A method, system and device for multi-objective collaborative optimization of rotating equipment

Abstract

The application discloses a kind of rotating equipment multi-objective collaborative optimization method, system and device, belong to equipment parameter optimization technical field.The steps of the method include: establishing parameterized geometric model;Establish finite element analysis model;With minimizing the overall quality, maximizing structural strength safety margin, minimizing structural deformation, minimizing resonance risk as target to build multi-objective optimization function;And with strength constraint, stiffness constraint, resonance avoidance constraint and geometric process constraint as constraint condition, establish multi-objective optimization mathematical model;Execute multi-objective optimization optimization;The optimal design scheme obtained by optimization is verified.The present application includes four core performance indicators of spindle and rack strength, anti-resonance, stiffness, lightweight into unified optimization framework, avoids the problem of losing one thing to gain another caused by single performance optimization in traditional design by combining parameterized design and optimization algorithm;And experimental design and proxy model are used to reduce simulation calculation amount and improve design efficiency.

Description

Technical Field

[0001] This invention relates to the field of equipment parameter optimization technology, and particularly to a multi-objective collaborative optimization method, system, and device for rotating equipment. Specifically, it relates to a multi-objective collaborative optimization method, system, and device for mixers that simultaneously considers spindle frame strength, resonance avoidance, and structural lightweighting. Background Technology

[0002] Pharmaceutical mixers are core equipment in the pharmaceutical industry for mixing powder and granular materials, and their structural performance directly determines the mixing accuracy and operational stability. Traditional pharmaceutical mixer designs have the following shortcomings:

[0003] When considering strength, vibration, or lightweighting in isolation, multiple performance indicators cannot be balanced in a coordinated manner.

[0004] The selection of key parameters for the spindle and frame based on experience makes it difficult to achieve the optimal balance between lightweight design and structural safety.

[0005] Poor matching between motor excitation and the structure's natural frequency leads to a high risk of resonance.

[0006] Most problems are discovered after the machine is assembled, resulting in high rework costs and low efficiency.

[0007] To address the aforementioned issues, this invention provides a collaborative optimization method, system, and device that unifies spindle frame strength, anti-resonance, and lightweighting, achieving optimal balance of multiple performance indicators during the design phase. Summary of the Invention

[0008] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a multi-objective collaborative optimization method, system, and device for rotating equipment.

[0009] Technical solution: In a first aspect, the present invention provides a multi-objective collaborative optimization method for rotating equipment, comprising the following steps:

[0010] Establish a parametric geometric model;

[0011] Establish a finite element analysis model;

[0012] A multi-objective optimization function is constructed with the objectives of minimizing the overall mass, maximizing the structural strength safety margin, minimizing the structural deformation, and minimizing the resonance risk; and a multi-objective optimization mathematical model is established with strength constraints, stiffness constraints, resonance avoidance constraints, and geometric and technological constraints as constraints.

[0013] Construct a proxy model and perform multi-objective optimization.

[0014] The optimal design scheme obtained through optimization is verified.

[0015] Rotary equipment refers to mechanical equipment that uses rotational motion as its core working mode to complete processes such as material mixing, crushing, granulation, tableting, separation, drying, and filling. Its working principle relies on rotating components such as turntables, drums, rotors, or turntables driven by motors. Changes in the physical state or displacement of materials are achieved through centrifugal force, shear force, extrusion force, or the gravitational drop caused by the material tumbling in the container. In the pharmaceutical industry, rotary equipment typically includes pharmaceutical mixers, rotary tablet presses, and tubular or disc centrifuges.

[0016] Taking a pharmaceutical mixer as an example, this paper illustrates the multi-objective collaborative optimization method described in the first aspect. This method first establishes a parametric geometric model of the pharmaceutical mixer, identifying and setting design variables. Then, it establishes a finite element model of the pharmaceutical mixer, assigning or assigning material properties, meshing, applying loads and boundary conditions, and conducting multi-condition collaborative calculations of static strength, modal dynamics, and transient dynamics to obtain an initial calculation dataset. Next, it constructs multi-objective optimization functions for spindle frame strength, anti-resonance, and lightweighting, setting strength constraints, stiffness constraints, resonance avoidance constraints, and geometric process constraints. Using a design-of-experiments method, it creates design variable sample points based on the design variable range. Geometric process constraints refer to the fact that the values ​​of each design variable are within a preset processing range, satisfying assembly and manufacturing process requirements, while there are no constraints on quality; the only objective is to minimize the overall machine mass. Then, based on the sample calculation results, a response surface surrogate model is constructed, and a multi-objective optimization algorithm is used for iterative optimization to generate a Pareto optimal solution set. Finally, the optimal design scheme is comprehensively verified for spindle frame strength, anti-resonance, and transient response. After satisfying all constraints, the optimal design parameter combination is output.

