A method for optimal design evaluation of a gilled drum based on a parametric model
By using parametric models and mathematical expressions to optimize design and evaluation methods, the challenges of rapid optimization and safety assessment in aero-engine drum design have been solved. This has enabled efficient and accurate drum structure optimization and safety assessment, ensuring the service safety of aero-engine drums.
Patent Information
- Application Number
- CN202610313016.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-16
- Publication Date
- 2026-05-15
- Estimated Expiration
- 2046-03-16
AI Technical Summary
Existing technologies make it difficult to quickly optimize and accurately assess the service safety of defective welded structures in the design of aero-engine drums, resulting in long design cycles, high computational costs, and risky assessment results, making it impossible to find the best balance between lightweighting and safety.
A mathematical model of a toothed drum cylinder is established using a parametric model-based approach. The stress expression is determined, the influence of initial defects is considered, and the design is optimized through the residual strength reserve coefficient and stress reserve coefficient. Combined with the self-sustaining radius ratio evaluation criterion, rapid structural optimization and safety assessment are achieved.
Significantly shortening the design cycle, reducing reliance on complex finite element analysis, making safety assessments more closely aligned with engineering realities, and providing more reliable results ensures safe service of the drum and achieves a balance between lightweight design and safety.
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Figure CN121835085B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of aero-engine technology, and in particular to an optimization design evaluation method for a welded ferrule based on a parametric model. Background Technology
[0002] The compressor drum of an aero-engine is a key component connecting the rotor disc and transmitting torque. For sealing purposes, the drum is often designed with a grate structure to seal the airflow between it and the stator. As aero-engine efficiency requirements increase, the compressor rotor diameter is becoming larger. Because the drum radius is larger than the rotor disc's self-sustaining radius, the drum's cross-section will experience significant deflection under high-speed rotation. To reduce mating interfaces and connectors, and to lighten the engine weight, the structural design aims to minimize the drum wall thickness, resulting in a higher load and stress level on the drum.
[0003] To reduce the number of mating interfaces and connectors, and to lighten the engine weight, the drum is often formed by welding. However, the weld joint is prone to becoming a weak point in mechanical properties, and initial defects (such as microcracks, porosity, inclusions, etc.) are inevitably introduced during the manufacturing process. Under high-speed rotating centrifugal loads, the stress state of the drum is exceptionally complex, and the maximum stress point may occur at the point of structural abrupt change or in the weld heat-affected zone.
[0004] Currently, domestic research on drum failure is scarce, and corresponding failure criteria have not yet been established, resulting in an incomplete system. Existing design methods mostly rely on iterative finite element analysis, leading to long design cycles and high computational costs. Furthermore, safety assessments often rely on ideal, defect-free models for strength verification, failing to fully consider the significant impact of initial defects on structural failure behavior. This results in assessments that are biased towards dangerous scenarios, making it impossible to find the optimal balance between lightweight design and safety.
[0005] Therefore, there is an urgent need for a method that can quickly optimize the design and accurately assess the service safety of defective welded drums. Summary of the Invention
[0006] In view of this, the present application provides an optimization design evaluation method for a toothed welded drum based on a parametric model. This method is an efficient and accurate safety evaluation method for toothed welded drums. It can achieve rapid optimization of the drum structure and scientifically evaluate its service safety considering initial defects.
[0007] This application provides an optimization design evaluation method for a welded grate drum based on a parametric model, the method comprising:
[0008] Determine the equivalent thickness of the toothed drum;
[0009] Based on the equivalent thickness, a parametric mathematical model of the toothed drum is established, and the stress expression of the toothed drum is determined.
[0010] The critical parts of the toothed drum at maximum operating speed are determined based on the parametric mathematical model. The critical parts include the welded parts and the parts with the greatest stress.
[0011] The average stress of the cross section at the critical location is determined based on the stress expression;
[0012] For the welded parts, the residual strength reserve coefficient based on the initial defects of the toothed drum is determined, and the stress reserve coefficient of the welded parts is determined based on the stress expression and the average stress of the section.
[0013] For the location of maximum stress, obtain the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the middle diameter of the toothed drum;
[0014] When the ratio does not meet the first preset condition, the stress reserve coefficient of the maximum stress location is determined based on the stress expression and the average stress of the cross section.
