A multi-stage planetary gear transmission design method based on hypergraph representation

Abstract

A kind of multi-stage planetary gear transmission design method based on hypergraph expression, comprising: establishing the function component identification rule and hypergraph mapping rule of planetary gear transmission mechanism;Establish the kinematic relationship diagram of planetary gear transmission mechanism;Simplify the hypergraph;Establish the combined hypergraph model of multi-stage planetary gear transmission mechanism;Convert the hypergraph model into the corresponding adjacency matrix;Establish the kinematic topological model of multi-stage planetary gear transmission mechanism, and construct the corresponding transmission ratio matrix;Generate the configuration of multi-stage planetary gear transmission mechanism, and generate the corresponding multi-stage planetary gear transmission mechanism configuration scheme;Identify and remove duplicate isomorphic configuration by using Hamming matrix method for isomorphism discrimination;Verify the effectiveness of isomorphism discrimination result, and obtain the effective multi-stage planetary gear transmission mechanism configuration scheme satisfying the constraint condition.The present application can improve the configuration design efficiency and structure analysis capability of complex multi-stage planetary gear transmission mechanism.

Description

Technical Field

[0001] This invention relates to the field of topology modeling and configuration design technology for mechanical transmission systems, and specifically to a design method for multi-stage planetary gear transmissions based on hypergraph representation. Background Technology

[0002] Planetary gear transmission mechanisms are widely used in transmission systems of large equipment such as wind power generation, aerospace, engineering machinery, and marine propulsion due to their advantages of compact structure, high load-bearing capacity, high transmission efficiency, and ease of achieving large transmission ratios. With the development of high-power, highly integrated, and complex transmission systems, the configuration design and structural analysis of multi-stage planetary gear transmission mechanisms have gradually become an important part of research on complex mechanical transmission systems. In particular, load-splitting multi-stage planetary gear transmission mechanisms, which achieve high power density output through load splitting, have become an important research direction in aerospace, high-end equipment, and new energy transmission systems because they can effectively improve the power transmission capacity per unit volume. This has also placed higher demands on topology design and structural optimization for achieving high power density output in multi-stage transmission systems within limited space.

[0003] Currently, the structural representation and configuration design of planetary gear transmission mechanisms typically employ methods such as structural diagrams, topological diagrams, and graph theory models to describe the connection relationships between mechanism components. Among these, traditional graph theory models can reflect the structural composition relationships of planetary gear mechanisms to a certain extent and provide a foundation for mechanism configuration analysis.

[0004] However, edges in traditional graph theory models can typically only describe binary relationships between two nodes. In contrast, multi-stage planetary gear transmission mechanisms commonly involve coupling, complex connections, and kinematic constraints between multiple components. This leads to the following shortcomings in traditional topological representation methods when modeling complex planetary gear mechanisms: (1) Existing topological models lack unified expression rules for functional components such as sun gear, planet gear, gear ring and planet carrier, making it difficult to achieve standardized description of complex multi-stage planetary gear mechanism structural information; (2) Existing topology models mainly focus on describing the connection relationship between components, and fail to fully reflect the kinematic topology characteristics of planetary gear mechanisms and the coupling relationship between multiple components, resulting in limitations in complex configuration analysis and structural identification; (3) In the process of designing the configuration of multi-stage planetary gear transmission mechanism, the existing methods lack a unified adjacency matrix expression form, which makes it difficult to realize the automatic generation of multi-stage configurations and the effective identification of isomorphic structures, resulting in low configuration design efficiency, difficulty in screening repeated configurations, and especially difficulty in supporting the rapid screening and optimization of multi-stage load splitting configurations for high power density targets. (4) Traditional graph theory models mainly describe the binary connection relationship between nodes. For the multi-component association, inter-stage coupling and complex motion constraint relationship in multi-stage planetary gear mechanism, there is a lack of unified and effective topological expression method, which is difficult to meet the needs of configuration modeling and structural analysis of complex multi-stage planetary gear transmission system.

[0005] The above problems mean that the efficiency of existing technologies in the configuration design and structural analysis capabilities of complex multi-stage planetary gear transmission mechanisms needs to be improved. Summary of the Invention

[0006] This invention addresses the problems of inconsistent structural relationship expression, difficulty in automatically generating complex configurations, and difficulty in effectively identifying isomorphic configurations in the existing multi-stage planetary gear transmission mechanism configuration design process. It provides a multi-stage planetary gear transmission design method based on hypergraph expression to improve the configuration design efficiency and structural analysis capability of complex multi-stage planetary gear transmission mechanisms.

[0007] A design method for multi-stage planetary gear transmissions based on hypergraph representation includes: Step S1: Establish functional component identification rules and hypergraph mapping rules for the planetary gear transmission mechanism. Define functional components including sun gear, planet gear, internal gear ring, planet carrier and frame in a unified manner, and establish a hypergraph representation of the connection relationship and motion coupling relationship between components. Step S2: Based on the functional component identification rules and hypergraph mapping rules established in Step S1, establish the motion relationship diagram of the planetary gear transmission mechanism, and construct the internal meshing motion unit and the external meshing motion unit according to the meshing relationship between the components. Step S3: Based on the motion relationship diagram established in step S2, the hypergraph of the single-stage planetary gear transmission system is simplified. In order to adapt to the unified modeling requirements of multi-stage planetary gear transmission systems, planetary gear nodes are omitted, and only key component nodes representing topological connection relationships are retained. Step S4: Based on the simplified hypergraph in Step S3, multiple single-stage planetary gear transmission mechanisms are combined and connected to establish a multi-stage planetary gear transmission mechanism combination hypergraph model, so as to uniformly abstract and express the complex structural relationship and multi-component coupling relationship of the multi-stage planetary gear system. Step S5: Convert the multi-stage planetary gear transmission mechanism combined hypergraph model established in step S4 into the corresponding adjacency matrix to realize the digital expression of the structural relationship of the multi-stage planetary gear transmission mechanism and establish the adjacency matrix model of the configuration scheme of the multi-stage planetary gear transmission mechanism. Step S6: Establish a motion topology model of the multi-stage planetary gear transmission mechanism based on the adjacency matrix model, and construct the corresponding transmission ratio matrix; based on the input component speed and the motion constraint relationship between components, establish the speed constraint equation of the multi-stage planetary gear transmission mechanism, and matrix-represent the speed constraint equation as a transmission ratio matrix to solve for the speed of each component and the total transmission ratio of the system. Step S7: Based on the adjacency matrix established in step S5 and the motion topology model established in step S6, the configuration of the multi-stage planetary gear transmission mechanism is generated, and the corresponding configuration scheme of the multi-stage planetary gear transmission mechanism is generated according to the connection relationship and constraint conditions between the components. Step S8: The Hamming matrix method is used to perform isomorphism discrimination on the multi-stage planetary gear transmission mechanism configuration scheme generated in step S7. By comparing the differences between the adjacency matrices of different configuration schemes, duplicate isomorphic configurations are identified and removed to obtain effective multi-stage planetary gear transmission configuration schemes that meet the constraints. Step S9: Verify the validity of the isomorphism discrimination result obtained in step S8, and obtain an effective multi-stage planetary gear transmission mechanism configuration scheme that satisfies the constraints.