[0017] Optionally, the strength objective function is to minimize stress utilization, as shown in the formula:

[0018] ;

[0019] In the formula, f is the stress utilization rate; The maximum equivalent stress of the main shaft under load; The yield strength of the main shaft material; The overall safety factor is determined according to the FKM guidelines.

[0020] Optionally, the anti-resonance objective function is to maximize the distance between the first six natural frequencies of the structure and the operating frequency of the motor, and the resonance avoidance constraint is to avoid the resonance interval at each frequency. The preset resonance interval is... It can also be adjusted according to the working conditions, among which For each frequency obtained from the calculation, for example, to calculate the 6th order, the corresponding i = 1~6; Here, it refers to the operating frequency of the motor.

[0021] Optionally, the lightweight objective function is to minimize the total frame mass M; the weight reduction ratio is used as the objective function: (M0-M) / M0, where M0 is the overall machine mass under the initial design parameters.

[0022] Optionally, the stiffness requirement stipulates that the dynamic deformation of the structure under the most extreme working conditions shall not exceed the preset allowable value.

[0023] Optionally, the step of establishing the parametric geometric model includes:

[0024] Construct a parametric geometric model for rotating equipment;

[0025] By selecting optimized design variables, the parametric geometric model can be fully parameterized and adjustable.

[0026] Optionally, the optimized design variables include the spindle opening diameter, the width of the bottom support feet of the frame, the hopper installation height, and the frame thickness. These design variables are generally parameters of key components. In this design, the shaft bears torque and is a critical rotating component; therefore, the shaft opening diameter is an important parameter. The hopper has a large mass after loading, and its installation height affects the overall frame's center of gravity. The center of gravity height and the bottom support width have a significant impact on the overall structural stability under dynamic conditions. The frame thickness primarily affects the overall structural strength and rigidity.

[0027] Optionally, the step of establishing the finite element analysis model includes:

[0028] A finite element analysis model is constructed based on a parametric geometric model to complete the assignment of structural material properties, mesh generation, and boundary condition application.

[0029] Perform multi-condition collaborative calculations to obtain an initial calculation dataset; the multi-condition collaborative calculations include static strength analysis, modal analysis and transient dynamic analysis.

[0030] Optionally, the step of performing multi-objective optimization includes:

[0031] Based on the value range of the optimization design variables, sample points are selected within the global design space;

[0032] The performance response data corresponding to each sample point is obtained. After the sample points are obtained, the results corresponding to each sample point are obtained through simulation calculation. The results in this scheme are stress value, deformation amount, frequency, etc., which are the performance response data. The sample database required for optimization is constructed through these performance response data.

[0033] A proxy model is built based on a sample database to replace direct finite element simulation;

[0034] Perform global iterative optimization to generate the optimal solution set, and then select the optimal design scheme that satisfies all constraints.

[0035] Optionally, the steps for constructing the proxy model based on the sample database are as follows:

[0036] Establish a nonlinear mapping relationship between the objective function and design variables to generate an initial response surface model:

[0037] ;

[0038] In the formula, y is the objective function of the response; Let i be the i-th design variable; For the constant term of the model; For the i-th design variable, this is a one-time coefficient; Let be the coefficient of the quadratic term of the i-th design variable; The coefficient of the interaction term between the i-th and j-th design variables; Let j be the j-th design variable, where j > i; The residual between the actual value and the approximate value;

[0039] Solving the model coefficients , , , This establishes an approximate mapping relationship between design variables and the objective function;

[0040] Through the coefficient of determination To evaluate the accuracy of the model, when When the preset accuracy requirements are met, the response surface model is considered reliable and can be used to replace finite element simulation.

[0041] In the optimization phase, the response surface model is embedded in the iterative process. New combinations of design variables are generated in each generation of the population. The response surface model quickly predicts the performance indicators and individuals are screened, cross-crossed, and mutated according to the objective function and constraints. Through multiple generations of iterative evolution, a Pareto front solution set that meets the requirements of strength, stiffness, resonance avoidance, and lightweighting is finally obtained.

[0042] Optionally, the verification of the optimal design scheme obtained through optimization includes strength verification, resonance avoidance verification, stiffness verification, and lightweight verification.

[0043] Secondly, the present invention provides a multi-objective collaborative optimization system for rotating equipment, comprising:

[0044] The basic model building module is configured to build parametric geometric models and finite element analysis models.

[0045] The optimization model building module is configured to build a multi-objective optimization mathematical model. The multi-objective optimization mathematical model constructs a multi-objective optimization function with the objectives of minimizing the overall mass, maximizing the structural strength, and minimizing the resonance risk, and uses strength, stiffness, resonance avoidance, and geometric process as constraints.

[0046] The proxy model building module is configured to build proxy models and perform multi-objective optimization.

[0047] as well as,

[0048] The verification module is configured to verify the optimal design solution.