[0015] The structural parameters of the toothed drum are optimized with the objective function of minimizing the weight of the drum and the constraint that the residual strength reserve coefficient and stress reserve coefficient do not exceed the material properties.
[0016] According to a specific implementation of an embodiment of this application, the step of establishing a parameterized mathematical model of the toothed drum and determining the stress expression of the toothed drum includes:
[0017] The toothed drum is equivalent to a cylindrical shell of equal thickness. Assuming that the working temperature of the drum is constant along the axial and radial directions, a micro-element is cut from the drum after the thickness is equivalent, and an expression for the radial displacement of the micro-element is established.
[0018] Based on the axial symmetry of the drum, the boundary conditions at the connection between the drum and the wheel and at the middle of the drum are determined.
[0019] Based on the expression for the radial displacement of the infinitesimal element and the boundary conditions, the expression for the radial displacement of the toothed drum is established using the Krylov function.
[0020] Based on the radial displacement expression of the toothed drum, the stress expression of the toothed drum is obtained.
[0021] According to a specific implementation of this application, the expression for the radial displacement of the micro-element is:
[0022] ,
[0023] Where y is the radial displacement of the drum and x is the axial displacement of the drum. For the density of the drum, For rotational speed, The inner diameter of the drum tube The equivalent thickness of the drum cylinder; For the displacement differential parameter, , D is Poisson's ratio; D is the bending stiffness of the drum. E is the elastic modulus of the drum cylinder;
[0024] The boundary conditions at the connection between the drum and the wheel are:
[0025] ,
[0026] in, This represents the radial displacement of the wheel at the drum. The axial bending moment of the drum;
[0027] The boundary conditions at the middle part of the drum are:
[0028] ,
[0029] in, For the drum tube corner, L represents the radial plane shear force of the drum, and L represents the axial length of the drum.
[0030] According to a specific implementation of an embodiment of this application, the radial displacement expression of the toothed drum is as follows:
[0031] ,
[0032] ,
[0033] in, For the radial displacement of the unconstrained drum, C1 is the first constant, C2 is the second constant, and C3 is the third constant;
[0034] The stress expression for the toothed drum is as follows:
[0035] ,
[0036] ,
[0037] ,
[0038] in, For the axial stress of the drum, For the circumferential stress of the drum, This refers to the radial stress of the drum.
[0039] According to a specific implementation of this application, the expression for the average stress of the cross section is:
[0040] ,
[0041] ,
[0042] in, The average axial stress of the axial section. The average circumferential stress of the circumferential section.
[0043] According to a specific implementation of an embodiment of this application, determining the residual strength reserve coefficient of the toothed drum based on initial defects includes:
[0044] Based on the fatigue limit test results representing the manufacturing process level of the welded parts of the drum, the equivalent initial defect size of the toothed drum is calculated.
[0045] Calculate the residual strength of the toothed drum based on the equivalent initial defect size;
[0046] The remaining strength reserve coefficient is calculated based on the remaining strength of the toothed drum and the vibration stress.
[0047] According to a specific implementation of an embodiment of this application, the expression for the equivalent initial defect size is:
[0048] ;
[0049] The expression for the residual strength of the toothed drum is:
[0050] ;
[0051] The expression for the remaining strength reserve coefficient is:
[0052] ,
[0053] ;
[0054] Where a0 is the equivalent initial defect size. The fatigue limit of the defective drum cylinder. The threshold value for the stress intensity factor of the drum cylinder. σ is the initial crack shape factor. res The remaining strength of the toothed drum cylinder. K represents the fracture toughness of the drum material. over The remaining strength reserve coefficient, σ is the equivalent stress at the maximum operating speed of the drum. a This refers to vibration stress.
[0055] According to a specific implementation of this application, the expression for the stress reserve coefficient is:
[0056] ,
[0057] in, The average circumferential tensile reserve coefficient of the drum cylinder. The mean circumferential yield reserve coefficient. The average axial yield reserve coefficient. σ is the minimum circumferential yield reserve coefficient. 0.2 σ is the yield strength of the material. b For the tensile strength of the material, This represents the maximum average axial stress at the critical location. This represents the maximum circumferential stress at the critical location.
