Construction method of rigid-flexible coupling dynamics model of tiltrotor reducer

Abstract

The application relates to the technical field of aircraft dynamics modeling and simulation technology, and discloses a tilt-rotor aircraft decelerator rigid-flexible coupling dynamics model construction method, load spectrum is subjected to time-frequency domain analysis to generate an excitation characteristic vector; a reserved mode with a contribution to the excitation characteristic vector exceeding a preset threshold is extracted to generate a reduced flexible body mode set; an initial interface model containing a basic rigid-flexible coupling relationship is generated; a local flexibility matrix is extracted and is differentially compared with a stiffness component of a transition unit, and a dynamic compensation layer unit is implanted in a hot spot area based on a stiffness deviation matrix; a gyroscopic effect term and a centrifugal stiffening effect term are introduced as correction coefficients to generate a complete displacement coordination equation containing kinematic correction; and the complete displacement coordination equation is embedded into a multibody dynamics simulation solver for numerical solution. The application solves the technical problems of mode truncation, interface stiffness distortion and local parasitic oscillation in the prior art.

Description

Technical Field

[0001] This invention relates to the field of aircraft dynamics modeling and simulation technology, and in particular to a method for constructing a rigid-flexible coupling dynamics model of a tiltrotor decelerator. Background Technology

[0002] Tiltrotor aircraft, as an important development direction for vertical takeoff and landing (VTOL) aircraft, combine the hovering capabilities of helicopters with the high-speed cruise characteristics of fixed-wing aircraft, showing broad application prospects in modern military transport, emergency rescue, and civil aviation. The gearbox, as the core power transmission component of a tiltrotor aircraft, undertakes the critical task of efficiently transferring engine power to the rotor system. It withstands complex dynamic loads and variable boundary conditions during tilt transition. Accurately predicting the dynamic response of the gearbox during tilt is of significant engineering importance for ensuring the structural safety of the aircraft and extending the service life of components. With the rapid development of multibody dynamics simulation technology, analyzing the dynamic characteristics of the gearbox by constructing a rigid-flexible coupled dynamic model has become the mainstream technical approach in the industry.

[0003] A search revealed a method for determining vibration limits for an aircraft transmission system, disclosed in patent publication number CN113221261B. This method includes determining the lifespan and material SN curves of the transmission system, establishing a multi-body dynamics model of the transmission system, measuring the vibration values ​​of each shaft system under different operating load conditions and calculating dynamic stress, compiling a load spectrum based on the load history, calculating the lifespan of each shaft system under different operating load conditions, and establishing a coupling relationship between vibration values ​​and lifespan. This patent determines vibration limits by combining simulation and experimentation, avoiding the cost of extensive testing. However, when this method is applied to the dynamics modeling of tiltrotor aircraft reducers, the conventional modal synthesis method is used for flexible body reduction during the construction of the multi-body dynamics model. For conditions with high gradient stress fields at the interface, modal truncation leads to the loss of local deformation information, and the force-displacement relationship at the rigid-flexible coupling interface exhibits stiffness distortion. Under dynamic impact loads, this induces high-frequency parasitic oscillations, resulting in disordered meshing force calculations and distorted bearing support reactions. Existing technologies have failed to solve the technical challenge of compensating for local deformation characteristics after modal truncation, resulting in insufficient accuracy in predicting the dynamic stress distribution of key parts of the reducer under tilting transition conditions, which directly affects the reliability of structural strength verification.

[0004] Therefore, there is an urgent need to provide a method for constructing a rigid-flexible coupled dynamic model of a tiltrotor gearbox to solve the technical problems of interface stiffness distortion and local parasitic oscillations caused by modal truncation in existing technologies. To this end, we propose a method for constructing a rigid-flexible coupled dynamic model of a tiltrotor gearbox. Summary of the Invention