[0008] The multi-stage planetary gear transmission design method based on hypergraph representation provided by the present invention has the following beneficial effects: 1. This invention maps functional components to hypergraph nodes using a unified symbol identification rule, and expresses inter-stage connections and load splitting relationships as cross-stage hyperedges through a combined hypergraph model. Since the hypergraph model can directly describe the load splitting topology of input nodes simultaneously connecting multiple transmission stages, this invention is particularly suitable for structural modeling and configuration analysis of high-power-density load-splitting multi-stage planetary gear transmission systems (such as wind turbine speed increasers and aerospace transmissions), providing a theoretical basis and technical support for the configuration design of complex mechanical transmission systems.

[0009] 2. This invention uses hypergraph theory to establish a topological representation model of a multi-stage planetary gear transmission mechanism. Since the hyperedges in the hypergraph can directly express the meshing, connection, and motion coupling relationships between multiple components, while traditional graph theory can only describe the pairwise connection relationships between nodes, this invention realizes a unified modeling of the topological structure of complex multi-stage planetary gear transmission mechanisms. It can fully reflect the motion topology characteristics and multi-component coupling relationships of the mechanism, improving the completeness, accuracy, and scalability of the mechanism representation. It is especially suitable for high power density load-splitting transmission systems.

[0010] 3. This invention establishes a standardized multi-stage planetary gear configuration expression system based on the mapping relationship between hypergraph models and adjacency matrices. Since hypergraph models can be converted into adjacency matrices for digital description and configuration schemes can be automatically generated based on connection relationships and constraints, this invention achieves digital description and automatic generation of configuration schemes for multi-stage planetary gear transmission mechanisms. This reduces the reliance on manual experience in the design of complex transmission system configurations and improves configuration design efficiency and scheme scalability.

[0011] 4. This invention constructs a method for isomorphic discrimination of multi-stage planetary gear configurations based on adjacency matrix and Hamming matrix. Since the Hamming matrix only depends on topological connection relationship and not on node symbols, it can quickly identify and filter out topologically equivalent repeating configurations. Therefore, this invention avoids redundant design and analysis, improves configuration screening efficiency and topology discrimination accuracy, and can be used for efficient configuration screening and analysis of load-splitting multi-stage planetary gear transmission structures. It is also suitable for structural design requirements in high power density transmission scenarios. Attached Figure Description

[0012] Figure 1 A flowchart illustrating the multi-stage planetary gear transmission design method based on hypergraph representation provided in an embodiment of the present invention; Figure 2 A simplified structural diagram of a single-stage planetary gear transmission system; Figure 3 A hypergraph model for a single-stage planetary gear transmission system; Figure 4 A kinematic hypergraph model of the internal and external meshing relationship; Figure 5 This is a simplified structural diagram of a two-stage planetary gear mechanism; Figure 6 This is a hypergraph model of a two-stage planetary gear mechanism; Figure 7 Simplified structural diagrams and hypergraph models of three two-stage planetary gear transmission mechanisms are provided. Figure 8 A simplified structural diagram of an exemplary load-splitting planetary gear transmission system; Figure 9 This is a supergraph model of an exemplary load-splitting planetary gear transmission system. Detailed Implementation

[0013] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0014] Please see Figure 1 The multi-stage planetary gear transmission design method based on hypergraph representation provided by this invention includes steps S1 to S9: Step S1: Establish functional component identification rules and hypergraph mapping rules for the planetary gear transmission mechanism. Define functional components including sun gear, planet gear, internal gear ring, planet carrier and frame in a unified manner, and establish a hypergraph representation of the connection relationship and motion coupling relationship between components.

[0015] Among these measures, the functional components in the planetary gear transmission mechanism will be uniformly labeled with symbols. Indicates planetary support, Represents the sun wheel, Indicates planetary gears, It represents the internal gear ring; and by appending numbers after the symbol to indicate the component identification of different levels in the multi-stage planetary gear transmission mechanism, the hierarchical expression of the multi-stage gear system is realized.

[0016] In the hypergraph topology model, each functional component is uniformly abstracted as a hypergraph node (which can be represented by a solid circle), and the kinematic pair connection relationship, gear meshing relationship and kinematic coupling relationship between components are corresponding to hyperedges.

[0017] The external meshing relationship between the sun gear and the planet gears is adopted This indicates that the internal meshing relationship between the planetary gears and the internal gear ring is adopted. It is indicated that in the bearing support relationship, the slewing pair, the frame fixing relationship, and the slewing pair respectively adopt... , , express.

[0018] In the isomorphism determination process, the connection relationship between hypergraph nodes is used as the determination criterion, and the node symbol is only used as a component identifier and does not affect the determination result of the topological isomorphism relationship.