[0049] The output of the proxy model establishment module is connected to the input of the verification module, and is used to send the optimal design scheme obtained by optimization to the verification module.

[0050] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described in the first aspect.

[0051] Fourthly, a computer device according to the present invention includes a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform the steps of the method described in the first aspect.

[0052] Fifthly, the present invention provides a rotating device, wherein the combination of design parameters of the rotating device is determined by the method described in the first aspect.

[0053] Beneficial effects:

[0054] The significant advantages of this invention compared to existing technologies are:

[0055] This invention incorporates four core performance indicators—spindle and frame strength, resonance prevention, stiffness, and lightweighting—into a unified optimization framework. By combining parametric design with optimization algorithms, it avoids the problem of sacrificing one aspect for another caused by single-performance optimization in traditional design. It adopts experimental design and surrogate models to reduce simulation computation, significantly shorten the design cycle, and improve design efficiency. The optimized structure effectively avoids resonance risks while meeting strength and stiffness requirements, achieving lightweight design. It can be widely applied to the structural optimization design of various rotating pharmaceutical equipment. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the steps of the multi-objective collaborative optimization method of the present invention;

[0057] Figure 2 This is a schematic diagram of the overall process of the multi-objective collaborative optimization method of the present invention;

[0058] Figure 3 This is a schematic diagram of the parametric geometric model of the pharmaceutical mixer of the present invention.

[0059] Figure 4 This is a schematic diagram of the multi-objective optimization iterative process of the present invention;

[0060] Figure 5 This is a schematic diagram of the Pareto front for equivalent stress optimization of the pharmaceutical mixer spindle of the present invention;

[0061] Figure 6 This is a schematic diagram of the Pareto front for equivalent stress optimization of the pharmaceutical mixer frame of the present invention;

[0062] Figure 7 This is a schematic diagram of the composition structure of the multi-objective collaborative optimization system for rotating equipment according to the present invention;

[0063] Figure 8 This is a schematic diagram of the internal structure of the computer device of the present invention.

[0064] The meanings of the various reference numerals in the attached figures are as follows:

[0065] 1. Main shaft; 2. Mixing container; 3. Bottom support surface of the frame; 4. Frame; 5. Drive motor; 6. Motor bearing housing. Detailed Implementation

[0066] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the embodiments of the present invention, and not all structures.

[0067] In the following description, specific details such as target system architecture and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0068] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0069] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0070] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0071] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0072] Figure 1 The diagram illustrates the specific steps of a multi-objective collaborative optimization method, which is used to determine the optimal combination of design parameters for rotating equipment. Figure 2 The overall flow of the method is shown. Figure 4 A flowchart of the multi-objective optimization iteration is shown. See also... Figure 1 The steps of the multi-objective collaborative optimization method include:

[0073] S100. Establish a parametric geometric model;

[0074] A parametric geometric model of rotating equipment is constructed. Based on the structural mechanics characteristics and dynamic response laws, key geometric and installation parameters that have a significant impact on shaft strength, frame stiffness, structural natural frequency and overall machine mass are selected as optimization design variables to achieve full parametric adjustability of the model.

[0075] S200. Establish a finite element analysis model;

[0076] A finite element analysis model is constructed based on a parametric geometric model, and the structural material properties are assigned, meshes are generated, and boundary conditions are applied. For the actual operating conditions of rotating equipment, multi-condition collaborative calculations of static strength analysis, modal analysis, and transient dynamic analysis are carried out to obtain initial calculation datasets such as structural stress, deformation, natural frequency, and dynamic response, providing basic data for subsequent optimization.

[0077] Among them, static strength analysis is carried out by establishing a linear elastic finite element model, applying bottom fixed constraints and rotational constraints, applying gravity, material load, motor excitation load and stirring reaction force, and solving the equivalent stress and deformation of the main shaft and frame; modal analysis is carried out by free mode solving to obtain the natural frequency and mode shape direction of the structure and to judge the resonance risk; transient dynamic analysis is carried out by applying time-domain braking load and excitation load to solve dynamic stress, overall displacement and motion response, and to complete the dynamic strength and stability verification.

[0078] S300: A multi-objective optimization function is constructed with the objectives of minimizing the overall mass, maximizing the structural strength safety margin, minimizing the structural deformation, and minimizing the resonance risk; and a multi-objective optimization mathematical model is established with strength constraints, stiffness constraints, resonance avoidance constraints, and geometric and process constraints as constraints.

[0079] Specifically, with structural strength assurance, resonance risk avoidance, minimization of deformation, and overall lightweighting as the core guiding principles, a multi-objective optimization function is constructed. Simultaneously, strength constraints, stiffness constraints, resonance avoidance constraints, and geometric and process constraints are set to form a complete multi-objective optimization mathematical model, ensuring that the optimization results meet the requirements of engineering use.

[0080] S400: Construct an agent model and perform multi-objective optimization.

