap... When this attenuation term is added, the calculated flow pulsation coefficient decreases accordingly, which perfectly matches the physical fact that helical gears can smooth transmission and suppress pulsation. By introducing this attenuation term, the performance evaluation model can more realistically reflect the synergistic effect of gear parameters on the two mutually constraining performance indicators of average flow rate and flow pulsation, thus enabling the optimization result to achieve a true, rather than a "pseudo" optimal balance under model distortion.

[0043] For example, axial overlap The calculation formula is: ; in, B , m n and These are tooth width, normal module, and helix angle, respectively.

[0044] Average flow Q and corrected flow pulsation The calculation is as follows: ; .

[0045] denominator This reflects the pulsation attenuation filtering effect brought about by the spiral interlacing. This indicates the rate of change of the rotation angle, i.e., the rotational angular velocity.

[0046] In this embodiment, when the addendum circle diameter of the candidate composite tooth profile is greater than the maximum permissible addendum circle diameter, the penalty applied by the size penalty term is positively correlated with the difference between the addendum circle diameter of the candidate composite tooth profile and the maximum permissible addendum circle diameter. For example, it can be designed to be proportional to the square of the difference; the larger the difference, the more exponentially the penalty value increases. This non-linear penalty mechanism is like forming a region outside the maximum permissible size boundary where the penalty value increases sharply. This effectively restricts the optimization search process within the physically permissible assembly space, ensuring that the final optimization result does not sacrifice assembly feasibility in pursuit of performance.

[0047] In this embodiment, the collaborative optimization method for the composite gear pump constrained by installation dimensions further includes, before iterative optimization using an optimization algorithm: performing a discrete pre-scan on the space of the target variable to find at least one set of initial values ​​for candidate parameter combinations that satisfy the target conditions; the target conditions include that the candidate composite gear profile can be geometrically effectively closed and that the addendum circle diameter of the candidate composite gear profile is less than the maximum allowable addendum circle diameter; and injecting the initial values ​​of the candidate parameter combinations into the initial population of the optimization algorithm.

[0048] This step involves performing a discrete pre-scan of the target variable space to find at least one set of initial values ​​for candidate parameter combinations that satisfy the target conditions, i.e., "feasible initial seeds." The target conditions are twofold: first, the candidate composite tooth profile generated by the parameter combination must be geometrically effective; second, the addendum circle diameter of the tooth profile must be less than or equal to the maximum permissible addendum circle diameter. After finding one or more such "safe" initial values, they are injected into the initial population of the optimization algorithm. The technical effect of this step is extremely significant, especially when dealing with optimization problems such as gear pumps with few teeth, where the feasible region itself is very narrow and demanding. Traditional random initialization populations are likely to fall entirely into infeasible regions, causing the algorithm to get stuck from the start and fail to converge. By injecting feasible initial seeds, the optimization algorithm is provided with one or more high-quality starting points, enabling it to explore promising regions from the beginning, thereby greatly improving the algorithm's convergence probability and global optimization ability.

[0049] The collaborative optimization framework in this embodiment has good versatility and can be combined with a variety of mainstream intelligent optimization algorithms. For example, the optimization algorithm can be any of the following: Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Differential Evolution (DE), or other advanced swarm intelligence optimization algorithms. These algorithms each have their own search characteristics, but they can all work efficiently within the optimization framework constructed in this embodiment, which includes a self-healing mechanism and an accurate physical model, to find the optimal solution that satisfies all constraints.

[0050] Finally, after optimization, the optimal parameter combination is extracted and substituted into the composite tooth profile analytical model to generate two-dimensional point cloud coordinates; the point cloud can be further used to generate CAD three-dimensional solid models or CNC machining code.

[0051] Reference Figure 2 The following calculation example will provide a more detailed explanation of the collaborative optimization method for the composite gear pump with installation size constraints in this embodiment.

[0052] Set the basic parameter to the number of teeth. z =7, Helix Angle β =31.828°, rated angular velocity ω =100rad / s, and set the maximum permissible addendum circle diameter to . Da_max =40.0mm. Normal module m n Normal pressure angle α and tooth width B Let be the variable to be optimized, where m n ∈[3.0,4.5]、 α ∈[18°,30°]、 B ∈[15mm,35mm].

[0053] The system performs a discrete pre-scan of the variable space, conducting a full-domain discrete mesh probing within a given variable interval using a minimal step size. Parameters are extracted from the mesh nodes, and a nonlinear equation solver is invoked to approximate the coordinates of the connection point B (end of the arc / start of the involute) and connection point C (end of the involute / start of the tooth root arc). Only when the following three criteria are simultaneously satisfied can this set of parameters be upgraded to a "safety baseline seed" capable of constructing a complete tooth profile that meets the requirements: 1. The residual L2 norm of the approximation equations for points B and C must satisfy high-precision convergence, i.e., E B <10 -3 And E C <10 -3 .