[0019] Through the aforementioned functional component identification rules and hypergraph mapping rules, a unified abstract expression of the structural and kinematic relationships of the planetary gear transmission mechanism is achieved. According to the hypergraph rules in step S1, the hypergraph of a single-stage planetary gear transmission system is obtained, as follows: Figure 2 and Figure 3 As shown.

[0020] Step S2: Based on the functional component identification rules and hypergraph mapping rules established in Step S1, establish the motion relationship diagram of the planetary gear transmission mechanism, and construct the internal meshing motion unit and the external meshing motion unit according to the meshing relationship between the components.

[0021] Specifically, step S2 includes: based on the functional component identification rules and hypergraph mapping rules established in step S1, dividing the four basic motion components in the planetary gear transmission mechanism—sun gear, internal gear ring, planet carrier, and planet gear—into external meshing motion units and internal meshing motion units according to their meshing relationships, and establishing a motion relationship diagram of the planetary gear transmission mechanism.

[0022] Specifically, based on the hypergraph representation of the gear transmission system, a kinematic hypergraph model representing the internal and external meshing relationship is further refined, such as... Figure 4 , Figure 4 middle, , , , These represent the rotational speeds of the sun gear, planet gears, planet carrier, and internal ring gear, respectively. This indicates the gear ratio between the sun gear and the planet gears. This indicates the ratio of the number of teeth between the planetary gears and the gear ring.

[0023] Step S3: Based on the motion relationship diagram established in step S2, the hypergraph of the single-stage planetary gear transmission system is simplified. To adapt to the unified modeling requirements of multi-stage planetary gear transmission systems, planetary gear nodes are omitted, and only key component nodes representing topological connection relationships are retained.

[0024] Step S4: Based on the simplified hypergraph from Step S3, multiple single-stage planetary gear transmission mechanisms are combined and connected to establish a multi-stage planetary gear transmission mechanism combined hypergraph model, so as to uniformly abstract and express the complex structural relationship and multi-component coupling relationship of the multi-stage planetary gear system.

[0025] Specifically, step S4 includes: combining and connecting the hypergraphs of multiple single-stage planetary gear transmission mechanisms simplified in step S3; transforming the planetary gear train structure diagram into a hypergraph topology model; establishing a combined hypergraph model of multi-stage planetary gear transmission mechanisms; and providing a unified abstract expression of the complex structural relationships and multi-component coupling relationships of multi-stage planetary gear trains.

[0026] Specifically, for a high power density load-splitting multi-stage planetary gear transmission mechanism, the input node in the hypergraph model is connected to both the first-stage planetary transmission unit and at least one subsequent-stage planetary transmission unit, so that the input node has a hyperedge association relationship corresponding to multiple transmission stages, thereby characterizing the load-splitting topology structure in which the input torque is simultaneously distributed to multiple planetary transmission stages.

[0027] Step S5: Convert the multi-stage planetary gear transmission mechanism combined hypergraph model established in step S4 into the corresponding adjacency matrix to realize the digital expression of the structural relationship of the multi-stage planetary gear transmission mechanism, and establish the adjacency matrix model of the configuration scheme of the multi-stage planetary gear transmission mechanism.

[0028] Hypergraphs, as a generalized extension of graph theory, are fundamentally composed of three basic elements: a node set, an edge set, and an adjacency matrix. The node set represents all independent basic unit nodes in the hypergraph; its total number corresponds to the number of independent components in a planetary gear transmission system, serving as the basic carrier for constructing the hypergraph model. The edge set represents the collection of hyperedges that characterize the collaborative relationships between multiple nodes; its quantity describes the higher-order coupling relationships between multiple components in the system. The adjacency matrix is ​​used to numerically represent the connection relationships between nodes in the planetary gear structure hypergraph; its matrix elements characterize the connection states between nodes.

[0029] In this embodiment, step S5 specifically includes: Step S51: Construct an initial adjacency matrix based on the multi-stage planetary gear transmission mechanism combined hypergraph model, where the matrix elements... Used to characterize nodes With nodes The connection state between them; when When, it indicates a node With nodes There is a connection between them, when When, it indicates a node With nodes There is no connection between them; Step S52: Establish the adjacency matrix corresponding to each level of planetary gear transmission unit. , , , They represent level 1, level 2, and level 3 respectively. The adjacency matrix corresponding to the stage planetary gear transmission unit. The total number of stages in a multi-stage planetary gear transmission mechanism is given, and a joint matrix is ​​constructed based on the actual component connection relationships between each stage. This is used to describe the overall topology of a multi-stage planetary gear mechanism. It is A block diagonal matrix, with adjacency matrices arranged sequentially along the main diagonal. A matrix in which all other off-diagonal positions are zero. It is the total number of all independent components in a multi-stage planetary gear transmission mechanism. , Indicates the first The number of independent components in a planetary gear transmission unit. The expression is:

[0030] in, For the first The adjacency matrix of a multi-stage planetary gear transmission unit. Indicates the first The extended transformation matrix corresponding to the multi-stage planetary gear transmission unit. The size is , Indicates transpose; Since the adjacency matrix of a multi-stage planetary gear mechanism is established based on a single-stage planetary gear mechanism, taking a two-stage planetary gear mechanism as an example, firstly, the adjacency matrix of the two single-stage planetary gear mechanisms is... adjacency matrix , adjacency matrix Through the joint matrix equation:

[0031] in, , These are the adjacency matrices for the first-stage planetary gear transmission unit and the second-stage planetary gear transmission unit, respectively. , They represent , The corresponding extended transformation matrix.

[0032] Then, we obtain the matrix. Expand to Joint matrix of two-stage planetary gear mechanism :

[0033] Step S53: The dimensions of the adjacency matrices at all levels are unified by matrix expansion operation. Zero elements are added to the original adjacency matrices to form an expanded matrix with the same order. Specifically, the matrix Expand to An order matrix, that is, a matrix Adding to the original elements OK The zero element of the column indicates that the matrix can be determined by linear algebra. The specific form is as follows:

[0034] in, for An identity matrix of order 1; Similarly, the matrix Extending, the resulting matrix The specific form is:

[0035] in, for An identity matrix of order 1.