[0081] Based on the value range of the optimized design variables, sample points are selected within the global design space using experimental design or space-filling sampling methods. Performance response data corresponding to each sample point is obtained through finite element numerical calculations, constructing a sample database required for optimization. Then, a high-precision surrogate model is built based on the sample database to replace time-consuming direct finite element simulation. A multi-objective optimization algorithm is used for global iterative optimization to generate a Pareto optimal solution set, from which the optimal design scheme that simultaneously satisfies all constraints is selected.

[0082] S500: Verify the optimal design scheme obtained through optimization.

[0083] The optimal design scheme is verified in four ways: strength check, resonance avoidance verification, stiffness, and lightweighting, to confirm that the scheme meets all design constraints. After the verification is passed, the optimal combination of design parameters and the corresponding structural performance indicators are output.

[0084] This invention overcomes the shortcomings of existing technologies through the above steps. Specifically, it determines the design variables of the parameters; obtains the initial dataset through multi-condition and multi-module calculations using finite element simulation; determines the overall structure's strength, stiffness, anti-resonance, and lightweight objectives and constraints; obtains initial sampling points through experimental design methods and obtains the corresponding sample set through finite element calculations; performs multi-objective algorithm optimization based on the response surface model to obtain the Pareto front solution set; verifies the optimal solution, achieving a balance between structural lightweighting and strength and stiffness, and effectively avoiding the resonance range, thereby improving the design efficiency of the equipment. It can be widely applied to the structural optimization of various rotating pharmaceutical equipment.

[0085] The Pareto front solution set is a set of non-dominated solutions that cannot be completely surpassed by any other solution, where each solution represents a trade-off between objective functions. Figure 5 and Figure 6 The Pareto front plots for optimizing the equivalent stress of the spindle and the frame of the pharmaceutical mixer are shown respectively.

[0086] The present invention will be described in detail below with reference to specific embodiments.

[0087] One embodiment uses a certain model of pharmaceutical mixer as an example, and employs the method of the present invention for collaborative optimization design. See [link to relevant documentation]. Figure 1 , Figure 2 and Figure 4 .in addition, Figure 3 The parametric geometric model of the pharmaceutical mixer is also shown, including the main shaft 1, mixing container 2, bottom support surface of the frame 3, frame 4, drive motor 5, motor bearing housing 6, and support components, etc. Figure 3 Taking the parametric geometric model shown as an example, the frame 4 is equipped with a support component, and the motor bearing seat 6 is installed on the support component. The main shaft 1 of the drive motor 5 passes through the motor bearing seat 6 and is fixed to the mixing container 2 through a flange. The bottom support surface 3 of the frame is used to support the frame 4.

[0088] In step S100, the model is preprocessed in the finite element software. The opening diameter d of the spindle 1, the width B of the bottom support surface 3 of the frame, the installation height H of the hopper, and the thickness T of the frame are set as optimization design variables, denoted as input parameters IP1, IP2, IP3, and IP4, respectively. The range of design variables is shown in Table 1.

[0089] Design variables symbol lower limit upper limit Spindle opening diameter (mm) d 6 15 Width of the bottom support legs of the frame (mm) B 5 30 Hopper installation height (mm) H 900 1100 Frame thickness (mm) T 2 6

[0090] Table 1

[0091] In step S200, parameters are set, and static, modal, and transient dynamic calculations are completed.

[0092] More specifically, the materials of each component are assigned in the material properties. For the main shaft 1, the material is 304 stainless steel with a Young's modulus of 200 GPa, Poisson's ratio of 0.3, and yield strength of 220 MPa. The material of the frame 4 is Q235B with a Young's modulus of 200 GPa, Poisson's ratio of 0.3, and yield strength of 235 MPa. The model structure is meshed. Shell elements are used for thin-walled structures such as the frame 4, while solid elements are used for solid structures such as the main shaft 1 and the mixing container 2. The mesh is refined for stress concentration areas such as shaft shoulders, keyways, and fillets to ensure computational accuracy and efficiency.

[0093] More specifically, in the statics calculation module, a bottom fixed constraint is applied, a rotating joint constraint is applied to the shaft, the bolts are connected, a preload is given, and a gravity load, a material load of 156 kg, and a motor load of 18 kg are applied. Under constant load, the equivalent stress of the main shaft 1 and the frame 4 is obtained.

[0094] More specifically, in the modal analysis, the bottom support surface 3 of the frame is fixed and constrained, the first six modal frequencies of the model are calculated, and the deformation trend and participation coefficient under different modes are observed.

[0095] More specifically, in the transient dynamics calculation, the bottom support surface 3 of the frame is fixedly constrained, the shaft is constrained by a rotating joint, the bolts are connected, a preload is given, and a gravity load, a material load of 156 kg, a motor load of 18 kg, a frame load of 10 kg are applied, and the acceleration during emergency braking is -3.14 rad / s2. The displacement of the frame under dynamic load is calculated.