[0005] This invention primarily addresses the technical problems existing in the prior art by providing a method for constructing a rigid-flexible coupling dynamic model of a tiltrotor aircraft gearbox. To achieve the above objective, this invention adopts the following technical solution: a method for constructing a rigid-flexible coupling dynamic model of a tiltrotor aircraft gearbox, comprising the following steps: S1: Obtain the load spectrum of the tiltrotor reducer under typical operating conditions, perform time-frequency domain analysis on the load spectrum, and generate an excitation feature vector to define the deformation contribution of the flexible body. S2: Based on the excitation feature vector, perform substructure division and modal analysis on the housing and transmission shaft in the three-dimensional solid model of the reducer, extract the modes that contribute to the excitation feature vector more than a preset threshold, and generate a reduced flexible body mode set. S3: Based on the flexible body mode set, establish a rigid-flexible coupling interface between a rigid body and a flexible body in a multibody dynamics simulation environment, and construct a transition unit on the interface to generate an initial interface model containing the basic rigid-flexible coupling relationship. S4: Identify hotspot regions of high gradient stress field in the initial interface model, perform sub-model ultra-refinement analysis on the hotspot regions, extract the local flexibility matrix and compare the difference with the stiffness components of the transition unit to generate a stiffness deviation matrix, and implant dynamic compensation layer units in the hotspot regions based on the stiffness deviation matrix to generate a rigid-flexible coupling interface correction model with local correction capability. S5: Apply boundary conditions under the tilting transition condition to the rigid-flexible coupling interface correction model, including tilting angular velocity and tilting angular acceleration, and introduce gyro effect term and centrifugal stiffening effect term as correction coefficients to generate a complete displacement compatibility equation containing kinematic correction. S6: Embed the complete displacement coordination equation into the multibody dynamics simulation solver for numerical solution, and output the dynamic response of the key parts of the reducer under tilting transition conditions.

[0006] Preferably, the acquisition of the load spectrum in step S1 further includes: acquiring time history load data of the input shaft, output shaft, and housing connection of the reducer under three typical operating conditions: hovering, cruise, and tilt transition, from the full-aircraft flight test data of the tiltrotor. The time history load data includes torque, axial force, radial force, and bending moment. The time history load data is subjected to a fast Fourier transform to obtain the load spectrum diagram under each operating condition. Frequency components with amplitudes exceeding 20% ​​of a reference amplitude are identified as key frequency components in the load spectrum diagram. The reference amplitude is the arithmetic mean of the amplitudes of all frequency components under each operating condition. The amplitude and phase information corresponding to the key frequency components are extracted, and the real and imaginary parts of the excitation feature vectors are constructed according to the operating condition category. The excitation feature vectors of the three operating conditions are combined into a multi-dimensional excitation feature matrix.

[0007] Preferably, the determination of the preset threshold in step S2 further includes: receiving the multidimensional excitation feature matrix output in step S1, performing principal component analysis on the multidimensional excitation feature matrix, and extracting the principal components with a cumulative contribution rate exceeding 95% as the main excitation directions; for the fixed interface modal analysis results of each substructure, calculating the modal participation factor of each retained principal mode and constraint mode, wherein the modal participation factor is defined as the absolute value of the product of the mode shape and the direction cosine of the main excitation direction; arranging the modal participation factors in descending order, calculating the cumulative participation factor, and the modal order corresponding to the first time the cumulative participation factor reaches 0.95 is the cutoff order of the retained mode, and the minimum modal participation factor value corresponding to this order is the preset threshold; discarding all higher-order local modes below the preset threshold, retaining modes higher than or equal to the preset threshold, and generating a reduced flexible body modal set.

[0008] Preferably, the construction of the transition unit in step S3 further includes: selecting a set of master nodes on the flexible body interface, wherein the master nodes are located at the center of the bearing seat, the projection position of the gear meshing point, and the flange connecting the housing and the support arm; establishing a rigid beam unit between the rigid body reference point and each of the master nodes, wherein the length direction of the rigid beam unit is perpendicular to the flexible body interface; establishing a displacement coordination relationship between the nodes of the rigid beam unit on the flexible body interface and the surrounding slave nodes through a multi-point constraint algorithm, wherein the displacement coordination relationship is realized by the Lagrange multiplier method, and the constraint equation is that the three translational degrees of freedom of each slave node are equal to the translational degrees of freedom of the master node plus the entrainment displacement caused by the rotational degrees of freedom of the master node; applying a force and a moment from the rigid body to the rigid body reference point of the rigid beam unit, wherein the force and moment are distributed to each slave node through the constraint equation, thereby forming a transition unit, wherein the stiffness characteristics of the transition unit are calculated by the modal stress stiffness matrix of each mode in the flexible body modal set output in step S2 through the modal superposition method.

[0009] Preferably, the identification of high-gradient stress field hotspot regions in step S4 further includes: receiving the initial interface model output in step S3; applying the tilt transition load from the excitation feature vector output in step S1 to the initial interface model; performing preliminary rigid-flexible coupling dynamic simulation; extracting the von Mises stress time history of each node on the flexible body interface; calculating the root mean square stress value of each node during the entire tilt transition time history; spatially interpolating the root mean square stress value in the flexible body interface region to generate a stress distribution cloud map; identifying continuous regions in the stress distribution cloud map where the root mean square stress value is greater than 1.5 times the global root mean square stress average value, and marking these regions as high-gradient stress field hotspot regions; extracting the node numbers and coordinates of all flexible body interface nodes covered by the hotspot regions to form an interface stress hotspot node set.

