Improvements in or relating to a variable cross-section multi-gap coupling arrangement for a driveline

Abstract

The application discloses a variable cross-section multi-gap coupling structure improvement method for a transmission system, relates to the technical field of coupling structure improvement, and comprises the following specific steps: performing finite element analysis on the coupling of the obtained initial material occupancy to obtain a growth guide potential field; calculating the maximum value of Chebyshev distance of an ideal performance state vector to obtain a global performance supply-demand deviation; and performing simulation solution on the reserved candidate variable cross-section multi-gap coupling geometric model to determine an optimal configuration. In the application, growth probes are arranged in each axial control section, the growth guide potential field and the energy local potential field are combined to guide the extension direction of the probes, the traditional empirical gap arrangement design is replaced, and according to the material density characteristic differentiation along the way, the high material density area is solidified into a solid reinforcing rib to strengthen the force transmission path, and the integration and collaborative forming of the reinforcing structure, the gap network and the variable cross-section profile are realized, so that stress concentration caused by boundary mutation is effectively avoided.

Description

Technical Field

[0001] This invention relates to the field of coupling structure improvement technology, specifically to a method for improving the structure of a variable cross-section multi-gap coupling for a transmission system. Background Technology

[0002] Couplings are core components of mechanical transmission systems, primarily used to connect two shafts to transmit torque and motion, while also compensating for shaft misalignment and providing damping and vibration reduction. Variable cross-section multi-gap couplings, through their variable cross-section profile design of elastic bodies and distributed gap structure, combine adjustable stiffness with damping and vibration reduction characteristics, and are widely used in transmission scenarios involving torsional vibration, such as those in automobiles, wind power, and industrial equipment.

[0003] Currently, the structural design of variable cross-section multi-gap couplings is mainly based on empirical design and parametric iteration. Typically, the basic cross-sectional form and gap arrangement rules are determined first, and then verified and adjusted through finite element simulation. However, the evolution of the gap topology distribution and cross-sectional profile lacks a systematic global optimization mechanism, making it difficult to simultaneously consider the torsional stiffness matching accuracy, damping energy dissipation efficiency, and heat dissipation performance of the gap network. This often results in problems such as excessive or insufficient stiffness and a mismatch between damping capacity and actual working conditions. Furthermore, existing schemes that apply topology optimization methods to coupling design often use binary material distribution models, resulting in overly rigid initial geometric boundaries. During the optimization process, checkerboard effects are prone to occur, leading to unsmooth configuration boundaries and poor subsequent processing capabilities. The optimization process often focuses on static mechanical performance as the core objective, rarely incorporating torsional vibration dynamic response and elastic wave energy distribution characteristics into the optimization closed loop. This makes it impossible to actively control energy distribution at the vibration propagation level, and it is difficult to fundamentally alleviate local vibration concentration and fatigue problems. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for improving the structure of a variable cross-section multi-clearance coupling for a transmission system, comprising the following specific steps: S1. The three-dimensional computational domain of the elastic body based on the variable cross-section multi-gap coupling is meshed to obtain hexahedral volume elements. After discretizing the initial profile of the coupling into an ordered point array, the initial material occupancy density value is assigned to the obtained hexahedral volume elements, and the obtained initial material occupancy is used for finite element analysis of the coupling to obtain the growth guiding potential field. S2. Apply torque load based on coupling configuration, introduce complex stiffness matrix of coupling material constitutive based on coupling model, perform solid-clearance partitioning based on coupling configuration, integrate the obtained torsional stiffness supply matching index, damping energy demand satisfaction index, and clearance network flow efficiency cost ratio into material distribution performance supply and demand vector, calculate the maximum value of Chebyshev distance from the ideal performance state vector, and obtain global performance supply and demand deviation. S3. Set growth probes for each axial control section of the coupling, and convert the material occupancy density field of all volume elements into an elastic wave equivalent refractive index field. Apply broadband torsional angular displacement excitation to all nodes on the inner ring connection interface of the coupling. Perform dynamic simulation of the coupling in the frequency domain. Use the weighted time-averaged energy density of the simulated elastic wave to determine the energy local center. Perform material coordination redistribution on the energy local potential field and the material distribution performance supply and demand vector. Update the growth guiding potential field according to the redistributed equilibrium material occupancy density field. Iteratively grow the growth probes. After growth, construct the gap network diagram and obtain the current final material occupancy density distribution. Generate the corresponding variable cross-section multi-gap coupling geometric model. Replace the current material and repeat S1-S3. Finally, retain several candidate variable cross-section multi-gap coupling geometric models. Perform simulation and solve the retained candidate variable cross-section multi-gap coupling geometric models to determine the optimal configuration.

[0005] Preferably, S1 performs structured meshing in the cylindrical coordinate system along the radial, circumferential and axial directions based on the three-dimensional computational domain of the elastic body of the variable cross-section multi-gap coupling to obtain several adjacent hexahedral volume elements, obtain the initial profile of the original design of the coupling, discretize the initial profile into a set of ordered points, and map the pre-set gap opening position into a circumferential angle range. Based on each volume element, the cylindrical coordinates of eight vertices in the ordered point sequence are extracted. The ratio of the radial coordinate of each vertex's cylindrical coordinate to the radial boundary of the initial profile at the axial section is used as the spatial mapping reference. The cylindrical coordinates of each vertex are then converted to the original design parameters for spatial position determination and assignment, including the following specific settings: If all eight vertices of any volume element are located within the solid region enclosed by the initial profile after spatial mapping, and the circumferential angle is not located within the circumferential angle range of any gap opening, then the initial material occupancy density of the corresponding volume element is assigned to one. If all eight vertices of any volume element are located outside the solid region and / or fall within the gap opening, assign the initial material occupancy density of the volume element to zero. After determining and assigning values ​​to the spatial positions of all volume units, the initial material occupancy field is obtained.

[0006] Preferably, the initial material occupancy field is converted into a finite element analysis model of the coupling, and a fixed constraint is applied to the inner ring mounting surface of the coupling, and a rated torque is applied to the outer ring connecting flange of the coupling. The overall stiffness matrix is ​​obtained through numerical solution of finite element analysis. The overall stiffness matrix is ​​decomposed based on sparse matrix, and the displacement vectors of all volume elements are calculated. Based on the displacement vectors and through spatial differential operators, the six strain components of each volume element are calculated. Based on the stress components of the coupling material constitutive matrix, tensor contraction operation is performed on the stress components and strain components to obtain the first principal strain energy density scalar of each volume element. The reciprocal of the first principal strain energy density of all volume elements is normalized by range to obtain the generation guiding potential of each volume element, and the spatial distribution field formed by the growth guiding potential of all volume elements is taken as the growth guiding potential field.