[0036] Step S54: Based on the connection relationships between components in the multi-stage planetary gear mechanism, perform a joint matrix analysis. Perform row and column rearrangement and matrix transformation processing to realize the mapping of the connection relationship between different levels of planetary transmission units; Specifically, the connection relationships of the components in the joint matrix of the multi-stage planetary gear mechanism are shifted and further transformed into an adjacency matrix. The specific mathematical description equation is as follows:

[0037] in, The number of components to be merged; , and It is an elementary transformation matrix; Indicates the first During the component merging process, the connection relationship features of one component are transferred to the connection relationship of another component through row and column transformation; Indicates the first During the component merging process, the row and column elements of the components to be eliminated after merging are transformed to the last row and column of the joint matrix; This indicates that in the joint matrix Clear the last row and last column to zero. The product order of the equation is from... arrive Multiply by the left in sequence.

[0038] Step S55: Adjust the position of the corresponding nodes of the associated components and reconstruct the connection relationship through matrix transformation; Specifically, when the joint matrix Right multiplication of a matrix When, the matrix's first... The connection characteristics of components in a row will be passed to the first row. In the line, where the letters and To merge component numbers, elementary transformation matrix The specific form is:

[0039] in: for An identity matrix of order 1; For the first Line 1 A matrix where each column element is 1 and all other elements are 0 (i.e., only the elements in the column are 1). 1).

[0040] More intuitively, The elements are:

[0041] When the joint matrix Right multiplication At that time, the first The column was added to the first On the list, thus realizing the components The connection relationship is transferred to the component. .

[0042] It is The elementary permutation matrix, whose function is to transform the first... Swap the row (and column) to the last row (and column). The specific structure is as follows: First, the identity matrix The Line and last line (the) By swapping rows, we obtain a permutation matrix. ; Then the first Swap the first column with the last column to get .

[0043] Because both rows and columns are swapped simultaneously, It is symmetrical and satisfies Its non-zero element positions are:

[0044] When the joint matrix Left multiplication At that time, the first Move the row to the last row; right multiply At that time, the first Move the column to the last column.

[0045] Step S56: Perform elimination processing on the joint matrix according to the inter-stage connection relationship to obtain an adjacency matrix that can completely represent the overall topology of the multi-stage planetary gear mechanism. Thus, an adjacency matrix model of the configuration scheme of the multi-stage planetary gear transmission mechanism is established.

[0046] in, It is A diagonal matrix is ​​used to clear the last row and last column of the current joint matrix to zero:

[0047] Right now The elements are:

[0048] When the joint matrix Left multiplication When the last row is cleared to zero; multiply by the right. At that time, the last column is cleared to zero.

[0049] Based on the above definition, the first The transformation matrix corresponding to the merge operation is: In turn, for Execute, and you can By gradually eliminating shared components between levels, the overall adjacency matrix is ​​finally obtained. .

[0050] Step S6: Establish a motion topology model of the multi-stage planetary gear transmission mechanism based on the adjacency matrix model, and construct the corresponding transmission ratio matrix; based on the input component speed and the motion constraint relationship between components, establish the speed constraint equation of the multi-stage planetary gear transmission mechanism, and matrix-represent the speed constraint equation as a transmission ratio matrix to solve for the speed of each component and the total transmission ratio of the system.

[0051] Specifically, step S6 includes: Step S61, using , , , The rotational speeds of the sun gear, planet gears, planet carrier, and internal gear ring are represented respectively, and the basic transmission ratio relationship of a common planetary gear transmission system is established based on the Willis equation. Specifically, according to Willis's equations, the transmission ratio expression for a typical planetary gear transmission system is as follows:

[0052] in, Indicates when the planetary frame When fixed, the gear With gears The transmission ratio. For the sun gear and the ring gear, there is... ,in, This represents the transmission ratio between the sun gear and the ring gear relative to the planet carrier. Indicates the number of teeth on the sun gear. This indicates the number of teeth on the gear ring.

[0053] Step S62: Based on the internal and external meshing relationships of the planetary gear mechanism, establish the speed constraint equations for each basic motion unit, and matrix-represent the speed constraint equations as a transmission ratio matrix. And satisfy , The transmission ratio matrix is ​​a column vector composed of the rotational speeds of each component in the system. The rotational speeds of each component and the total transmission ratio of the system are obtained by solving the transmission ratio matrix.

[0054] Among them, combined Figure 2The hypergraph model of the planetary gear transmission with internal and external meshing relationships shown can be used to derive and establish the speed constraint equations for the external meshing pairs (sun gear and planet gears) and internal meshing pairs (planet gears and ring gear) of the mechanism.

[0055] The speed constraint equation for the external meshing pair is:

[0056] The speed constraint equation for the internal meshing pair is:

[0057] in, , This represents the gear ratio between the sun gear and the planet gears. The number of teeth on the sun gear. This represents the number of teeth on the planetary gear. , The ratio of the number of teeth between the planetary gears and the ring gear is given. This represents the number of teeth on the gear ring.

[0058] Equating the above two equations together, we can eliminate the planetary gear speed. From this, we can obtain the transmission ratio between the sun gear and the ring gear relative to the planet carrier:

[0059] In a planetary gear mechanism, each basic motion unit essentially corresponds to the dynamic coupling relationship of a gear pair. Therefore, the number of basic units is consistent with the number of gear pairs involved in meshing. After expressing the constraints between these motion units in matrix form, the transmission ratio matrix can be defined. And satisfy In a planetary gear mechanism, the number of basic motion units is equal to the number of gear pairs. As long as the rotational speed of the input component is given, the overall transmission ratio of the planetary gear transmission system and the rotational speed of each component can be calculated.

[0060] Step S7: Based on the adjacency matrix established in step S5 and the motion topology model established in step S6, the configuration of the multi-stage planetary gear transmission mechanism is generated, and the corresponding configuration scheme of the multi-stage planetary gear transmission mechanism is generated according to the connection relationship and constraint conditions between the components.