[0054] 2. The determination of the topology generation direction must be strictly true, that is, the roll angle of the involute generation must evolve sequentially from the outside to the inside. > ).

[0055] 3. The theoretical outer diameter calculated from this set of parameters Da It must be absolutely less than or equal to the upper limit of the installation size. Da_max (40.0mm).

[0056] A failure prevention initialization mechanism is implemented by obtaining geometrically valid initial solutions through pre-scanning and injecting them into the initial population. This verifies the geometric closure of each connection boundary point of the composite tooth profile and simultaneously determines whether the current parameters meet the requirements. Da ≤ Da_max After high-density scanning and depth filtering, the system captured a perfect initial security baseline seed and used it as input for initial parameters. Initial parameters, m n0 =3.85mm α 0 = 22.733° B 0 = 23.0 mm.

[0057] In calculating average flow Q At that time, a fluid dynamics dead zone compensation coefficient is introduced. K Because the basic static geometric formula fails to fully cover the increased fluid storage volume at the root arc of a composite tooth profile with a small number of teeth, and does not account for the fluid entrainment effect at the tooth tip clearance during high-speed rotation, the theoretical calculation value is underestimated. This compensation coefficient... K This is used to correct the static geometric sweep volume to the actual fluid dynamic displacement, and its value is preferably in the range of 1.10 ≤ K ≤1.25. In this example ( z =7), verified by three-dimensional flow field dynamics (CFD) calibration, compensation coefficient K The preferred setting is 1.15.

[0058] Therefore, at a given rotational angular velocity Introducing tooth width under working conditions B After that, average flow Q and corrected flow pulsation The calculation is as follows: ; ; Among them, the denominator This reflects the pulsation attenuation filtering effect brought about by the spiral interlacing.

[0059] Substitute the base data into the settings to calculate the average flow rate before optimization. Q 0 = 19.41 L / min and the flow pulsation before optimization =2.204%.

[0060] Then, this feasible initial parameter m n0 =3.85mm α 0 = 22.733° B 0 = 23.0 mm, the initial population of the optimization algorithm is injected. A shape constraint mechanism is constructed by installing size over-limit penalties, and a self-healing optimization mechanism is used to guide infeasible solutions back to the feasible region through continuous penalties. The objective function Score is constructed as follows: 1. Geometric penalty term for maximum tooth tip circle diameter constraint : Whenever the optimization operator generates new parameters, the system immediately calculates the current addendum circle diameter. .

[0061] Calculate the current tip circle diameter .like This triggers a quadratic volume penalty, guiding the particle back to the safe zone. .

[0062] 2. Residual-based continuous penalty guidance mechanism : A self-healing optimization mechanism guides infeasible solutions back to the feasible region through continuous penalty. When randomly generated parameters (normal modulus, pressure angle, etc.) cause the arc segment and the involute segment to not be smoothly tangent, the underlying nonlinear solver will report an error or fail to converge. For invalid particles that fail the above geometric closure criterion (i.e., breakage or self-intersection occurs), the residual information of the equation system exposed when the solution fails is extracted, and a continuous penalty gradient is constructed: the solution error E is extracted. B E C In addition to the rolling angle difference value, the continuous penalty value is calculated to provide gradient guidance for the algorithm to slide into the feasible region: ; Among them, cross-penalty exist Triggered by time, the calculation formula is: ;otherwise .

[0063] 3. Fluid synthesis objective function considering spiral filter correction Score : ; in, Constitutes the first objective function. This constitutes the second objective function.

[0064] A set of interference-free initial parameters is found by pre-scanning the entire radar grid and injected as a seed into the initial population of PSO. The optimization is carried out iteratively with the goal of minimizing the objective function value Score.

[0065] When the candidate parameter combination satisfies the nonlinear closure criterion of the composite tooth profile (i.e., the solution of the nonlinear equations converges and there is no cross interference of the roll angle), the equation calculation that satisfies geometric closure is performed.

[0066] When the candidate parameter combination fails to pass the nonlinear geometric closure criterion (i.e., topological breakage or cross interference occurs), the equation that satisfies the geometric closure invalidity is calculated.

[0067] The system ceases calculations of fluid dynamics performance indices and instead constructs a continuous geometric penalty term based on the nonlinear analytical approximation residuals and roll angle deviations. This penalty term transforms the discrete Boolean decision states of the infeasible region into an evaluation space with continuous mathematical gradients; the greater the error of the candidate parameter deviating from the closure condition, the higher the output value of this penalty term. The optimization algorithm utilizes this continuous gradient information to guide the parameters in the geometrically ineffective region to evolve in a direction that reduces geometric approximation errors until they revert to the geometrically closure feasible region. The purpose of retaining the geometric penalty term in this calculation formula is to limit the candidate parameter from deviating from the maximum installation size boundary due to excessively increasing the normal modulus during the iterative evolution towards the geometrically effective region.