[0096] In step S300, the objective function is set. The constraints of the objective function are very important. This embodiment is based on a multi-objective optimization framework and selects 10 objective functions such as stress value, deformation amount, and modal frequency to evaluate the strength, stiffness, and structural frequency of the overall structure and important components of the frame 4. On the basis of satisfying the strength constraint, stiffness constraint, and resonance constraint, the lightweight design of the overall mechanism is achieved.

[0097] In step S300, the objective function and constraints are set. The selection of the objective function and constraints directly determines whether the optimization direction is reasonable. Therefore, in this embodiment, based on the actual working requirements and structural safety requirements of the pharmaceutical mixer, starting from the four core requirements of "strength and safety, no resonance, small deformation, and light weight", 10 indicators are selected as the objective function, including principal shaft stress, frame stress, frame mass, first 6 modal frequencies, and dynamic deformation, comprehensively covering structural strength, operational stability, dynamic stiffness, and lightweight level.

[0098] Strength indicators are used to ensure that the spindle and frame do not suffer damage, cracking, or deformation failure under conditions such as stirring and braking; stiffness and dynamic deformation indicators are used to ensure that the equipment operates smoothly with minimal shaking and that mixing accuracy is not affected by excessive deformation; modal frequency indicators are used to determine whether the structure will resonate with the motor excitation frequency, thus avoiding severe vibration, excessive noise, or even damage to the equipment; lightweight indicators are used to reduce material usage, lower costs, and improve equipment energy efficiency while ensuring safety.

[0099] Based on this, this embodiment further sets constraints:

[0100] Strength constraints require that the stress on the spindle and frame does not exceed the allowable stress to ensure structural safety; stiffness constraints require that the dynamic deformation is within a reasonable range to ensure stable operation; resonance constraints require that the structure's natural frequency be far away from the motor's operating frequency to prevent resonance from occurring at the source; geometric and process constraints ensure that all optimized dimensions are machinable and assembleable.

[0101] By setting the above objectives and constraints in a coordinated manner, the design scheme with the lightest weight and the best overall performance can be automatically found under the hard requirements of "sufficient strength, sufficient stiffness, and no resonance", thus achieving a balance between safety and lightweighting.

[0102] See Figure 5 and Figure 6 It can be seen that there is a certain contradiction between structural strength and lightweighting. Increasing the amount of material can improve the structural strength, but this contradicts the goal of lightweighting.

[0103] Figure 5 This is a Pareto tradeoff diagram showing the relationship between frame mass and equivalent spindle stress. Figure 6 This is a Pareto trade-off diagram showing the relationship between frame mass and equivalent stress. As the diagram shows, as the frame mass decreases, the equivalent stress of the spindle and frame generally increases, indicating a clear negative correlation between mass and strength. This phenomenon reflects the inherent contradiction between structural strength and lightweighting goals: reducing structural dimensions and material usage to achieve lightweighting leads to a decrease in the structural load-bearing cross-section and an increase in stress levels; conversely, increasing material usage to reduce stress and improve strength safety margins leads to an increase in frame mass. This invention uses a multi-objective optimization algorithm to find the optimal balance between mass and strength while ensuring that the frame stress does not exceed allowable values, achieving lightweight design within a safe range.

[0104] Furthermore, the change in the overall mass of rack 4 will affect the modal frequencies of each order, necessitating a re-evaluation of resonance. Therefore, the overall optimization objective is set as follows:

[0105] The strength and stiffness meet the allowable requirements;

[0106] Avoid the resonance zone;

[0107] The overall mass is the smallest.

[0108] More specifically, the principal axis equivalent stress value of the static strength calculation result is denoted as objective function OP1, the equivalent stress value of the frame is denoted as objective function OP2, the frame mass is denoted as objective function OP3, the first 6 modal frequencies are denoted as objective functions OP4~OP9, and the overall displacement of the frame calculated in transient dynamics is denoted as objective function OP10.

[0109] More specifically, the constraints on the objective function for the intensity index are: ; The stiffness and mass objective function values ​​OP3 and OP10 are required to be minimized, and the values ​​for each frequency are required to be at least close to the frequency of the drive motor 5. maximum.

[0110] In step S400, the number of samples for design variables is created, and the objective function values ​​of each item under the sample scheme are obtained through numerical calculation.

[0111] More specifically, the Latin Hypercube Sampling Design method was used in the design of experiments to create 20 sample sizes, as shown in Table 2.