[0007] Preferably, in step S2, a torque load is applied to the coupling configuration corresponding to the current material occupancy location, increasing linearly from zero to the rated value. A static torque loading numerical simulation is performed to obtain a continuous torque-torque angle curve. Based on the initial point where both torque and torsion angle are zero in the torque-torque angle curve, the torsion angle is increased by taking an integer multiple of the curve sampling resolution as the trial step size based on the direction of torsion angle increase. Local linear regression is performed on the torque increment and torsion angle increment corresponding to each trial step size to obtain the tangential stiffness at zero torsion angle. Based on the design target stiffness of the transmission system, the ratio of the tangential stiffness to the design target stiffness is calculated, and the obtained ratio is mapped using a logarithmic function with the natural logarithm as the base to obtain the torsional stiffness supply matching index. Based on the complex stiffness matrix of the coupling material constitutive model, a complex characteristic equation containing inertia terms and a complex stiffness matrix is ​​constructed. Complex eigenvalues ​​and complex eigenvectors are obtained by iterative solution based on eigenvalues. The real part of each complex eigenvalue is taken as the natural frequency of the mode, and the ratio of the imaginary part to the real part is taken as the modal loss factor of the mode. The equivalent static load projection amplitude of the rated torque is taken as the modal participation factor of each mode. Based on the modal participation factor as the weight, all modal loss factors are weighted and summed to obtain the weighted modal loss factor. Based on the ratio of the equivalent target loss factor under all working conditions required by the design to the weighted modal loss factor, the damping energy consumption demand satisfaction index is obtained. Then, based on the material occupancy field of the current coupling configuration, the solid-void partitioning is performed. Specifically, the partitioning threshold is determined by the material occupancy density value of all volume units based on the Otsu's method. The moving cube algorithm is used to generate the interface mesh of solid and void composed of triangular facets with the boundary between solid and void as the isosurface. The total area of ​​all triangular facets is calculated to obtain the total interface area. The volume of all volume units with material occupancy density lower than the boundary between solid and void is accumulated to obtain the void volume. The ratio of the total interface area to the void volume is used as the flow efficiency cost ratio of the void network. The torsional stiffness supply matching index, damping energy demand satisfaction index, and gap network flow efficiency cost ratio are sequentially constructed into a three-dimensional vector, which serves as the material distribution performance supply and demand vector. An ideal performance state vector is set, and the Chebyshev distance between the material distribution performance supply and demand vector and the ideal performance state vector is calculated. The maximum value of the Chebyshev distance is taken as the global performance supply and demand deviation.

[0008] Preferably, in step S3, seed points are selected along the circumferential direction at predetermined angular intervals based on the initial material occupancy field and the growth guiding potential field on each axial control section of the coupling. Then, a growth probe consisting of a curve structure composed of a sequence of discrete nodes connected end to end is initialized at each seed point. The initial spatial position of the growth probe is set to the center of the volume unit with the highest material occupancy density value on the control section, and the spatial gradient vector direction where the growth guiding potential field is located is used as the initial extension direction of the growth probe. Based on the reference high refractive index value of pure solid materials and the reference low refractive index value of materials with complete porosity, the material occupancy density field of all current volume units is transformed into an elastic wave equivalent refractive index field.

[0009] Preferably, S3 applies a broadband torsional angular displacement excitation covering the torsional vibration characteristic frequency range of the transmission system to all nodes on the inner ring connection interface of the coupling model based on the elastic wave equivalent refractive index field, and obtains the normalized excitation weight coefficient at each discrete frequency point in the broadband torsional angular displacement excitation through discrete sampling. The equivalent material modulus of each discrete frequency point is obtained by converting it into the equivalent refractive index field of the elastic wave at the corresponding frequency. The equivalent material modulus of each volume element is substituted into the numerical integration process of the element stiffness matrix to obtain the overall dynamic stiffness matrix. The reset displacement response vector of all volume elements is solved by the complex domain sparse matrix, and the elastic wave weighted time average energy density of each volume element is calculated based on the normalized excitation weight coefficient.

[0010] Preferably, in step S3, the full-field arithmetic mean and full-field standard deviation of the elastic wave weighted time-averaged energy density of all volume elements are calculated. Volume elements with elastic wave weighted time-averaged energy density values ​​higher than the full-field arithmetic mean plus the full-field standard deviation are marked as high-energy localized elements. Spatial connectivity analysis is performed on the high-energy localized elements, and adjacent high-energy localized elements at all faces, edges and / or vertices in the coupling are merged into connected clusters. The equivalent diameter of each connected cluster is calculated. When the equivalent diameter of any connected cluster is smaller than the wavelength of the elastic wave in the solid material at the upper limit of the excitation frequency, it is determined to be an energy local center, and all the determined energy local centers are combined into a global energy local center set. For volumetric units belonging to any energy local center, the normalized value of the ratio of the elastic wave weighted time-averaged energy density to the maximum elastic wave weighted time-averaged energy density in the entire field is taken as the energy local potential. For volumetric units that do not belong to any energy local center but are adjacent to any energy local center, the potential value of the energy local center closest to them is taken as the energy local potential. The energy local potential of volumetric units that are not adjacent to any energy local center is taken as a negative value. The spatial distribution field formed by the energy local potential of all volume units is taken as the energy local potential field.

[0011] Preferably, in step S3, the initial material occupancy density value of all volume units is used as the initial material holding amount, and a material density adjustment intention is generated based on the corresponding local energy potential value and the current material holding amount. The arithmetic mean of the current material holding amount of all volume units is set as the global material density average equivalent. A release request is generated for each volume unit that generates a material density adjustment intention, and an application request is generated for each volume unit that generates an application intention. All release requests and application requests within the same axial control section and / or between two adjacent axial control sections are aggregated and coordinated for allocation. Perform a global material holding update based on all release and request requests, and use the current material holding of all volume cells as the equilibrium material occupancy density field after redistribution.