[0068] After multiple iterations, the optimal parameter combination is obtained. In this computational example, the optimal parameter combination is: m nopt =3.83mm α opt =18.00° B opt =35.0mm. Finally, the optimal parameters are substituted into the composite tooth profile geometric model, outputting a discrete point cloud coordinate array, and a two-dimensional end face view is generated based on this (refer to...). Figure 3 ) or 3D solid model (refer to) Figure 4 This is used in the subsequent manufacturing of the gear pump rotor, which is ultimately assembled into a pump casing with limited dimensional constraints (see reference). Figure 5 and Figure 6 This constitutes a complete composite gear pump with both high specific displacement and low flow pulsation.

[0069] In one exemplary embodiment, a computer device is also provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0070] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0071] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0072] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0073] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0074] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0075] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0076] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A collaborative optimization method for a composite gear pump with installation size constraints, characterized in that, An optimization algorithm is used to iteratively optimize the target variables of the gear pump with the goal of minimizing the objective function value. During the iteration process, the following steps are performed for each candidate parameter combination consisting of the target variable: The tooth profile closure verification mechanism is used to determine whether the candidate composite tooth profile generated by the combination of the candidate parameters can be geometrically and effectively closed. If so, the objective function value corresponding to the candidate parameter combination is calculated through the first objective function. The first objective function includes a performance evaluation term and a size penalty term. The performance evaluation term is used to calculate the performance index of the candidate composite tooth profile under the premise of considering the filtering effect of the helix angle on the flow pulsation. The size penalty term is used to apply a penalty when the tooth tip circle diameter of the candidate composite tooth profile is greater than the maximum allowable tooth tip circle diameter determined by the pump casing. If not, the objective function value corresponding to the candidate parameter combination is calculated by the second objective function, which includes a geometric penalty term and a size penalty term. The geometric penalty term is used to apply a penalty when the candidate compound tooth profile fails to close geometrically effectively.

2. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, The target variables include normal module, normal pressure angle, and tooth width.

3. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, The tooth-shaped closure verification mechanism includes: For any theoretically sequentially connected first arc segment, involute segment, and second arc segment on the candidate composite tooth profile, based on the candidate parameter combination and by solving the arc equation, the endpoint of the first arc segment and the starting point of the second arc segment are determined. The endpoint of the first arc segment and the starting point of the second arc segment are respectively taken as the boundary approximation targets of the involute segment. The starting roll angle and the ending roll angle of the involute segment are determined by a nonlinear equation solving algorithm. If the solution errors of the endpoint of the first arc segment and the starting point of the second arc segment are both less than the threshold, and the starting roll angle of the involute segment is greater than the ending roll angle and the two satisfy the preset directional relationship, it is determined that the candidate compound tooth profile can be geometrically effectively closed; otherwise, it is determined that the candidate compound tooth profile has failed to be geometrically effectively closed.

4. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, The performance evaluation term is used to characterize the synergistic relationship between the average flow rate and the flow pulsation. An attenuation term related to the axial overlap is introduced into the calculation of the flow pulsation to characterize the filtering effect of the helix angle on the flow pulsation.

5. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, When the tip circle diameter of the candidate composite tooth profile is greater than the maximum allowable tip circle diameter, the penalty applied by the size penalty term is positively correlated with the difference between the tip circle diameter of the candidate composite tooth profile and the maximum allowable tip circle diameter.

6. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 3, characterized in that, The penalty imposed by the geometric penalty term is calculated based on the solution error of the end point of the first arc segment and the starting point of the second arc segment, as well as the roll angle error.

7. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, Before performing iterative optimization using the aforementioned optimization algorithm, the following steps are also included: A discrete pre-scan is performed on the space of the target variable to find at least one set of initial values ​​for the candidate parameter combinations that satisfy the target conditions; the target conditions include that the candidate compound tooth profile can be geometrically effectively closed and that the addendum circle diameter of the candidate compound tooth profile is less than the maximum allowable addendum circle diameter. The initial values ​​of the candidate parameter combinations are injected into the initial population of the optimization algorithm.

8. The method for collaborative optimization of a composite gear pump constrained by installation dimensions according to claim 1, characterized in that, The optimization algorithm is one of particle swarm optimization, genetic algorithm, or differential evolution algorithm.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the co-optimization method for a composite gear pump with installation dimensions constrained according to any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the collaborative optimization method for composite gear pumps with installation size constraints as described in any one of claims 1-8.

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