[0112] No. IP1 (mm) IP2 (mm) IP3 (mm) IP4 (mm) 1 9.38 9.38 1035 3.7 2 8.48 14.38 975 5.5 3 11.18 18.13 965 2.1 4 7.13 10.63 1025 3.1 5 14.78 11.88 935 4.7 6 8.93 20.63 915 4.5 7 12.53 19.38 905 5.7 8 11.63 25.63 1065 4.1 9 7.58 6.88 1095 5.1 10 13.43 13.12 1005 4.9 11 14.33 24.38 1055 2.9 12 12.08 21.88 1085 5.9 13 8.03 23.13 955 2.3 14 6.23 15.62 1015 4.3 15 13.88 5.63 995 2.5 16 10.73 29.38 1075 3.3 17 9.83 8.13 925 3.9 18 12.98 16.88 1045 2.7 19 6.68 28.13 945 3.5 20 10.27 26.88 985 5.3

[0113] Table 2

[0114] The numerical values ​​of 10 objective functions under 20 sample sizes were obtained through numerical calculation, as shown in Table 3. Each row contains the calculated values ​​of the 10 objective functions under a set of sample point schemes. A set of sample schemes includes: spindle 1 opening diameter IP1, frame bottom support surface 3 width IP2, hopper installation height IP3, and frame thickness IP4; the objective functions include: spindle equivalent stress value OP1, frame equivalent stress value OP2, overall structural mass OP3, first 6 modal frequencies OP4~OP9, and frame 4 deformation under dynamic load OP10.

[0115] No. OP1 (MPa) OP2 (MPa) OP3(t) OP4(Hz) OP5(Hz) OP6(Hz) OP7(Hz) OP8(Hz) OP9(Hz) OP10 (mm) 1 75.0 39.4 0.52 9.1 12.8 18.5 61.5 96.5 96.8 0.69 2 71.1 28.9 0.55 10.1 12.9 22.8 67.7 98.5 99.2 0.64 3 76.1 61.9 0.49 7.4 11.7 14.5 52.4 93.1 94.2 0.79 4 78.3 45.4 0.51 8.6 12.6 17.0 58.5 95.2 96.0 0.71 5 74.1 32.6 0.54 9.6 12.4 21.6 65.5 97.6 97.7 0.67 6 71.6 33.8 0.53 9.5 12.3 21.3 64.5 96.6 97.5 0.67 7 74.6 28.1 0.56 10.0 12.4 24.0 68.4 98.5 98.9 0.65 8 75.1 36.4 0.53 9.4 12.9 19.5 63.2 97.3 97.5 0.68 9 73.9 30.6 0.55 10.0 13.1 21.7 66.5 98.4 99.1 0.65 10 79.4 31.5 0.54 9.8 12.9 21.4 66.1 98.1 98.7 0.66 11 77.3 47.9 0.50 8.4 12.5 16.4 57.9 95.5 95.7 0.74 12 74.9 27.3 0.56 10.4 13.2 23.3 68.9 99.1 100.8 0.64 13 74.6 57.4 0.49 7.7 11.8 15.2 53.6 93.2 94.6 0.76 14 72.7 35.0 0.53 9.5 13.0 20.0 63.7 97.2 97.5 0.67 15 76.7 53.8 0.50 7.9 12.1 15.4 55.4 94.3 95.0 0.76 16 73.4 42.9 0.51 8.8 12.7 17.5 59.7 96.1 96.4 0.71 17 75.7 37.9 0.52 9.1 12.2 19.8 62.2 95.7 96.9 0.68 18 76.9 50.7 0.50 8.2 12.4 15.8 56.6 95.0 95.4 0.74 19 71.2 41.0 0.52 8.8 12.3 18.6 60.4 95.0 96.4 0.69 20 74.3 29.5 0.55 10.0 12.9 22.3 67.2 98.4 99.0 0.65

[0116] Table 3

[0117] Based on the results calculated from the above sample set, a response surface model is constructed, and an optimization is performed using a multi-objective genetic algorithm to generate a Pareto front solution set.

[0118] Among them, the response surface model is a surrogate model constructed through mathematical fitting methods (such as multinomial regression and Kriging interpolation) to approximate the nonlinear relationship between design variables and objective functions, replacing computationally expensive physical simulations;

[0119] A multi-objective genetic algorithm is a method that simulates the natural process of survival of the fittest, supporting the finding of the optimal equilibrium solution under multiple conflicting objectives.

[0120] The Pareto front solution set is a set of non-dominated solutions that cannot be completely surpassed by other solutions. Each solution represents a trade-off between objective functions (for example, sacrificing 5% structural strength to obtain 10% lightweight results).

[0121] Specifically, the response surface model is constructed using the parameters and objective function in the sample set, and the steps are as follows:

[0122] In this embodiment, a second-order polynomial regression model is used to construct the initial model. Specifically, a nonlinear mapping relationship between the objective function and the design variables is established using a quadratic polynomial to generate the initial response surface model. In this embodiment, the response surface model can be defined as:

[0123] ;

[0124] Where y is the objective function of the response; Let i be the i-th design variable; For the constant term of the model; For the i-th design variable, this is a one-time coefficient; Let be the coefficient of the quadratic term of the i-th design variable; The coefficient of the interaction term between the i-th and j-th design variables; Let j be the j-th design variable, where j > i; This represents the residual between the actual value and the approximate value.