[0010] Preferably, the sub-model ultra-refinement analysis in step S4 further includes: receiving the interface stress hotspot node set output in step S6; extracting a local geometric model containing the hotspot node set and at least three layers of surrounding unit regions from the original three-dimensional solid model of the reducer; re-meshing the local geometric model, setting the unit size to one-fifth of the original global mesh size, and performing secondary refinement at stress concentration locations to ensure that the minimum unit size does not exceed 0.1 mm; applying displacement boundary conditions to the local geometric model, the displacement boundary conditions being taken from the displacement time history of the hotspot region boundary nodes at the corresponding time in the preliminary rigid-flexible coupling dynamic simulation; applying dynamic loads at the corresponding time to the internal nodes of the local geometric model, the dynamic loads including gear meshing force, bearing force, and inertial force; solving the transient dynamic equations of the local geometric model, extracting the displacement response of each master node in the hotspot node set, and constructing a displacement response matrix; and inverting the displacement response matrix to obtain the local compliance matrix.

[0011] Preferably, the parameter determination of the dynamic compensation layer unit in step S4 further includes: extracting stiffness matrix blocks corresponding to the master nodes in the hotspot region from the transition unit generated in step S3. These blocks have a dimension of 6×6 and represent the modal stiffness contributions of the master nodes across their six degrees of freedom. The local stiffness matrix is ​​obtained by inverting the local flexibility matrix output in step S7; this local stiffness matrix also has a dimension of 6×6. The difference between the local stiffness matrix and the modal stiffness matrix blocks is calculated to obtain the stiffness deviation matrix. DK A nonlinear spring-damper model is established, wherein the force-displacement relationship of the nonlinear spring-damper is as follows: F=kx+c(dx / dt) ,in k This is a nonlinear function resulting from multiplying the initial stiffness coefficient by the direction weights. c The damping coefficient is taken as 0.1 times the critical damping ratio; the nonlinear spring-damper is implanted in parallel into the transition unit to form a dynamic compensation layer unit.

[0012] Preferably, the activation criterion for the dynamic compensation layer unit in step S4 further includes: within each simulation integration step, reading the instantaneous load vector F of the rigid body acting on the master node, the load vector containing three force and three moment components; calculating the Euclidean norm Fi of the load vector F; defining a spherical neighborhood with a radius of 10 mm centered on the master node, statistically analyzing the coordinates of all slave nodes within the neighborhood, and calculating the distance vector from the slave nodes to the master node; projecting the load vector F onto the radial direction of each slave node to obtain the radial load components of each slave node; calculating the spatial rate of change of the radial load components within the neighborhood, i.e., the difference between the maximum and minimum values ​​of the radial load components divided by the distance from the master node to the farthest slave node, to obtain the load gradient value. G; and obtaining the load gradient value G with a preset threshold G 0 for comparison, wherein the preset threshold G 0 has a value of 1.2 times the maximum slope of the load spectrum under the tilt transition condition in step S1; if G<G0, it is determined that the load gradient is lower than the threshold, and only the transition unit is enabled; if G≥G0, it is determined that the load gradient is higher than the threshold, and the dynamic compensation layer unit is enabled in parallel for local correction.

[0013] Preferably, the calculation of the gyroscopic effect term and the centrifugal stiffening effect term in step S5 further comprises: extracting the tilt angular velocity under the tilt transition condition from the excitation feature vector output in step S1 oh and tilt angular acceleration α , wherein the tilt angular velocity oh is a vector comprising angular velocity components around three body axes of the aircraft; establishing a motion equation for any microelement on the flexible body in the follow-up coordinate system, and introducing the gyroscopic moment term M gyro =-2 oh , wherein v is a relative velocity vector of the microelement in the follow-up coordinate system; introducing the centrifugal stiffening effect term K cf = pAω 2 r , wherein r is material density, A is the cross-sectional area of the microelement, oh =ǀ oh ǀ is the magnitude of the angular velocity, r is the distance from the microelement to the rotation axis; adding the gyroscopic moment term and the centrifugal stiffening effect term as additional load vectors to the right-hand terms of the displacement coordination equation respectively; meanwhile, adding the derivative form of the gyroscopic moment term with respect to displacement as an additional stiffness matrix to the left-hand coefficient matrix of the displacement coordination equation, so as to form a modified displacement coordination equation, which describes the dynamic displacement coordination relationship between the rigid body and the flexible body under tilt motion.