[0012] Preferably, S3 inputs the redistributed equilibrium material occupancy density field to S1 to perform numerical solution of finite element analysis, obtains the second principal strain energy density of each volume element, and obtains the updated growth guiding potential field; Based on the material occupancy density values ​​of all volume units in the current equilibrium material occupancy density field, statistical analysis is performed to determine the high density threshold and the low density threshold. Then, based on the updated growth guiding potential field, two direction vectors are calculated for the current growth front node of each growth probe and synthesized into the final growth direction. The growth probe is extended forward along the synthesized direction by a preset spatial step. Based on the iterative process of the growth probe, and based on the determined high density threshold and low density threshold, the volume units traversed by the growth probe path are marked with material attribution. After growth, all volumetric units marked as gaps are formed into a gap network graph. Based on each energy local center in the global energy local center set as a mandatory node that must be connected, the maximum fully connected subgraph containing all mandatory nodes is found using the maximum clique search algorithm in graph theory. Isolated energy local centers are identified. Based on the updated growth guiding potential field and energy local potential field, the shortest spatial path connecting the isolated energy local centers and the maximum fully connected subgraph is planned to form a micro-connection channel. Based on the current final material occupancy density distribution, the boundary equivalence between the solid and the gap in the current material occupancy field is recalculated according to the operation of S2. The isosurface where the material occupancy density equals the boundary equivalence is extracted as the precise interface between the solid and the gap, and a three-dimensional geometric model is generated as the corresponding geometric model of the variable cross-section multi-gap coupling.

[0013] Preferably, after changing the current material in step S3, the S2 operation is repeated for several geometric models of variable cross-section multi-clearance couplings. The coupling configuration with the smallest global performance supply-demand deviation is selected as the optimal configuration. After simulating and solving the optimal configuration, the time-domain signal including the torque-torsion angle relationship curve, the torsional angular acceleration at the output end, and the maximum equivalent stress value of each volume unit in the time history are extracted and compared with the initial coupling configuration to obtain the improved result.

[0014] Beneficial effects This invention provides a method for improving the structure of a variable cross-section multi-gap coupling for a transmission system, which has the following advantages: growth probes are arranged on each axial control section, and the growth guiding potential field and the energy local potential field jointly guide the extension direction of the probes, replacing the traditional empirical gap arrangement design. The shaping is differentiated according to the material density characteristics along the way, and solidification is carried out in the high material density area to form solid reinforcing ribs, which strengthens the force transmission path, etc. The integrated and coordinated shaping of the reinforcing structure, gap network and variable cross-section profile effectively avoids stress concentration caused by boundary abrupt changes. By mapping the material density to elastic wave propagation parameters through an equivalent refractive index field, and combining the frequency domain simulation of broadband torsional excitation to accurately identify the local energy center and construct the local energy potential field, the spatial distribution characteristics of torsional vibration energy are transformed into the direct driving force of structural evolution. The material release and application requirements of the unit are triggered by the local energy potential, and the material share is coordinated and allocated within the axial section and between adjacent sections. Under the premise of controllable global material usage, dynamic equilibrium of material distribution is achieved. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating an improved method for a variable cross-section multi-gap coupling structure used in a transmission system according to the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] Please see Figure 1This invention provides a method for improving the structure of a variable cross-section multi-gap coupling for a transmission system, comprising the following specific steps: S1. The three-dimensional computational domain of the elastic body based on the variable cross-section multi-gap coupling is meshed to obtain hexahedral volume elements. After discretizing the initial profile of the coupling into an ordered point array, the initial material occupancy density value is assigned to the obtained hexahedral volume elements, and the obtained initial material occupancy is used for finite element analysis of the coupling to obtain the growth guiding potential field. S1 is based on the three-dimensional computational domain of the elastic body of the variable cross-section multi-gap coupling. The structured mesh is divided along the radial, circumferential and axial directions in the cylindrical coordinate system to obtain several adjacent hexahedral volume elements. The initial profile of the original design of the coupling is obtained, the initial profile is discretized into a set of ordered points, and the pre-set gap opening position is mapped to the circumferential angle range. Based on each volume element, the cylindrical coordinates of eight vertices in the ordered point sequence are extracted. The ratio of the radial coordinate of each vertex's cylindrical coordinate to the radial boundary of the initial profile at the axial section is used as the spatial mapping reference. The cylindrical coordinates of each vertex are then converted to the original design parameters for spatial position determination and assignment, including the following specific settings: If all eight vertices of any volume element are located within the solid region enclosed by the initial profile after spatial mapping, and the circumferential angle is not located within the circumferential angle range of any gap opening, then the initial material occupancy density of the corresponding volume element is assigned to one. If all eight vertices of any volume element are located outside the solid region and / or fall within the gap opening, assign the initial material occupancy density of the volume element to zero. Furthermore, if only some vertices of a volume element satisfy the solid condition, the number of vertices that satisfy the solid condition is counted, and the ratio obtained by dividing the number by eight is used as the initial material density value of the volume element. After determining and assigning values ​​to the spatial positions of all volume units, the initial material occupancy field is obtained.

[0018] Therefore, a scalar value continuously ranging from zero to one is defined for each volume cell as the material occupancy density of that volume cell. A material occupancy density of one indicates that the volume cell is completely filled with the elastic material of the coupling, a value of zero indicates that the volume cell is completely void, and a value between zero and one indicates that the volume cell is a transition interface region between material and void. It should be noted that this application utilizes the original design profile and gap opening angle range of the coupling to perform spatial mapping and assignment determination on the vertices of the discretized volume element. When all vertices of the volume element are located within the solid region and do not fall into the gap opening angle, the material occupancy density of the volume element is assigned to the full solid state. When all vertices are not in the solid region or fall into the gap opening, they are assigned to the full void state. When some vertices meet the conditions, a transition value between 0 and 1 is assigned according to the proportion of the number of vertices that meet the conditions to the total number of vertices. Therefore, according to the above operation, the geometric boundary and gap distribution of the original design are transformed into a material occupancy density numerical field that can be iteratively evolved. Compared with the prior art, it avoids the need for a binary initial representation based on a fixed mesh boundary in traditional topology optimization. The transition density is generated by interpolation of the vertex proportion, preserving the geometric smoothness of the material distribution at the profile boundary.