[0061] Step S8: The Hamming matrix method is used to perform isomorphism discrimination on the multi-stage planetary gear transmission mechanism configuration scheme generated in step S7. By comparing the differences between the adjacency matrices of different configuration schemes, duplicate isomorphic configurations are identified and removed to obtain effective multi-stage planetary gear transmission configuration schemes that meet the constraints.

[0062] The Hamming matrix can determine whether kinematic chains with the same number of components are isomorphic. It is a feature array obtained by arranging the Hamming number of the kinematic chain and the Hamming value of each component in descending order as the judgment index. That is, if the feature arrays of the Hamming matrix of each kinematic chain are completely the same, then the two kinematic chains are isomorphic (the Hamming number refers to the sum of all elements in the Hamming matrix, and the Hamming value refers to the sum of the elements in each row of the Hamming matrix).

[0063] Specifically, step S8 employs the Hamming matrix method for isomorphism discrimination. By constructing a Hamming matrix feature array and comparing the Hamming count and the Hamming values ​​of each component, isomorphism identification of multi-stage planetary gear configurations is achieved. The Hamming matrix of the kinematic chain is built upon its adjacency matrix, and consists of diagonal elements with zeros. A square matrix of order 1, with off-diagonal elements By comparing the adjacency matrix column by column, the first... row and number Each element in the row is analyzed, and an XOR operation is performed to determine its order. The specific formula is as follows:

[0064]

[0065] in, It is the th in the Hamming matrix Line 1 Row elements, As an intermediate variable, Adjacency matrix The Middle Line 1 Column elements, Adjacency matrix The Middle Line 1 Column elements, Represents the XOR operation; The Hamming matrix feature array is then calculated, and the kinematic chains are determined to be isomorphic by judging whether the feature arrays are the same.

[0066] Step S9: Verify the validity of the isomorphism discrimination result obtained in step S8, and obtain an effective multi-stage planetary gear transmission mechanism configuration scheme that satisfies the constraints.

[0067] Specifically, step S9 includes: validating the isomorphism judgment result of the Hamming matrix method using the eigenvalue and eigenvector method; wherein, the eigenvalue and eigenvector method calculates the eigenvalues ​​and eigenvectors of the adjacency matrix of the multi-stage planetary gear mechanism configuration scheme, compares the eigenvalues ​​and corresponding eigenvectors of each adjacency matrix one by one, if the eigenvalues ​​are completely the same, and their eigenvector matrix can be transformed into the eigenvector matrix of another adjacency matrix through row transformation or column transformation, then the two configuration schemes of the multi-stage planetary gear mechanism are isomorphic and this configuration needs to be removed; otherwise, a new configuration is obtained.

[0068] In this embodiment, the discrimination process of the eigenvalue and eigenvector method is specifically as follows: set up and These are the adjacency matrices of two multi-stage planetary gear mechanism configurations. and eigenvalues; and These are the eigenvectors corresponding to the eigenvalues; according to matrix theory, a nonsingular matrix is ​​constructed using the eigenvectors as column vectors. and ,but:

[0069]

[0070] If two multi-stage planetary gear mechanism configurations are isomorphic, then the matrices established using the eigenvectors corresponding to their adjacency matrices can be mutually converted through row or column transformations, i.e.:

[0071] in, Represents a diagonal matrix. This represents an invertible transformation matrix.

[0072] By comparing and analyzing the results, the results of the Hamming matrix method are completely consistent with those of the eigenvalue and eigenvector method, which shows that the Hamming matrix method is effective in isomorphic discrimination of multi-stage planetary gear mechanism configuration schemes.

[0073] The following is a specific example to illustrate the above method in detail.

[0074] by Figure 5 and Figure 6 Taking the adjacency matrix of the two-stage planetary gear mechanism shown in the figure as an example, a 1. a 2. a 3 represents the nodes of the sun gear, planet carrier, and gear ring in the first-stage planetary array, respectively;b 1. b 2. b 3 represents the nodes of the sun gear, planet carrier, and gear ring in the second-stage planetary array, respectively; p a , p b These are auxiliary markers used in hypergraph models to indicate meshing relationships and do not represent independent component nodes; in Indicates the power input port. out This indicates the power output port. Comparing the elements in the first and second rows yields... h 12 = (0) + (1 + 0) = 1, and thus its Hamming matrix can be obtained. as follows:

[0075] The Hamming values ​​of each component are 2, 4, 2, 4, respectively, and the corresponding Hamming number is 12. Their feature arrays are arranged in descending order as 12[4,4,2,2].

[0076] Similarly, Figure 7 Isomorphism discrimination of the three configurations: Based on the adjacency matrix form and transformation rules of planetary gear trains, establish two-level planetary gear train adjacency matrices for schemes 1, 2, and 3, namely:

[0077]

[0078]

[0079] After step S8, the Hamming matrices corresponding to schemes 1, 2, and 3 are calculated as follows: Option 1:

[0080] Option 2:

[0081] Option 3:

[0082] Calculations show that the Hamming matrix feature array of scheme 1 is 14 [5,3,3,3]; the feature arrays of schemes 2 and 3 are 8 [2,2,2,2]. Since the feature array is a key criterion for determining the isomorphism of a kinematic chain, when the feature arrays of two schemes are completely identical, they can be considered isomorphic kinematic chains, such as schemes 2 and 3; while schemes 1 and 2 or 3 are non-isomorphic.

[0083] To further illustrate the application capability of the hypergraph representation method proposed in this invention in complex multi-stage planetary gear transmission systems, Figure 8 and Figure 9 The load-splitting planetary gear transmission system shown is analyzed as an example. Among them, s 1. s 2 is a double-row sun gear. r 1 represents the first-stage internal gear ring. cr It is a compound planetary carrier (also serving as the second-stage internal gear ring). r 2) p 1. p 2 is a compound double planetary gear. s 3 is the second-order sun gear. p 3 is a second-stage planetary gear. c For a secondary planetary carrier, to address the issue of non-standard topological closure caused by component reuse, a virtual fixed component is introduced. rd The actual physical connection relationships are converted into a standard closed hypergraph structure, and a complete hypergraph model and corresponding adjacency matrix are established accordingly.