[0058] According to a specific implementation of an embodiment of this application, the constraint condition is as follows:
[0059] .
[0060] According to a specific implementation of an embodiment of this application, the first preset condition is: , k is the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the mean diameter of the toothed drum. The formula for calculating the self-supporting radius is: R f The radius is the self-sustaining radius.
[0061] Beneficial effects:
[0062] The optimization design and evaluation method for toothed welded drum cylinders based on a parametric model in this application establishes a parametric mathematical model of the toothed drum cylinder, enabling rapid stress calculation and guiding structural optimization, significantly shortening the design cycle and reducing reliance on complex finite element analysis. For critical failure points of the drum cylinder, the influence of initial defects is considered, making the safety assessment more closely aligned with engineering realities and resulting in more reliable results. The method proposes a physical meaning centered on the ratio of the self-sustaining radius to the neutral layer radius of the drum cylinder, clearly defines failure assessment criteria, establishes a complete safety assessment system, and designs a reasonable safety margin, effectively ensuring the service safety of the drum cylinder. Attached Figure Description
[0063] To more clearly illustrate the technical solutions of the embodiments of this application, 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.
[0064] Figure 1 This invention relates to an optimization design and evaluation method for a welded ferrule based on a parametric model, according to an embodiment of the present invention.
[0065] Figure 2 This is a schematic diagram of the stress analysis of a micro-element of a welded drum with comb teeth according to an embodiment of the present invention;
[0066] Figure 3 This is a schematic diagram of the equivalent wall thickness of a drum according to an embodiment of the present invention;
[0067] Figure 4 This is another flowchart of an evaluation method according to an embodiment of the present invention. Detailed Implementation
[0068] The embodiments of this application will now be described in detail with reference to the accompanying drawings.
[0069] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0070] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this application, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.
[0071] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this application. The illustrations only show the components related to this application and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0072] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.
[0073] This application provides an optimization design evaluation method for a welded ferrule based on a parametric model, which will be described in detail below with reference to the figures.
[0074] In one embodiment, taking the high-pressure compressor drum of a certain type of aero-engine as an example, refer to... Figure 1 The optimization design and evaluation method for welded grate drums based on parametric models includes the following steps:
[0075] Step S101: Determine the equivalent thickness of the toothed drum.
[0076] Step S102: Based on the equivalent thickness, establish a parameterized mathematical model of the toothed drum and determine the stress expression of the toothed drum.
[0077] Step S103: Determine the dangerous parts of the toothed drum at the maximum operating speed based on the parametric mathematical model. The dangerous parts include the welded parts and the parts with the greatest stress.
[0078] Step S104: Determine the average stress of the section at the critical location based on the stress expression;
[0079] Step S105: For the welded part, determine the residual strength reserve coefficient of the toothed drum based on the initial defects, and determine the stress reserve coefficient of the welded part based on the stress expression and the average stress of the section.
[0080] Step S106: For the location of maximum stress, obtain the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the middle diameter of the toothed drum.
[0081] Step S107: When the ratio does not meet the first preset condition, the stress reserve coefficient of the maximum stress location is determined based on the stress expression and the average stress of the cross section.
[0082] Step S108: With the goal of minimizing the weight of the toothed drum, and with the constraint that the residual strength reserve coefficient and stress reserve coefficient do not exceed the material properties, optimize the structural parameters of the toothed drum.
[0083] In this embodiment, by establishing a parametric mathematical model of the drum with serrated teeth, stress can be quickly calculated and structural optimization can be guided, significantly shortening the design cycle and reducing reliance on complex finite element analysis. For the critical failure points of the drum, the influence of initial defects is considered, making the safety assessment more closely aligned with engineering practice and the results more reliable. The physical meaning of the ratio of the self-sustaining radius to the neutral layer radius of the drum is proposed, along with clear failure assessment criteria. A complete safety assessment system is established, and a reasonable safety margin is designed to effectively ensure the service safety of the drum.