[0019] Next, S1 transforms the initial material occupancy field into a finite element analysis model of the coupling, applies a fixed constraint to the inner ring mounting surface of the coupling, and applies a rated torque to the outer ring connecting flange of the coupling. The numerical solution is obtained through finite element analysis. The numerical solution process is as follows: First, the material stiffness matrix of the solid is interpolated according to the material occupancy density of each volume element to obtain the element stiffness matrix of each volume element. A virtual stiffness value is assigned to the void element with zero material occupancy density. The virtual stiffness value is set by the geometric mean of the stiffness of all solid volume elements. The element stiffness matrix and the void element are assembled to obtain the overall stiffness matrix. The overall stiffness matrix is ​​decomposed based on the sparse matrix, and the displacement vector of all volume elements is calculated. Based on the displacement vector, the six strain components of each volume element are calculated using the spatial differential operator. Based on the stress components of the coupling material constitutive matrix, the stress components and strain components are subjected to tensor contraction operation, that is, the half value of the product of each component is obtained to obtain the first principal strain energy density scalar of each volume element. The reciprocal of the first principal strain energy density of all volume elements is normalized by range, that is, the minimum value among all reciprocals is subtracted from each reciprocal value, and then divided by the difference between the maximum value and the minimum value. The result is mapped to the interval between zero and one, thereby mapping the region with low strain energy and high damping potential to a high guiding potential value, obtaining the generation guiding potential of each volume element, and using the spatial distribution field composed of the growth guiding potential of all volume elements as the growth guiding potential field. In this application, the mechanical response of the coupling under rated torque is converted into a perceptible potential field signal, providing a physical explanation for the extension direction of the growth probe and the retention tendency in the coordinated redistribution of materials in subsequent steps.

[0020] S2. Apply torque load based on coupling configuration, introduce complex stiffness matrix of coupling material constitutive based on coupling model, perform solid-clearance partitioning based on coupling configuration, integrate the obtained torsional stiffness supply matching index, damping energy demand satisfaction index, and clearance network flow efficiency cost ratio into material distribution performance supply and demand vector, calculate the maximum value of Chebyshev distance from the ideal performance state vector, and obtain global performance supply and demand deviation. S2 applies a torque load linearly increasing from zero to the rated value to the coupling configuration corresponding to the current material occupancy location, performing a static torsional loading numerical simulation to obtain a continuous torque-torque angle curve. Based on the initial point where both torque and torsion angle are zero in the torque-torque angle curve, the torsion angle is increased in trial steps using integer multiples of the curve sampling resolution, based on the direction of torsion angle increase. Local linear regression is performed on the torque increment and torsion angle increment corresponding to each trial step to obtain the tangential stiffness at zero torsion angle. That is, when the goodness of fit of the linear regression first exceeds the preset line... When the linearity threshold is set, the trial step size is used as the numerical differential step size. The torque increment within the step size is divided by the torsion angle increment. The linearity threshold in this application is set based on the theoretical linear characteristics of the torque-torsion angle curve in the elastic segment and adaptively selected considering the simulation noise level. Based on the design target stiffness of the transmission system, the ratio of the tangential stiffness to the design target stiffness is calculated, and the obtained ratio is mapped using a logarithmic function with the natural logarithm as the base to obtain the torsional stiffness supply matching index. The smaller the absolute value of this index, the more accurate the matching between the stiffness supply and the design requirements. Based on the complex stiffness matrix of the coupling material constitutive model, where the real part represents the energy storage stiffness and the imaginary part represents the energy dissipation modulus, a complex characteristic equation containing inertia terms and a complex stiffness matrix is ​​constructed. Complex eigenvalues ​​and complex eigenvectors are obtained by iteratively solving based on eigenvalues. The real part of each complex eigenvalue is taken as the natural frequency of the mode, and the ratio of the imaginary part to the real part is taken as the modal loss factor of the mode. The equivalent static load projection amplitude of the rated torque is taken as the modal participation factor of each mode. Based on the modal participation factor as the weight, all modal loss factors are weighted and summed to obtain the weighted modal loss factor. Based on the ratio of the equivalent target loss factor under all working conditions required by the design to the weighted modal loss factor, the damping energy dissipation demand satisfaction index is obtained. In the above process, dynamic mechanical analysis data for elastic materials are obtained by applying sinusoidal strain excitation to the material sample in the frequency domain and measuring its stress response. Under steady-state harmonic conditions, the stress response of the material leads the strain by a phase angle. The tangent of this phase angle is the material loss factor, which characterizes the ratio of dissipated energy to stored energy in each vibration cycle. The ratio of the amplitudes of stress and strain in the frequency domain is defined as the complex modulus. Its real part is the storage modulus, which is in phase with the strain and represents the energy stored and released by the material during elastic deformation. Its imaginary part is the dissipation modulus, which is in phase with the strain rate and represents the energy dissipated by the material in the form of heat due to internal friction and other mechanisms. Therefore, this application directly uses the complex modulus of the material as the coefficient of the elastic matrix, replacing the real elastic modulus in the classical linear elastic constitutive model. This yields the constitutive relation of the material's complex stiffness matrix, i.e., the complex stiffness matrix of the coupling material constitutive model. Its form is that, after finite element discretization, the element complex stiffness matrix of each volume element is obtained by interpolating the material occupancy density of that element with the complex stiffness matrix of the solid material. Assembling the full coupling model yields the overall complex stiffness matrix, where the real part is the overall energy storage stiffness matrix and the imaginary part is the overall energy dissipation stiffness matrix. The reason for constructing the complex characteristic equation is that, under the condition of neglecting external excitation and considering the assumption of simple harmonic motion, the governing equation for the free vibration of the coupling elastic body can be written as the total mass matrix multiplied by the acceleration vector plus the total complex stiffness matrix multiplied by the displacement vector equals zero. Assuming the displacement vector is in simple harmonic form, i.e., the displacement vector equals the complex eigenvector multiplied by the natural exponential function, where the exponent is the complex eigenvalue multiplied by time, substituting this into the governing equation and eliminating the time factor, we obtain the structural dynamics complex characteristic equation, i.e., the square of the complex eigenvalue multiplied by the total mass matrix multiplied by the complex eigenvector plus the total complex stiffness matrix multiplied by the complex eigenvector equals zero. This complex characteristic equation is a nonlinear eigenvalue problem; therefore, this application uses an algorithm based on eigenvalue iterative solution. Then, based on the material occupancy field of the current coupling configuration, solid-void partitioning is performed. Specifically, a partitioning threshold is determined for the material occupancy density values ​​of all volume elements using the Otsu's method. Specifically, after dividing all volume elements into solid-oriented elements and void-oriented elements according to this threshold, the inter-class variance of the material occupancy density values ​​of the two types of elements reaches its maximum. This partitioning threshold is used as the boundary equivalence between solids and voids. The moving cube algorithm is used with the boundary equivalence between solids and voids as the isosurface to generate the interface mesh between solids and voids composed of triangular facets. The meshes of all triangular facets are then calculated. The total area is obtained by summing the areas of all the volume elements. The volume of all volume elements with a material density lower than the boundary between the solid and the gap is accumulated to obtain the void volume. The ratio of the total area of ​​the interface to the void volume is used as the flow efficiency cost ratio of the gap network. The lower the cost ratio, the more efficient the gap topology. Thus, this application automatically finds the optimal solid-void boundary through the principle of maximizing inter-class variance, so that the interface area calculation is not affected by the fixed threshold. On this basis, the topological efficiency of the gap network configuration is measured by the interface area corresponding to the unit void volume. The torsional stiffness supply matching index, damping energy demand satisfaction index, and clearance network flow efficiency cost ratio are sequentially arranged to form a three-dimensional vector, which serves as the material distribution performance supply and demand vector. An ideal performance state vector is set, with its three components having values ​​of 0, 1, and 0 respectively. The Chebyshev distance between the material distribution performance supply and demand vector and the ideal performance state vector is calculated. That is, the absolute value of the difference between the current vector component and the ideal vector component is calculated in each of the three dimensions. The maximum value of the Chebyshev distance is taken as the global performance supply and demand deviation. The smaller the global performance supply and demand deviation, the better the comprehensive balance of the coupling structure in multi-dimensional transmission performance.