[0125] The least squares method is used to fit the sample data, and the model coefficients are solved. , , , This establishes an approximate mapping relationship between design variables and the objective function;

[0126] Through the coefficient of determination To evaluate the accuracy of the model, when Meets the preset accuracy requirements (e.g.) When the value is ≥0.9, the response surface model is considered reliable and can be used to replace finite element simulation.

[0127] Based on the trained response surface model, the objective function value corresponding to any combination of design variables can be quickly predicted, avoiding the time-consuming finite element calculation for each new scheme.

[0128] During the optimization phase, the response surface model is embedded into the multi-objective genetic algorithm iterative process: the algorithm generates new combinations of design variables in each generation of the population, the response surface model quickly predicts its performance indicators, and individuals are screened, crossovered and mutated according to the objective function and constraints. Through multiple generations of iterative evolution, a Pareto front solution set that meets the requirements of strength, stiffness, resonance avoidance and lightweighting is finally obtained, providing a basis for subsequent optimization and verification.

[0129] In step S500, the calculation results are verified and the optimal calculation scheme is output.

[0130] The MOGA algorithm was used for 20 iterations, generating 800 sample points for each iteration, resulting in three sets of optimal sample solutions, as shown in Table 4. The first three rows of Table 4 contain the result values ​​under the three sets of optimal design variables, and the fourth row contains the objective function values ​​under the initial design variables.

[0131] No. Spindle opening diameter (mm) Width of the bottom support legs of the frame (mm) Hopper installation height (mm) Frame thickness (mm) Group 1 6.5 5.0 900 4.3 Group 2 6.9 5.0 1075 4.3 Group 3 6.9 5.0 1055 4.3 Initial Design 6.0 15.0 1000 6.0

[0132] Table 4

[0133] Table 5 shows the numerical comparison after optimization. The first three rows are the optimal solution set, and the fourth row is the initial values. Objective functions OP1 and OP2 are the strength values, both within the allowable range of 147MPa and 157MPa, respectively. Objective function 3 is the overall frame mass, both 0.53t, with 6th modal frequencies of OP4~OP9. All frequency values ​​avoid the resonance range [42.5Hz, 57.5Hz]. The deformation OP10 under the emergency stop transient condition is 0.66mm. In summary, the strength values ​​meet the standard requirements, avoid the resonance range, have small deformation, and the frame mass is reduced by 30kg compared to the initial design.

[0134] No. OP1 (MPa) OP2 (MPa) OP3(t) OP4(Hz) OP5(Hz) OP6(Hz) OP7(Hz) OP8(Hz) OP9(Hz) OP10 (mm) 1 73.5 29.8 0.53 9.2 12.7 19.3 64.0 96.7 97.1 0.66 2 74.7 32.6 0.53 9.3 13.0 19.5 64.1 96.8 97.2 0.66 3 74.8 32.9 0.53 9.2 12.7 19.3 64.0 96.7 97.2 0.66 4 73.6 26.9 0.56 10.3 13.1 23.6 69.0 98.9 100 0.63

[0135] Table 5

[0136] This embodiment verifies that the method of the present invention can effectively achieve lightweighting of the overall structure of the pharmaceutical mixer, while simultaneously meeting the synergistic goals of structural strength of the frame and main shaft, stability under emergency stop, and anti-resonance, thereby improving the design efficiency of the pharmaceutical mixer.

[0137] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0138] This invention employs a multi-objective collaborative optimization framework, for the first time integrating three core performance indicators—spindle strength, anti-resonance, and lightweighting—into a unified optimization framework. This avoids the problem of sacrificing some aspects for others in traditional design, achieving comprehensive optimization of structural parameters. The optimization strategy, combining parametric modeling and surrogate models, significantly reduces the number of finite element calculations, shortens the design cycle, and improves design efficiency. This method can be extended to the multi-objective collaborative optimization design of other rotating mechanical equipment, demonstrating its wide applicability.

[0139] In one embodiment, Figure 7 The structure of a multi-objective cooperative optimization system for rotating equipment is shown, including:

[0140] The basic model building module is configured to build parametric geometric models and finite element analysis models.

[0141] The optimization model building module is configured to build a multi-objective optimization mathematical model. The multi-objective optimization mathematical model constructs a multi-objective optimization function with the objectives of minimizing the overall mass, maximizing the structural strength, and minimizing the resonance risk, and uses strength, stiffness, resonance avoidance, and geometric process as constraints.

[0142] The proxy model building module is configured to build proxy models and perform multi-objective optimization.

[0143] as well as,

[0144] The verification module is configured to verify the optimal design solution.

[0145] The output of the proxy model establishment module is connected to the input of the verification module, and is used to send the optimal design scheme obtained by optimization to the verification module.