[0084] In one embodiment, establishing a parameterized mathematical model of the toothed drum and determining the stress expression for the toothed drum includes:
[0085] The toothed drum is equivalent to a cylindrical shell of uniform thickness. Assuming the drum's operating temperature remains constant along both the axial and radial directions, a small element is extracted from the drum after the thickness is equivalent. An expression for the radial displacement of this small element is then established. Figure 2 and Figure 3 As shown, X represents the axial direction of the drum, R represents the radial direction, and Y represents the circumferential direction. An XOY coordinate system is established with the connection point between the left end mid-section of the drum and the wheel disk as the origin O, the drum length as the X direction, and the drum radial direction as the Y direction. An expression for the radial displacement of the drum element is established by analyzing the relationship between stress, strain, and displacement.
[0086] Based on the axial symmetry of the drum, half the length of the drum is taken as the research object, and the connection point between the drum and the wheel (the origin of the coordinate system) is determined. ) and the middle part of the drum tube ( Boundary conditions at ( );
[0087] Based on the expression for the radial displacement of the infinitesimal element and the boundary conditions, the expression for the radial displacement of the toothed drum is established using the Krylov function.
[0088] Based on the radial displacement expression of the toothed drum, the stress expression of the toothed drum is obtained.
[0089] Furthermore, the expression for the radial displacement of the infinitesimal element is:
[0090] (1),
[0091] Where y is the radial displacement of the drum and x is the axial displacement of the drum. For the density of the drum, For rotational speed, The inner diameter of the drum tube The equivalent thickness of the drum cylinder; For the displacement differential parameter, , D is Poisson's ratio; D is the bending stiffness of the drum. E is the elastic modulus of the drum cylinder;
[0092] The boundary conditions at the connection between the drum and the wheel are:
[0093] (2),
[0094] in, This represents the radial displacement of the wheel at the drum. The axial bending moment of the drum;
[0095] The boundary conditions at the middle part of the drum are:
[0096] (3),
[0097] in, For the drum tube corner, L represents the radial plane shear force of the drum, and L represents the axial length of the drum.
[0098] Furthermore, the radial displacement expression of the toothed drum is as follows:
[0099] (4),
[0100] (5),
[0101] in, For the radial displacement of the unconstrained drum, C1 is the first constant, C2 is the second constant, and C3 is the third constant;
[0102] In practical implementation, the equivalent thickness of the drum is determined by the principle that the circumferential bearing surface area of the comb-tooth drum remains unchanged, such as... Figure 3 As shown, the equivalent thickness is calculated using the following formula:
[0103] (6),
[0104] Where A is the area of the circumferential bearing surface of the toothed drum, and L is the axial length of the drum. The equivalent thickness of the drum cylinder;
[0105] The stress expression for the toothed drum is as follows:
[0106] (7),
[0107] (8),
[0108] (9),
[0109] in, For the axial stress of the drum, For the circumferential stress of the drum, This refers to the radial stress of the drum.
[0110] Furthermore, the expression for the average stress of the cross section is:
[0111] (10)
[0112] (11),
[0113] in, The average axial stress of the axial section. The average circumferential stress of the circumferential section.
[0114] In one embodiment, determining the residual strength reserve factor for the toothed drum based on initial defects includes:
[0115] Based on the fatigue limit test results representing the manufacturing process level of the welded parts of the drum, the equivalent initial defect size of the toothed drum is calculated.
[0116] Calculate the residual strength of the toothed drum based on the equivalent initial defect size;
[0117] The remaining strength reserve coefficient is calculated based on the remaining strength of the toothed drum and the vibration stress.
[0118] Furthermore, the expression for the equivalent initial defect size is:
[0119] (12);
[0120] The expression for the residual strength of the toothed drum is:
[0121] (13);
[0122] The expression for the remaining strength reserve coefficient is:
[0123] (14)
[0124] (15);
[0125] Where a0 is the equivalent initial defect size. The fatigue limit of the defective drum cylinder. The threshold value for the stress intensity factor of the drum cylinder. σ is the initial crack shape factor. res The remaining strength of the toothed drum cylinder. K represents the fracture toughness of the drum material. over The remaining strength reserve coefficient, σ is the equivalent stress at the maximum operating speed of the drum. a This refers to vibration stress.