[0084] Figure 8 This is a load-splitting planetary gear transmission system. By connecting the first-stage planetary carrier and the second-stage internal gear ring, the input torque is shared by both the first-stage and second-stage planetary gear sets during transmission, thus forming a multi-stage planetary gear transmission structure with load-splitting characteristics. This structure is one of the typical solutions for achieving high power density transmission requirements. According to the hypergraph mapping rules in steps S1 to S4, the transmission system is converted into the corresponding hypergraph model, i.e. Figure 9 .

[0085] To further illustrate the applicability of the hypergraph representation method proposed in this invention to complex load-splitting planetary gear transmission systems, the following is discussed: Figure 8 The kinematic characteristics of the load-splitting planetary gear transmission system shown are analyzed. Kinematic models of the transmission system are established using both the traditional transformation mechanism method and the Willis unified modeling method based on hypergraph theory, and the transmission ratio results obtained by the two methods are compared.

[0086] According to the transformation mechanism method, the speed ratio of the driving and driven gears relative to the planetary carrier satisfies the following relationship with the number of teeth:

[0087] in, The speed ratio between the driving wheel and the driven wheel. , These are the rotational speeds of the two central gears (sun gear or ring gear). The rotational speed of the planetary carrier, , These represent the number of teeth on the two central gears. Gear to gear The number of times the two parts mesh (determines the sign; odd numbers are negative and even numbers are positive).

[0088] The above is the general expression of the transformation mechanism method. Below, we will combine it with... Figure 8 and Figure 9 A specific example analysis is conducted on the load-splitting planetary gear transmission system shown.

[0089] Based on the structural composition and gear meshing relationship of a high-speed, heavy-duty compound planetary gear transmission system, corresponding transmission ratio constraint equations can be established. For a single planetary gear set, when one basic component is fixed and the other two components are used as the input and output ends respectively, a definite transmission ratio relationship can be obtained. When multiple planetary gear sets are coupled according to a specific topological relationship to form a compound transmission structure, the system transmission ratio is jointly determined by the kinematic constraint relationships of each stage of the planetary gear set.

[0090] In this embodiment, a compound internal gear ring is provided. r 1. Fixed, with a double planetary carrier cr As an input component, the secondary sun gear s 3. As the output component, the following transmission ratio relationship can be established according to the conversion mechanism method:

[0091] in, This indicates that when the planet carrier is fixed, the sun gear... s 1 and the first-stage internal gear ring r The transmission ratio between 1 and 1 For the sun wheel s 1 rotational speed, Dual planetary carrier cr The rotational speed (which also serves as the first-stage planetary carrier and the second-stage internal gear ring). For the first stage internal gear ring r 1 rotational speed, For the first stage internal gear ring r Number of teeth 1 For the sun wheel s The number of teeth in a 1.

[0092] because , can be obtained s 1 and cr The relationship between rotational speeds:

[0093] For a compound planetary gear structure, by combining the fixed constraint relationship of the double planetary gears and the connection relationship of each level of components, it is possible to further obtain... s 2 and cr The relationship between rotational speeds:

[0094] in, For the sun wheel s 2 rotational speed (and) s 1. Fixed or coaxial). For the first-stage planetary gear p Number of teeth 1 For the second-stage planetary gear p Number of teeth 2 (and) p 1. Fixed connection to form a double planetary gear. For the sun wheel s 2. Number of teeth.

[0095] And the transmission ratio relationship of the second-stage planetary gear set:

[0096] in, When the planetary carrier is fixed, the second-stage sun gear s 3. Gear ring (here, the gear ring is a compound planetary carrier) cr The transmission ratio between (both of which are combined); Secondary sun gear s 3 revolutions per minute; For the second-stage planetary support c The rotational speed; Dual planetary carrier cr The rotational speed; Dual planetary carrier cr The number of teeth when used as an internal gear ring (i.e., the number of teeth of the second-stage internal gear ring). Secondary sun gear s 3 teeth.

[0097] By combining the above constraint equations, the overall transmission ratio of this load-splitting planetary gear transmission system can be obtained:

[0098] in, For a compound planetary carrier cr For input, secondary sun gear s 3 represents the total transmission ratio of the system at output.

[0099] On the other hand, based on the hypergraph representation rules established in steps S1 to S4, the transmission system is represented as a hypergraph model composed of component nodes, meshing hyperedges, and kinematic constraint hyperedges. The hypergraph method uses system components as nodes and meshing and kinematic constraint relationships as hyperedges. By constructing structural correlation matrices and kinematic constraint matrices, the kinematic relationships of the complex planetary gear transmission system are uniformly represented as a system of linear algebraic equations, namely: Specifically:

[0100] in, , , For planetary wheels p 1. p 2. p 3 rotational speeds.

[0101] according to Figure 9 The hypergraph model can be used to establish the system matrix equations as follows:

[0102] By eliminating variables from the above matrix equations, the total transmission ratio of this load-splitting planetary gear transmission system can be obtained:

[0103] Comparing the total transmission ratio obtained based on hypergraph theory with the calculation results from the transformation mechanism method, it was found that the results obtained by the two methods are completely consistent, indicating that the hypergraph model established in this invention can accurately describe the kinematic constraint relationships and transmission characteristics of complex load-splitting planetary gear transmission systems. These results demonstrate that the hypergraph representation method proposed in this invention can not only realize the configuration expression and isomorphism discrimination of multi-stage planetary gear transmission mechanisms, but also be further applied to the unified kinematic modeling and transmission characteristic analysis of complex planetary gear transmission systems, thus verifying the applicability and effectiveness of this method in the analysis of complex multi-stage planetary gear transmission systems.