[0021] S3. Set growth probes for each axial control section of the coupling, and convert the material occupancy density field of all volume elements into an elastic wave equivalent refractive index field. Apply broadband torsional angular displacement excitation to all nodes on the inner ring connection interface of the coupling. Perform dynamic simulation of the coupling in the frequency domain. Use the weighted time-averaged energy density of the simulated elastic wave to determine the energy local center. Perform material coordination redistribution on the energy local potential field and the material distribution performance supply and demand vector. Update the growth guiding potential field according to the redistributed equilibrium material occupancy density field. Iteratively grow the growth probes. After growth, construct the gap network diagram and obtain the current final material occupancy density distribution. Generate the corresponding variable cross-section multi-gap coupling geometric model. Replace the current material and repeat S1-S3. Finally, retain several candidate variable cross-section multi-gap coupling geometric models. Perform simulation and solve the retained candidate variable cross-section multi-gap coupling geometric models to determine the optimal configuration.

[0022] S3, based on the initial material occupancy field and growth guiding potential field, selects seed points along the circumferential direction at predetermined angular intervals, with a number equal to one-quarter of the total number of circumferential grids, on each axial control section of the coupling. At each seed point, a growth probe consisting of a curve structure composed of a sequence of discrete nodes connected end to end is initialized. The initial spatial position of the growth probe is set to the center of the volume cell with the highest material occupancy density on the control section. The spatial gradient vector direction where the growth guiding potential field is located is used as the initial extension direction of the growth probe. This gradient direction is obtained by performing a central difference operation on the growth guiding potential field. Thus, this application establishes a set of geometric probes carrying spatial position and direction information, transforming the subsequent network growth process from the abstract optimization of an undirected scalar field into the extension of a node sequence with a clear geometric path. Based on the reference high refractive index value of pure solid materials and the reference low refractive index value of completely porous materials, the material occupancy density field of all current volume units is transformed into an elastic wave equivalent refractive index field. For each volume unit, its current material occupancy density value is obtained, and the conversion is performed using the power law mixing rule. Specifically, the elastic wave equivalent refractive index of the volume unit is equal to the reference high refractive index value multiplied by the cube of the material occupancy density of the volume unit, plus the reference low refractive index value multiplied by one minus the cube of the material occupancy density of the volume unit. The spatial distribution field composed of the elastic wave equivalent refractive indices of all volume units is the elastic wave equivalent refractive index field.

[0023] S3 applies a broadband torsional angular displacement excitation covering the torsional vibration characteristic frequency range of the transmission system to all nodes on the inner ring connection interface of the coupling model based on the elastic wave equivalent refractive index field. This torsional vibration characteristic frequency range is determined by performing modal analysis under backlash-free conditions on the original coupling design to obtain its first-order torsional mode natural frequency. A preset multiple of this natural frequency is used as the upper limit of the frequency, and the lower limit starts from zero to ensure that the frequency range covers all possible resonance areas and major harmonic bands of the transmission system. The spectral distribution of this broadband torsional angular displacement excitation is constructed based on a measured power spectral density function of the transmission shaft torsional vibration load. This power spectral density function has a high value in the low-frequency region and gradually decays with increasing frequency. The normalized excitation weight coefficient at each discrete frequency point in the broadband torsional angular displacement excitation is obtained through discrete sampling. The equivalent material modulus of each discrete frequency point, obtained by converting the equivalent refractive index field of the elastic wave at the corresponding frequency, is substituted into the numerical integration process of the element stiffness matrix according to the standard method for forming the element stiffness matrix in the finite element method, to obtain the overall dynamic stiffness matrix. This overall dynamic stiffness matrix is ​​a complex matrix. The reset displacement response vector of all volume elements is solved by the complex domain sparse matrix, and the elastic wave weighted time-averaged energy density of each volume element is calculated based on the normalized excitation weight coefficient. Specifically, at each discrete frequency point of a certain volume element, the six complex strain components of the volume element are obtained by spatial differentiation of the reset displacement response vector of the node to which the volume element belongs through the finite element shape function, referring to S2, and the complex stiffness matrix of the coupling material is used. By performing complex matrix multiplication with the complex strain components and extracting the real part, the real part of the complex strain energy density at that frequency point is obtained. This real part of the complex strain energy density is multiplied by the normalized excitation weighting coefficient at that frequency point to obtain the weighted strain energy density contribution. Simultaneously, the reset displacement vector at that frequency point is multiplied by the angular frequency to transform it into a complex velocity vector. The square of the velocity is calculated, multiplied by the mass density, and the real part is obtained to obtain the real part of the kinetic energy density. This is also multiplied by the normalized excitation weighting coefficient to obtain the weighted kinetic energy density contribution. The weighted strain energy density contributions at all discrete frequency points are accumulated to obtain the weighted cumulative strain energy density. The weighted kinetic energy density contributions are accumulated to obtain the weighted cumulative kinetic energy density. The weighted cumulative strain energy density and the weighted cumulative kinetic energy density of the volume element are added together, and their sum is used as the elastic wave weighted time-averaged energy density of the volume element.