[0126] Furthermore, the expression for the stress reserve coefficient is as follows:
[0127] (16)
[0128] in, The average circumferential tensile reserve coefficient of the drum cylinder. The mean circumferential yield reserve coefficient. The average axial yield reserve coefficient. σ is the minimum circumferential yield reserve coefficient. 0.2 σ is the yield strength of the material. b For the tensile strength of the material, This represents the maximum average axial stress at the critical location. This represents the maximum circumferential stress at the critical location.
[0129] Furthermore, the constraints are as follows:
[0130] (17).
[0131] In one embodiment, the first preset condition is: , k is the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the mean diameter of the toothed drum. The formula for calculating the self-supporting radius is:
[0132] (18)
[0133] Among them, R f The radius is the self-sustaining radius.
[0134] The following is a specific embodiment of the optimization design and evaluation method for the welded ferrule based on a parametric model, which includes the following steps:
[0135] Step 1: Establish a mathematical model of the structural parameters and stress of the welded drum with serrated teeth.
[0136] A parameterized mathematical model of the toothed drum is established, treating it as a cylindrical shell of uniform thickness. Assuming the drum's operating temperature remains constant along both the axial and radial directions, a micro-element is taken from the thickness-equivalent drum, such as... Figure 2 As shown. By analyzing the relationship between stress, strain and displacement of the drum cylinder micro-element, the radial displacement expression of the drum cylinder micro-element is established, as shown in formula (1).
[0137] Considering the axial symmetry of the drum, half the length of the drum is taken as the research object, and the origin of the coordinate system is determined. (The connection between the drum and the wheel) and The boundary conditions at the middle of the drum are given by formulas (2) and (3) respectively.
[0138] The radial displacement expression of the toothed drum is established using the Krylov function, as shown in formula (4), and the stress expression of the toothed drum is established, as shown in formulas (7) to (9).
[0139] Step 2: Establish a failure assessment method for welded drums with serrated teeth, which specifically includes the following aspects:
[0140] 1. Determine the assessment location and stress at that location. Using the mathematical model described in step one, determine the critical location of the drum at its maximum operating speed. The critical location is the point of maximum stress and the welding location. The location of maximum stress and the welding location of the drum are determined by formulas (7) to (9). Figure 2 middle The stress of ).
[0141] Then, determine the average axial stress of the axial section where the maximum stress point of the drum is located and the average circumferential stress of the entire circumferential section of the drum, referring to formula (10) and formula (11) respectively.
[0142] 2. Introduce initial defects to calculate the residual strength of the drum. Based on the fatigue limit test results representing the manufacturing process level of the welded parts of the drum, calculate the equivalent initial defect size of the drum, as shown in formula (12). Introduce initial defects and calculate the residual strength of the drum according to formula (13).
[0143] 3. Establish failure assessment criteria. Calculate the self-sustaining radii of the two discs connected to the drum, using formula (18); use the minimum self-sustaining radius of the two discs. The ratio of the drum's inner diameter to the drum's inner diameter The dangerous parts of the drum are assessed as evaluation criteria. For the welded areas, calculate the welding position of the drum. , , , and For the location of maximum stress, it is necessary to determine based on the first preset condition, that is: if Then calculate the location of the maximum stress. , , and ;like Therefore, it is not necessary to evaluate the location of the greatest stress.
[0144] 4. Determine the safety margin of the assessment location. Calculate the circumferential average stress reserve coefficient, axial average stress reserve coefficient, and minimum circumferential stress reserve coefficient of the drum according to formula (16).
[0145] For areas with initial defects, a certain amount of vibration stress should also be considered. The remaining strength reserve of the drum is calculated according to formula (14), and the equivalent stress at the maximum operating speed of the drum is calculated. Calculate according to formula (15).