[0104] In summary, the multi-stage planetary gear transmission design method based on hypergraph representation according to the above embodiments has the following beneficial effects: 1. This invention maps functional components to hypergraph nodes using a unified symbol identification rule, and expresses inter-stage connections and load splitting relationships as cross-stage hyperedges through a combined hypergraph model. Since the hypergraph model can directly describe the load splitting topology of input nodes simultaneously connecting multiple transmission stages, this invention is particularly suitable for structural modeling and configuration analysis of high-power-density load-splitting multi-stage planetary gear transmission systems (such as wind turbine speed increasers and aerospace transmissions), providing a theoretical basis and technical support for the configuration design of complex mechanical transmission systems.

[0105] 2. This invention uses hypergraph theory to establish a topological representation model of a multi-stage planetary gear transmission mechanism. Since the hyperedges in the hypergraph can directly express the meshing, connection, and motion coupling relationships between multiple components, while traditional graph theory can only describe the pairwise connection relationships between nodes, this invention realizes a unified modeling of the topological structure of complex multi-stage planetary gear transmission mechanisms. It can fully reflect the motion topology characteristics and multi-component coupling relationships of the mechanism, improving the completeness, accuracy, and scalability of the mechanism representation. It is especially suitable for high power density load-splitting transmission systems.

[0106] 3. This invention establishes a standardized multi-stage planetary gear configuration expression system based on the mapping relationship between hypergraph models and adjacency matrices. Since hypergraph models can be converted into adjacency matrices for digital description and configuration schemes can be automatically generated based on connection relationships and constraints, this invention achieves digital description and automatic generation of configuration schemes for multi-stage planetary gear transmission mechanisms. This reduces the reliance on manual experience in the design of complex transmission system configurations and improves configuration design efficiency and scheme scalability.

[0107] 4. This invention constructs a method for isomorphic discrimination of multi-stage planetary gear configurations based on adjacency matrix and Hamming matrix. Since the Hamming matrix only depends on topological connection relationship and not on node symbols, it can quickly identify and filter out topologically equivalent repeating configurations. Therefore, this invention avoids redundant design and analysis, improves configuration screening efficiency and topology discrimination accuracy, and can be used for efficient configuration screening and analysis of load-splitting multi-stage planetary gear transmission structures. It is also suitable for structural design requirements in high power density transmission scenarios.

[0108] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A design method for multi-stage planetary gear transmission based on hypergraph representation, characterized in that, include: Step S1: Establish functional component identification rules and hypergraph mapping rules for the planetary gear transmission mechanism. Define functional components including sun gear, planet gear, internal gear ring, planet carrier and frame in a unified manner, and establish a hypergraph representation of the connection relationship and motion coupling relationship between components. Step S2: Based on the functional component identification rules and hypergraph mapping rules established in Step S1, establish the motion relationship diagram of the planetary gear transmission mechanism, and construct the internal meshing motion unit and the external meshing motion unit according to the meshing relationship between the components. Step S3: Based on the motion relationship diagram established in step S2, the hypergraph of the single-stage planetary gear transmission system is simplified. In order to adapt to the unified modeling requirements of multi-stage planetary gear transmission systems, planetary gear nodes are omitted, and only key component nodes representing topological connection relationships are retained. Step S4: Based on the simplified hypergraph in Step S3, multiple single-stage planetary gear transmission mechanisms are combined and connected to establish a multi-stage planetary gear transmission mechanism combination hypergraph model, so as to uniformly abstract and express the complex structural relationship and multi-component coupling relationship of the multi-stage planetary gear system. Step S5: Convert the multi-stage planetary gear transmission mechanism combined hypergraph model established in step S4 into the corresponding adjacency matrix to realize the digital expression of the structural relationship of the multi-stage planetary gear transmission mechanism and establish the adjacency matrix model of the configuration scheme of the multi-stage planetary gear transmission mechanism. Step S6: Establish a motion topology model of the multi-stage planetary gear transmission mechanism based on the adjacency matrix model, and construct the corresponding transmission ratio matrix; based on the input component speed and the motion constraint relationship between components, establish the speed constraint equation of the multi-stage planetary gear transmission mechanism, and matrix-represent the speed constraint equation as a transmission ratio matrix to solve for the speed of each component and the total transmission ratio of the system. Step S7: Based on the adjacency matrix established in step S5 and the motion topology model established in step S6, the configuration of the multi-stage planetary gear transmission mechanism is generated, and the corresponding configuration scheme of the multi-stage planetary gear transmission mechanism is generated according to the connection relationship and constraint conditions between the components. Step S8: The Hamming matrix method is used to perform isomorphism discrimination on the multi-stage planetary gear transmission mechanism configuration scheme generated in step S7. By comparing the differences between the adjacency matrices of different configuration schemes, duplicate isomorphic configurations are identified and removed to obtain effective multi-stage planetary gear transmission configuration schemes that meet the constraints. Step S9: Verify the validity of the isomorphism discrimination result obtained in step S8, and obtain an effective multi-stage planetary gear transmission mechanism configuration scheme that satisfies the constraints. Step S1 specifically includes: The functional components in planetary gear transmission mechanisms are identified by standardized symbols. Indicates planetary support, Represents the sun wheel, Indicates planetary gears, This represents the internal gear ring; and by appending numbers after the symbol to indicate the component identifiers of different levels in the multi-stage planetary gear transmission mechanism, a hierarchical expression of the multi-stage gear system is achieved; in the hypergraph topology model, each functional component is uniformly abstracted as a hypergraph node, and the kinematic pair connection relationship, gear meshing relationship, and kinematic coupling relationship between components correspond to hyperedges; among them, the external meshing relationship between the sun gear and the planet gears adopts... This indicates that the internal meshing relationship between the planetary gears and the internal gear ring is adopted. It is indicated that in the bearing support relationship, the slewing pair, the frame fixing relationship, and the slewing pair respectively adopt... , , This indicates that in the isomorphism determination process, the connection relationship between hypergraph nodes is used as the basis for determination, and the node symbol is only used as a component identifier and does not affect the determination result of the topological isomorphism relationship.

2. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 1, characterized in that, Step S5 specifically includes: Step S51: Construct an initial adjacency matrix based on the multi-stage planetary gear transmission mechanism combined hypergraph model, where the matrix elements... Used to characterize nodes With nodes The connection state between them; when When, it indicates a node With nodes There is a connection between them, when When, it indicates a node With nodes There is no connection between them; Step S52: Establish the adjacency matrix corresponding to each level of planetary gear transmission unit. , , , They represent level 1, level 2, and level 3 respectively. The adjacency matrix corresponding to the stage planetary gear transmission unit. The total number of stages in a multi-stage planetary gear transmission mechanism is given, and a joint matrix is ​​constructed based on the actual component connection relationships between each stage. This is used to describe the overall topology of a multi-stage planetary gear mechanism. It is A block diagonal matrix, with adjacency matrices arranged sequentially along the main diagonal. A matrix in which all other off-diagonal positions are zero. It is the total number of all independent components in a multi-stage planetary gear transmission mechanism. , Indicates the first The number of independent components in a planetary gear transmission unit. The expression is: in, For the first The adjacency matrix of a multi-stage planetary gear transmission unit. Indicates the first The extended transformation matrix corresponding to the multi-stage planetary gear transmission unit. The size is , Indicates transpose; Step S53: The dimensions of the adjacency matrices at all levels are unified by matrix expansion operation. Zero elements are added to the original adjacency matrices to form an expanded matrix with the same order. Step S54: Based on the connection relationships between components in the multi-stage planetary gear mechanism, perform a joint matrix analysis. Perform row and column rearrangement and matrix transformation processing to realize the mapping of the connection relationship between different levels of planetary transmission units; Step S55: Adjust the position of the corresponding nodes of the associated components and reconstruct the connection relationship through matrix transformation; Step S56: Perform elimination processing on the joint matrix according to the inter-stage connection relationship to obtain the adjacency matrix that can completely represent the overall topology of the multi-stage planetary gear mechanism. Thus, an adjacency matrix model of the configuration scheme of the multi-stage planetary gear transmission mechanism is established.

3. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 2, characterized in that, Step S6 specifically includes: Step S61, using , , , Let $\mathbf$ represent the rotational speeds of the sun gear, planet gears, planet carrier, and internal ring gear, respectively. Based on Willis's equations, the fundamental transmission ratio relationships of a typical planetary gear transmission system are established, where the transmission ratios of the sun gear and ring gear relative to the planet carrier are... , Indicates the number of teeth on the sun gear. Indicates the number of teeth on the gear ring; Step S62: Based on the internal and external meshing relationships of the planetary gear mechanism, establish the speed constraint equations for each basic motion unit, and matrix-represent the speed constraint equations as a transmission ratio matrix. And satisfy , The transmission ratio matrix is ​​a column vector composed of the rotational speeds of each component in the system. The rotational speeds of each component and the total transmission ratio of the system are obtained by solving the transmission ratio matrix.

4. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 3, characterized in that, Step S8 employs the Hamming matrix method for isomorphism discrimination. By constructing a Hamming matrix feature array and comparing the Hamming count and Hamming values ​​of each component, isomorphism identification of multi-stage planetary gear configurations is achieved. Specifically, the Hamming matrix of the kinematic chain is built upon its adjacency matrix, and consists of diagonal elements with zeros. Off-diagonal elements of a Hamming matrix (or similar square matrix). Determined by the following formula: in, It is the th in the Hamming matrix Line number Row elements, As an intermediate variable, Adjacency matrix The Middle Line number Column elements, Adjacency matrix The Middle Line number Column elements, Represents the XOR operation; The Hamming matrix feature array is then calculated, and the kinematic chains are determined to be isomorphic by judging whether the feature arrays are the same.

5. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 4, characterized in that, Step S9 specifically includes: verifying the effectiveness of the isomorphism determination result of the Hamming matrix method using the eigenvalue and eigenvector method; wherein, the eigenvalue and eigenvector method calculates the eigenvalues ​​and eigenvectors of the adjacency matrix of the multi-stage planetary gear mechanism configuration scheme, compares the eigenvalues ​​and corresponding eigenvectors of each adjacency matrix one by one, and if the eigenvalues ​​are completely the same, and their eigenvector matrix can be transformed into the eigenvector matrix of another adjacency matrix through row transformation or column transformation, then the two configuration schemes are determined to be isomorphic.

6. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 5, characterized in that, The specific process of the eigenvalue and eigenvector method for discrimination is as follows: set up and These are the adjacency matrices of two multi-stage planetary gear mechanism configurations. and eigenvalues; and These are the eigenvectors corresponding to the eigenvalues; according to matrix theory, a nonsingular matrix is ​​constructed using the eigenvectors as column vectors. and ,but: If two multi-stage planetary gear mechanism configurations are isomorphic, then the matrices established using the eigenvectors corresponding to their adjacency matrices can be mutually converted through row or column transformations, i.e.: in, Represents a diagonal matrix. This represents an invertible transformation matrix.

7. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 1, characterized in that, Step S2 specifically includes: based on the functional component identification rules and hypergraph mapping rules established in step S1, dividing the four basic motion components in the planetary gear transmission mechanism—sun gear, internal gear ring, planet carrier, and planet gear—into external meshing motion units and internal meshing motion units according to their meshing relationships, and establishing a motion relationship diagram of the planetary gear transmission mechanism.

8. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 1, characterized in that, Step S4 specifically includes: combining and connecting the hypergraphs of multiple single-stage planetary gear transmission mechanisms simplified in step S3; transforming the planetary gear train structure diagram into a hypergraph topology model; establishing a combined hypergraph model of multi-stage planetary gear transmission mechanisms; and providing a unified abstract expression of the complex structural relationships and multi-component coupling relationships of multi-stage planetary gear trains.

9. The multi-stage planetary gear transmission design method based on hypergraph representation according to claim 8, characterized in that, The input node in the hypergraph model is connected to both the first-stage planetary transmission unit and at least one subsequent-stage planetary transmission unit, giving the input node a hyperedge association relationship corresponding to multiple transmission stages. This characterizes the load splitting topology where the input torque is simultaneously distributed to multiple planetary transmission stages.

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