[0024] S3 calculates the full-field arithmetic mean and full-field standard deviation of the elastic wave weighted time-averaged energy density of all volume elements. Volume elements with elastic wave weighted time-averaged energy density values ​​higher than the full-field arithmetic mean plus the full-field standard deviation are marked as high-energy localized elements. Spatial connectivity analysis is performed on high-energy localized elements. All adjacent high-energy localized elements at all faces, edges and / or vertices in the coupling are merged into connected clusters. The equivalent diameter of each connected cluster is calculated. The equivalent diameter is defined as the diameter of a sphere with the same volume as the connected cluster. When the equivalent diameter of any connected cluster is smaller than the wavelength of the elastic wave in the solid material at the upper limit of the excitation frequency, it is determined to be an energy local center, and all the determined energy local centers are combined into a global energy local center set. For volumetric cells belonging to any energy local center, the normalized value of the ratio of the elastic wave weighted time-averaged energy density to the maximum elastic wave weighted time-averaged energy density in the entire field is taken as the energy local potential. For volumetric cells that do not belong to any energy local center but are adjacent to any energy local center, the potential value of the nearest energy local center is taken as the energy local potential. The energy local potential of volumetric cells that are not adjacent to any energy local center is taken as a negative value, and the absolute value of the negative value is equal to the difference between the energy density of the cell and the average energy density of the entire field divided by the standard deviation of the entire field. The spatial distribution field formed by the energy local potential of all volume units is called the energy local potential field. The high-energy local potential region represents the hot spot where elastic waves are bound, and the low or negative energy local potential region represents the fast channel or cold spot for elastic wave propagation.

[0025] S3 uses the initial material occupancy density value of all volume units as the initial material holding amount, and generates a material density adjustment intention based on the corresponding local energy potential value and the current material holding amount. It sets the arithmetic mean of the current material holding amounts of all volume units as the global average material density equivalent, and generates a release request for each volume unit that generates a material density adjustment intention, and an application request for each volume unit that generates an application intention. In this step, if the local energy potential value of a volume unit is higher than a preset active threshold, it indicates that the elastic wave is excessively restrained, and the volume unit generates a release request for releasing a share of material; the amount of material to be released is derived from the excess portion of the local energy potential exceeding the active threshold. If the local energy potential value of a volume unit is lower than a preset lower critical value and its current material holding amount is less than 1, the volume unit generates an application request for applying for a share of material. A material release request means that the volume unit tends to reduce its own material occupancy density to form more voids, while a material application request means that the volume unit tends to increase its own material occupancy density to enhance the load-bearing capacity of the entity. Therefore, the release request includes the quantity of material to be released and the minimum receiving equivalent that the unit can accept; the minimum receiving equivalent is set by obtaining the growth guiding potential value of the volume unit, and the minimum receiving equivalent is equal to the current global average material density equivalent multiplied by 1 plus the growth guiding potential value. For the application request, the quantity of the material share to be requested and the maximum equivalent that the unit can bear are included, and the accepted equivalent is linearly adjusted according to the material vacancy of the volume unit itself. All release requests and application requests within the same axial control section and / or between two axially adjacent control sections will be aggregated and coordinated for allocation. Perform a global material holding update based on all release and request requests, and use the current material holding of all volume cells as the equilibrium material occupancy density field after redistribution.

[0026] S3 inputs the redistributed equilibrium material occupancy density field into S1 to perform numerical solution of finite element analysis, obtains the second principal strain energy density of each volume element, and obtains the updated growth guiding potential field. Based on the material occupancy density values ​​of all volume units in the current equilibrium material occupancy density field, statistics are performed to determine the high density threshold and the low density threshold. The high density threshold is set as the arithmetic mean plus the standard deviation of the preset high density standard deviation multiple, and the low density threshold is set as the arithmetic mean minus the standard deviation of the preset low density standard deviation multiple. Based on the updated growth guiding potential field, for each growth probe's current growth front node, two direction vectors are calculated and synthesized into the final growth direction. One is the local gradient direction of the updated growth guiding potential field at the node, and the other is the valley direction of the local energy potential field at the node, i.e., the direction in which the local energy potential decreases the fastest. The growth probe is extended forward along the synthesis direction by a preset spatial step. Based on the iterative process of the growth probe, and based on the determined high-density threshold and low-density threshold, the volume cells traversed by the growth probe path are labeled with material classification. Specifically, when the probe continuously traverses a cluster of volumetric units where the material occupancy density is generally higher than the high density threshold, the probe path is solidified into a reinforcing fiber path, and the material occupancy density of the volumetric units on this path is ultimately locked to 1, forming a solid reinforcing rib structure inside the coupling. When the probe passes through a cluster of volumetric cells where the material occupancy density is generally below the low density threshold, the probe breaks and degenerates. The material occupancy density of the volumetric cells in this region is locked at 0, becoming part of the void network. When the material density is in the transition region between the low density threshold and the high density threshold, the probe direction is retained as a control line for a smooth transition interface between the solid and the void, and a continuous variable cross-section line is subsequently generated. After growth, all volumetric units marked as voids are assembled into a gap network graph. Nodes in the graph are void volumetric units, and edges represent face adjacency. Each energy local center in the global energy local center set is used as a mandatory node that must be connected. The maximum clique search algorithm based on graph theory is used to find the maximum fully connected subgraph containing all mandatory nodes. Isolated energy local centers are identified. If an energy local center is not included in the maximum clique, it is considered an isolated energy local center. Based on the updated growth guidance potential field and energy local potential field, the shortest spatial path connecting the isolated energy local centers and the maximum fully connected subgraph is planned. The material occupancy density of all volumetric units on this path with a material occupancy density higher than the low density threshold is forcibly modified to the low density threshold, thereby forming a micro-connection channel. Therefore, this application constructs a map of void volume elements according to their surface adjacency and marks all energy local centers as forced connected nodes. It uses a maximum clique search to check whether there are any isolated local centers that are not connected. For isolated ones, it forces the excavation of a connecting channel along the shortest path under the joint guidance of the two potential fields, and deletes tiny voids that do not contain local centers and restores them to solids. Based on the current final material occupancy density distribution, the boundary equivalence between the solid and the gap in the current material occupancy field is recalculated according to the operation of S2. The isosurface where the material occupancy density equals the boundary equivalence is extracted as the precise interface between the solid and the gap, and a three-dimensional geometric model is generated as the corresponding geometric model of the variable cross-section multi-gap coupling.