[0146] Step 3: Establish a failure assessment process (see...) Figure 4 Specifically, it includes the following steps:
[0147] 1. Determine the equivalent thickness of the toothed drum;
[0148] 2. Based on the structure and stress characteristics of the toothed drum, establish a mathematical model of the toothed drum and obtain expressions for the radial displacement and stress of the drum in relation to structural parameters;
[0149] 3. Based on the established mathematical model of the toothed drum, determine the high-stress areas and welding points of the drum;
[0150] 4. Calculate the equivalent initial defect size at the welded area of the drum. To obtain the point stress at the welded part of the drum. and Cross-sectional mean stress and residual strength ;
[0151] 5. Calculate the welding position of the drum cylinder. , , , and ;
[0152] 6. Obtain the point stress at the high-stress location of the drum. and cross-sectional mean stress ;
[0153] 7. Calculate the minimum self-sustaining radius. With the drum wall thickness median diameter ratio For the high-stress areas of the drum, The value is used as the evaluation criterion to determine the evaluation content. If Calculate the dangerous location of the drum. , , and ;like No analysis is required.
[0154] Step 4: Establish a rapid structural optimization of the welded drum cylinder with grating teeth using a parameterized model.
[0155] Based on the stress calculation formula in step one, with the goal of minimizing the weight of the drum and the constraint that the maximum stress does not exceed the allowable stress of the material, a design optimization program is developed to optimize the design of the drum.
[0156] Parametric modeling is performed based on the established mathematical model, using the drum structure parameter variables. , , As optimization variables, the input sample points are obtained through different combinations of the values of these three variables. The drum stress is obtained according to formulas (7) to (11). , , , , The output sample points.
[0157] According to the failure assessment method determined in step three, the constraint condition is that the stress of the drum does not exceed the material properties, as shown in formula (17).
[0158] Based on the weight of the drum tube The objective is to achieve the lightest weight, and the objective function is given in formula (19):
[0159] (19).
[0160] An optimization program was developed using a multi-objective genetic optimization algorithm to find a design scheme that achieves the optimal solution for the stress and weight of the drum.
[0161] By combining parametric models with optimization algorithms, the performance of drums under different combinations of structural parameters can be quickly evaluated and selected, effectively shortening the design cycle. During the optimization process, the system automatically calculates the drum stress corresponding to the input sample points and judges whether it meets the design requirements based on the constraints. Unsuitable solutions are promptly eliminated, retaining only the design parameter combinations that meet safety standards and have the best weight. After multiple rounds of iterative optimization, the lightest welded drum structure parameters with serrated teeth are finally obtained while meeting all performance indicators, providing an efficient and reliable design basis for practical engineering applications.
[0162] The embodiments provided by this invention achieve intelligent optimization of the structural parameters of a welded drum with serrated teeth by establishing a collaborative mechanism between a parametric model and an optimization algorithm. During the optimization process, the system can automatically generate and evaluate a large number of structural parameter combinations based on preset objective functions and constraints. For each set of input structural parameter variables, the optimization program calls the stress mathematical model established in step one to accurately calculate various stress indices of the drum, including maximum stress, average axial stress, and average circumferential stress, and compares these stress values with the allowable stress of the material to determine whether the scheme meets the strength requirements. For schemes that meet the constraints, the system further calculates the corresponding drum weight and searches and iterates in the solution space using a multi-objective genetic optimization algorithm to gradually select a lighter design scheme with a better stress distribution. This deep integration of parametric modeling and optimization algorithms not only avoids the limitations of relying on trial and error in traditional design methods but also greatly improves design efficiency and optimization accuracy. This ensures that the final drum structural parameters can minimize material consumption while guaranteeing safety performance, achieving an organic unity of structural lightweighting and reliability.
[0163] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.
Claims
1. A method for optimizing the design and evaluation of a welded grate drum based on a parametric model, characterized in that, The method includes: Determine the equivalent thickness of the toothed drum; Based on the equivalent thickness, a parametric mathematical model of the toothed drum is established, and the stress expression of the toothed drum is determined. The critical parts of the toothed drum at maximum operating speed are determined based on the parametric mathematical model. The critical parts include the welded parts and the parts with the greatest stress. The average stress of the cross section at the critical location is determined based on the stress expression; For the welded parts, the residual strength reserve coefficient based on the initial defects of the toothed drum is determined, and the stress reserve coefficient of the welded parts is determined based on the stress expression and the average stress of the section. For the location of maximum stress, obtain the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the middle diameter of the toothed drum; When the ratio does not meet the first preset condition, the stress reserve coefficient of the maximum stress location is determined based on the stress expression and the average stress of the cross section. The structural parameters of the toothed drum are optimized with the objective function of minimizing the weight of the drum and the constraint that the residual strength reserve coefficient and stress reserve coefficient do not exceed the material properties.