[0146] Figure 8 An internal structural diagram of a computer device in one embodiment is shown. This computer device can specifically be a terminal or a server. Figure 8 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program causes the processor to perform all the steps of the above-described method. The internal memory may also store a computer program, which, when executed by the processor, causes the processor to perform all the steps of the above-described method. Those skilled in the art will understand that... Figure 8The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0147] In some embodiments, a computer device is provided, including a memory and a processor, the memory storing a computer program, which, when executed by the processor, causes the processor to perform a multi-objective collaborative optimization method for rotating devices.

[0148] In some embodiments, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, causes the processor to perform a multi-objective collaborative optimization method for rotating devices.

[0149] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0150] In one embodiment, a rotating device is provided, wherein the combination of design parameters of the rotating device is determined by a multi-objective collaborative optimization method for rotating devices.

[0151] It should be emphasized that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A multi-objective collaborative optimization method for determining the optimal combination of design parameters for rotating equipment, characterized in that, Includes the following steps: Establish a parametric geometric model; Establish a finite element analysis model; A multi-objective optimization function is constructed with the objectives of minimizing the overall mass, maximizing the structural strength safety margin, minimizing the structural deformation, and minimizing the resonance risk; and a multi-objective optimization mathematical model is established with strength constraints, stiffness constraints, resonance avoidance constraints, and geometric and technological constraints as constraints. Construct a proxy model and perform multi-objective optimization. The optimal design scheme obtained through optimization is verified.

2. The method according to claim 1, characterized in that, The steps for establishing the parametric geometric model include: Construct a parametric geometric model for rotating equipment; By selecting optimized design variables, the parametric geometric model can be fully parameterized and adjustable.

3. The method according to claim 2, characterized in that, The optimized design variables include the spindle opening diameter, the width of the bottom support feet of the frame, the hopper installation height, and the frame thickness.

4. The method according to claim 1, characterized in that, The steps for establishing the finite element analysis model include: A finite element analysis model is constructed based on a parametric geometric model to complete the assignment of structural material properties, mesh generation, and boundary condition application. Perform multi-condition collaborative calculations to obtain an initial calculation dataset; the multi-condition collaborative calculations include static strength analysis, modal analysis and transient dynamic analysis.

5. The method according to claim 2, characterized in that, The steps for performing multi-objective optimization include: Based on the value range of the optimization design variables, sample points are selected within the global design space; Obtain the performance response data corresponding to each sample point and construct the sample database required for optimization; A proxy model is built based on a sample database to replace direct finite element simulation; Perform global iterative optimization to generate the optimal solution set, and then select the optimal design scheme that satisfies all constraints.

6. The method according to claim 5, characterized in that, The steps for constructing the proxy model based on the sample database are as follows: Establish a nonlinear mapping relationship between the objective function and design variables to generate an initial response surface model: ； In the formula, y is the objective function of the response; Let i be the i-th design variable; For the constant term of the model; For the i-th design variable, this is a one-time coefficient; Let be the coefficient of the quadratic term of the i-th design variable; The coefficient of the interaction term between the i-th and j-th design variables; Let j be the j-th design variable, where j > i; The residual between the actual value and the approximate value; Solving the model coefficients , , , This establishes an approximate mapping relationship between design variables and the objective function; Through the coefficient of determination To evaluate the accuracy of the model, when When the preset accuracy requirements are met, the response surface model is considered reliable and can be used to replace finite element simulation. In the optimization phase, the response surface model is embedded in the iterative process. New combinations of design variables are generated in each generation of the population. The response surface model quickly predicts the performance indicators and individuals are screened, cross-crossed, and mutated according to the objective function and constraints. Through multiple generations of iterative evolution, a Pareto front solution set that meets the requirements of strength, stiffness, resonance avoidance, and lightweighting is finally obtained.

7. A multi-objective collaborative optimization system for rotating equipment, characterized in that, include: The basic model building module is configured to build parametric geometric models and finite element analysis models. The optimization model building module is configured to build a multi-objective optimization mathematical model. The multi-objective optimization mathematical model constructs a multi-objective optimization function with the objectives of minimizing the overall mass, maximizing the structural strength, and minimizing the resonance risk, and uses strength, stiffness, resonance avoidance, and geometric process as constraints. The proxy model building module is configured to build proxy models and perform multi-objective optimization. as well as, The verification module is configured to verify the optimal design solution. The output of the proxy model establishment module is connected to the input of the verification module, and is used to send the optimal design scheme obtained by optimization to the verification module.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, the processor performs the steps of the method as described in any one of claims 1 to 6.

9. A computer device, comprising a memory and a processor, characterized in that, The memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the method as described in any one of claims 1 to 6.

10. A rotating device, characterized in that, The combination of design parameters for the rotating device is determined by the method described in any one of claims 1 to 6.

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