[0027] After changing the current material in S3, repeat the S2 operation on several resulting geometric models of variable cross-section multi-clearance couplings. Select the coupling configuration with the smallest global performance supply-demand deviation as the optimal configuration. After simulating and solving the optimal configuration, extract the time-domain signal including the torque-torsion angle relationship curve, the torsional angular acceleration at the output end, and the maximum equivalent stress value of each volume element in the time history. Compare this with the initial coupling configuration to obtain the improved result.

Claims

1. A method for improving the structure of a variable cross-section multi-gap coupling for a transmission system, characterized in that: The specific steps include the following: S1. The three-dimensional computational domain of the elastic body based on the variable cross-section multi-gap coupling is meshed to obtain hexahedral volume elements. After discretizing the initial profile of the coupling into an ordered point array, the initial material occupancy density value is assigned to the obtained hexahedral volume elements, and the obtained initial material occupancy is used for finite element analysis of the coupling to obtain the growth guiding potential field. S2. Apply torque load based on coupling configuration, introduce complex stiffness matrix of coupling material constitutive based on coupling model, perform solid-clearance partitioning based on coupling configuration, integrate the obtained torsional stiffness supply matching index, damping energy demand satisfaction index, and clearance network flow efficiency cost ratio into material distribution performance supply and demand vector, calculate the maximum value of Chebyshev distance from the ideal performance state vector, and obtain global performance supply and demand deviation. S3. Set growth probes for each axial control section of the coupling, and convert the material occupancy density field of all volume elements into an elastic wave equivalent refractive index field. Apply broadband torsional angular displacement excitation to all nodes on the inner ring connection interface of the coupling. Perform dynamic simulation of the coupling in the frequency domain. Use the weighted time-averaged energy density of the simulated elastic wave to determine the energy local center. Perform material coordination redistribution on the energy local potential field and the material distribution performance supply and demand vector. Update the growth guiding potential field according to the redistributed equilibrium material occupancy density field. Iteratively grow the growth probes. After growth, construct the gap network diagram and obtain the current final material occupancy density distribution. Generate the corresponding variable cross-section multi-gap coupling geometric model. Replace the current material and repeat S1-S3. Finally, retain several candidate variable cross-section multi-gap coupling geometric models. Perform simulation and solve the retained candidate variable cross-section multi-gap coupling geometric models to determine the optimal configuration.

2. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 1, characterized in that: The S1-based three-dimensional computational domain of the elastic body of the variable cross-section multi-gap coupling is divided into structured meshes in the cylindrical coordinate system along the radial, circumferential and axial directions to obtain several adjacent hexahedral volume elements, obtain the initial profile of the original design of the coupling, discretize the initial profile into a set of ordered points, and map the pre-set gap opening position into a circumferential angle range. Based on each volume element, the cylindrical coordinates of eight vertices in the ordered point sequence are extracted. The ratio of the radial coordinate of each vertex's cylindrical coordinate to the radial boundary of the initial profile at the axial section is used as the spatial mapping reference. The cylindrical coordinates of each vertex are then converted to the original design parameters for spatial position determination and assignment, including the following specific settings: If all eight vertices of any volume element are located within the solid region enclosed by the initial profile after spatial mapping, and the circumferential angle is not located within the circumferential angle range of any gap opening, then the initial material occupancy density of the corresponding volume element is assigned to one. If all eight vertices of any volume element are located outside the solid region and / or fall within the gap opening, assign the initial material occupancy density of the volume element to zero. After determining and assigning values ​​to the spatial positions of all volume units, the initial material occupancy field is obtained.

3. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 2, characterized in that: S1 transforms the initial material occupancy field into a finite element analysis model of the coupling, applies a fixed constraint to the inner ring mounting surface of the coupling, applies a rated torque to the outer ring connecting flange of the coupling, and obtains the overall stiffness matrix through numerical solution of finite element analysis. Based on sparse matrix decomposition of the overall stiffness matrix, the displacement vectors of all volume elements are calculated. Based on the displacement vectors and through spatial differential operators, the six strain components of each volume element are calculated. Based on the stress components of the coupling material constitutive matrix, tensor contraction operation is performed on the stress components and strain components to obtain the first principal strain energy density scalar of each volume element. The reciprocal of the first principal strain energy density of all volume elements is normalized by range to obtain the generation guiding potential of each volume element, and the spatial distribution field formed by the growth guiding potential of all volume elements is taken as the growth guiding potential field.

4. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 1, characterized in that: S2 applies a torque load that linearly increases from zero to the rated value to the coupling configuration corresponding to the current material occupancy location, performs a static torsional loading numerical simulation to obtain a continuous torque-torsion angle curve, takes the initial point where both torque and torsion angle are zero in the torque-torsion angle curve as the base point, increases the torsion angle by taking an integer multiple of the curve sampling resolution as the trial step size based on the direction of torsion angle increase, performs local linear regression on the torque increment and torsion angle increment corresponding to each trial step size to obtain the tangential stiffness at zero torsion angle, calculates the ratio of tangential stiffness to design target stiffness based on the transmission system design target stiffness, and maps the obtained ratio to a logarithmic function with the natural logarithm as the base to obtain the torsional stiffness supply matching index; Based on the complex stiffness matrix of the coupling material constitutive model, a complex characteristic equation containing inertia terms and a complex stiffness matrix is ​​constructed. Complex eigenvalues ​​and complex eigenvectors are obtained by iterative solution based on eigenvalues. The real part of each complex eigenvalue is taken as the natural frequency of the mode, and the ratio of the imaginary part to the real part is taken as the modal loss factor of the mode. The equivalent static load projection amplitude of the rated torque is taken as the modal participation factor of each mode. Based on the modal participation factor as the weight, all modal loss factors are weighted and summed to obtain the weighted modal loss factor. Based on the ratio of the equivalent target loss factor under all working conditions required by the design to the weighted modal loss factor, the damping energy consumption demand satisfaction index is obtained. Then, based on the material occupancy field of the current coupling configuration, the solid-void partitioning is performed. Specifically, the partitioning threshold is determined by the material occupancy density value of all volume units based on the Otsu's method. The moving cube algorithm is used to generate the interface mesh of solid and void composed of triangular facets with the boundary between solid and void as the isosurface. The total area of ​​all triangular facets is calculated to obtain the total interface area. The volume of all volume units with material occupancy density lower than the boundary between solid and void is accumulated to obtain the void volume. The ratio of the total interface area to the void volume is used as the flow efficiency cost ratio of the void network. The torsional stiffness supply matching index, damping energy demand satisfaction index, and gap network flow efficiency cost ratio are sequentially constructed into a three-dimensional vector, which serves as the material distribution performance supply and demand vector. An ideal performance state vector is set, and the Chebyshev distance between the material distribution performance supply and demand vector and the ideal performance state vector is calculated. The maximum value of the Chebyshev distance is taken as the global performance supply and demand deviation.

5. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 1, characterized in that: S3 selects seed points along the circumferential direction at predetermined angular intervals on each axial control section of the coupling based on the initial material occupancy field and the growth guiding potential field. At each seed point, a growth probe consisting of a curve structure composed of a sequence of discrete nodes connected end to end is initialized. The initial spatial position of the growth probe is set to the center of the volume unit with the highest material occupancy density on the control section, and the spatial gradient vector direction where the growth guiding potential field is located is used as the initial extension direction of the growth probe. Based on the reference high refractive index value of pure solid materials and the reference low refractive index value of materials with complete porosity, the material occupancy density field of all current volume units is transformed into an elastic wave equivalent refractive index field.

6. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 5, characterized in that: S3 applies a broadband torsional angular displacement excitation covering the torsional vibration characteristic frequency range of the transmission system to all nodes on the inner ring connection interface of the coupling model based on the elastic wave equivalent refractive index field, and obtains the normalized excitation weight coefficient at each discrete frequency point in the broadband torsional angular displacement excitation through discrete sampling. The equivalent material modulus of each discrete frequency point is obtained by converting it into the equivalent refractive index field of the elastic wave at the corresponding frequency. The equivalent material modulus of each volume element is substituted into the numerical integration process of the element stiffness matrix to obtain the overall dynamic stiffness matrix. The reset displacement response vector of all volume elements is solved by the complex domain sparse matrix, and the elastic wave weighted time average energy density of each volume element is calculated based on the normalized excitation weight coefficient.

7. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 6, characterized in that: S3 calculates the full-field arithmetic mean and full-field standard deviation of the elastic wave weighted time-averaged energy density of all volume elements. Volume elements with elastic wave weighted time-averaged energy density values ​​higher than the full-field arithmetic mean plus the full-field standard deviation are marked as high-energy local elements. Spatial connectivity analysis is performed on the high-energy local elements, and all adjacent high-energy local elements at faces, edges and / or vertices in the coupling are merged into connected clusters. The equivalent diameter of each connected cluster is calculated. When the equivalent diameter of any connected cluster is smaller than the wavelength of the elastic wave in the solid material at the upper limit of the excitation frequency, it is determined to be an energy local center, and all the determined energy local centers are combined into a global energy local center set. For volumetric units belonging to any energy local center, the normalized value of the ratio of the elastic wave weighted time-averaged energy density to the maximum elastic wave weighted time-averaged energy density in the entire field is taken as the energy local potential. For volumetric units that do not belong to any energy local center but are adjacent to any energy local center, the potential value of the energy local center closest to them is taken as the energy local potential. The energy local potential of volumetric units that are not adjacent to any energy local center is taken as a negative value. The spatial distribution field formed by the energy local potential of all volume units is taken as the energy local potential field.

8. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 1, characterized in that: S3 takes the initial material density value of all volume units as the initial material holding amount, generates a material density adjustment intention based on the corresponding local energy potential value and the current material holding amount, sets the arithmetic mean of the current material holding amount of all volume units as the global material density average equivalent, generates a release request for each volume unit that generates a material density adjustment intention, and generates an application request for each volume unit that generates an application intention. All release requests and application requests within the same axial control section and / or between two axially adjacent control sections will be aggregated and coordinated for allocation. Perform a global material holding update based on all release and request requests, and use the current material holding of all volume cells as the equilibrium material occupancy density field after redistribution.

9. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 8, characterized in that: S3 inputs the redistributed equilibrium material occupancy density field into S1 to perform numerical solution of finite element analysis, obtains the second principal strain energy density of each volume element, and obtains the updated growth guiding potential field. Based on the material occupancy density values ​​of all volume units in the current equilibrium material occupancy density field, statistical analysis is performed to determine the high density threshold and low density threshold. Based on the updated growth guiding potential field, for each growth probe's current growth front node, two direction vectors are calculated and synthesized into the final growth direction. The growth probe is extended forward along the synthesized direction by a preset spatial step. Based on the growth probe's iterative process, and based on the determined high-density threshold and low-density threshold, the volume cells traversed by the growth probe path are labeled with material attribution. After growth, all volumetric units marked as gaps are formed into a gap network graph. Based on each energy local center in the global energy local center set as a mandatory node that must be connected, the maximum fully connected subgraph containing all mandatory nodes is found using the maximum clique search algorithm in graph theory. Isolated energy local centers are identified. Based on the updated growth guiding potential field and energy local potential field, the shortest spatial path connecting the isolated energy local centers and the maximum fully connected subgraph is planned to form a connection channel. Based on the current final material occupancy density distribution, the boundary equivalence between the solid and the gap in the current material occupancy field is recalculated. The isosurface where the material occupancy density equals the boundary equivalence is extracted as the precise interface between the solid and the gap, and a three-dimensional geometric model is generated as the corresponding geometric model of the variable cross-section multi-gap coupling.

10. The improved method for a variable cross-section multi-gap coupling structure for a transmission system according to claim 1, characterized in that: After replacing the current material in step S3, repeat step S2 for the resulting geometric models of several variable cross-section multi-clearance couplings. Select the coupling configuration with the smallest global performance supply-demand deviation as the optimal configuration. After simulating and solving the optimal configuration, extract the time-domain signal including the torque-torsion angle relationship curve, the torsional angular acceleration at the output end, and the maximum equivalent stress value of each volume unit in the time history. Compare this with the initial coupling configuration to obtain the improved result.

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