2. The optimization design and evaluation method for welded grate drums based on a parametric model according to claim 1, characterized in that, The establishment of a parameterized mathematical model for the toothed drum and the determination of its stress expression include: The toothed drum is equivalent to a cylindrical shell of equal thickness. Assuming that the working temperature of the drum is constant along the axial and radial directions, a micro-element is cut from the drum after the thickness is equivalent, and an expression for the radial displacement of the micro-element is established. Based on the axial symmetry of the drum, the boundary conditions at the connection between the drum and the wheel and at the middle of the drum are determined. Based on the expression for the radial displacement of the infinitesimal element and the boundary conditions, the expression for the radial displacement of the toothed drum is established using the Krylov function. Based on the radial displacement expression of the toothed drum, the stress expression of the toothed drum is obtained.
3. The optimization design and evaluation method for welded grate drums based on a parametric model according to claim 2, characterized in that, The expression for the radial displacement of the infinitesimal element is: ， Where y is the radial displacement of the drum and x is the axial displacement of the drum. For the density of the drum, For rotational speed, The inner diameter of the drum tube The equivalent thickness of the drum cylinder; For the displacement differential parameter, , D is Poisson's ratio; D is the bending stiffness of the drum. E is the elastic modulus of the drum cylinder; The boundary conditions at the connection between the drum and the wheel are: ， in, This represents the radial displacement of the wheel at the drum. The axial bending moment of the drum; The boundary conditions at the middle part of the drum are: ， in, For the drum tube corner, L represents the radial plane shear force of the drum, and L represents the axial length of the drum.
4. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 3, characterized in that, The radial displacement expression of the toothed drum is as follows: ， ， in, For the radial displacement of the unconstrained drum, C1 is the first constant, C2 is the second constant, and C3 is the third constant; The stress expression for the toothed drum is as follows: ， ， ， in, For the axial stress of the drum, For the circumferential stress of the drum, This refers to the radial stress of the drum.
5. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 4, characterized in that, The expression for the average stress of the cross section is: ， ， in, The average axial stress of the axial section. The average circumferential stress of the circumferential section.
6. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 4, characterized in that, The determination of the residual strength reserve coefficient based on initial defects for the toothed drum includes: Based on the fatigue limit test results representing the manufacturing process level of the welded parts of the drum, the equivalent initial defect size of the toothed drum is calculated. Calculate the residual strength of the toothed drum based on the equivalent initial defect size; The remaining strength reserve coefficient is calculated based on the remaining strength of the toothed drum and the vibration stress.
7. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 6, characterized in that, The expression for the equivalent initial defect size is: ； The expression for the residual strength of the toothed drum is: ； The expression for the remaining strength reserve coefficient is: ， ； Where a0 is the equivalent initial defect size. The fatigue limit of the defective drum cylinder. The threshold value for the stress intensity factor of the drum cylinder. σ is the initial crack shape factor. res The remaining strength of the toothed drum cylinder. K represents the fracture toughness of the drum material. over The remaining strength reserve coefficient, σ is the equivalent stress at the maximum operating speed of the drum. a This refers to vibration stress.
8. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 7, characterized in that, The expression for the stress reserve coefficient is: ， in, The average circumferential tensile reserve coefficient of the drum cylinder. The mean circumferential yield reserve coefficient. The average axial yield reserve coefficient. σ is the minimum circumferential yield reserve coefficient. 0.2 σ is the yield strength of the material. b For the tensile strength of the material, This represents the maximum average axial stress at the critical location. This represents the maximum circumferential stress at the critical location.
9. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 8, characterized in that, The constraints are as follows: 。 10. The optimization design and evaluation method for a welded grate drum based on a parametric model according to claim 8, characterized in that, The first preset condition is , k is the ratio of the minimum self-supporting radius of the two discs connected to the toothed drum to the mean diameter of the toothed drum. The formula for calculating the self-supporting radius is: R f The radius is the self-sustaining radius.