[0014] A rigid-flexible coupling dynamics simulation system for a tiltrotor reducer is further provided, comprising: a load spectrum analysis module configured to acquire a load spectrum of the tiltrotor reducer under typical working conditions, perform time-frequency domain analysis on the load spectrum, and generate an excitation feature vector for defining the deformation contribution of a flexible body; The modal reduction module, connected to the load spectrum analysis module, is used to receive the excitation feature vector, perform substructure division and modal analysis on the housing and transmission shaft in the three-dimensional solid model of the reducer based on the excitation feature vector, extract the modes that contribute to the excitation feature vector more than a preset threshold, and generate a reduced flexible body modal set. The interface construction module, connected to the modal reduction module, is used to receive the flexible body modal set, establish a rigid-flexible coupling interface between the rigid body and the flexible body in the multibody dynamics simulation environment, and construct transition units on the interface to generate an initial interface model containing basic rigid-flexible coupling relationships. The local compensation module, connected to the interface construction module, is used to receive the initial interface model, identify hotspot regions of high gradient stress field in the initial interface model, perform sub-model ultra-refinement analysis on the hotspot regions, extract the local flexibility matrix and compare the difference with the stiffness components of the transition unit to generate a stiffness deviation matrix, and implant dynamic compensation layer units in the hotspot regions based on the stiffness deviation matrix to generate a rigid-flexible coupling interface correction model with local correction capability. The kinematic correction module, connected to the local compensation module, is used to receive the rigid-flexible coupling interface correction model, apply boundary conditions under the tilting transition condition to the model, including tilting angular velocity and tilting angular acceleration, and introduce gyro effect terms and centrifugal stiffening effect terms as correction coefficients to generate a complete displacement compatibility equation containing kinematic corrections. The solution output module, connected to the kinematic correction module, is used to receive the complete displacement coordination equation, embed the complete displacement coordination equation into the multibody dynamics simulation solver for numerical solution, and output the dynamic response of the key parts of the reducer under tilting transition conditions. Beneficial effects

[0015] This invention provides a method for constructing a rigid-flexible coupled dynamic model of a tiltrotor aircraft gearbox. It has the following beneficial effects: This method for constructing a rigid-flexible coupled dynamic model of a tiltrotor reducer identifies hotspot regions with high-gradient stress fields within the global rigid-flexible coupled model. For these hotspot regions, ultra-refined finite element analysis at the sub-model level is performed to extract local compliance matrices. The inverse of these local compliance matrices is then compared with the stiffness components of the transition elements in the hotspot regions to generate a stiffness deviation matrix. Finally, based on this stiffness deviation matrix, dynamic compensation layer elements are implanted between the rigid body master nodes and the flexible body interface slave nodes. By activating these dynamic compensation layer elements in parallel under impact loads, local deformation information is compensated back into the model in real time, avoiding the generation of high-frequency parasitic oscillations and significantly improving the calculation accuracy of gear meshing forces and bearing support reactions.

[0016] This method for constructing a rigid-flexible coupled dynamic model of a tiltrotor reducer involves performing time-frequency domain analysis on the load spectrum during the tilt transition condition to generate excitation feature vectors. Principal component analysis is then performed on these feature vectors to extract the main excitation directions. Next, the modal participation factors for each mode are calculated, and the truncation order of the retained modes is determined based on a cumulative contribution rate of 0.95. Finally, the minimum modal participation factor value corresponding to the truncation order is used as a preset threshold. This method achieves adaptive matching between the retained mode set and the actual excitation characteristics, preserving the contribution of key dynamic characteristics while maintaining computational efficiency.

[0017] This method for constructing a rigid-flexible coupled dynamic model of a tiltrotor reducer extracts the tilt angular velocity and tilt angular acceleration under tilt transition conditions from the excitation eigenvectors. It then establishes the motion equations of a flexible body element in a follower coordinate system, introducing a gyroscopic torque term as an additional load vector and a centrifugal stiffening effect term as an additional stiffness matrix into the displacement compatibility equations. By modifying the displacement compatibility equations, it achieves an accurate description of the bending and torsional deformations of the rigid-flexible interface inside and outside the tilt plane, making the model's dynamic response under tilt transition conditions highly consistent with the actual physical process.

[0018] This method for constructing a rigid-flexible coupled dynamic model of a tiltrotor reducer begins with the generation of excitation eigenvectors through load spectrum time-frequency analysis. It then proceeds sequentially through modal reduction based on excitation contribution, construction of rigid-flexible coupling interface transition elements, hotspot region identification and dynamic compensation layer element implantation, and establishment of kinematically corrected displacement compatibility equations. Finally, the complete displacement compatibility equations are embedded into the solver to output the dynamic response. The system includes a load spectrum analysis module, a modal reduction module, an interface construction module, a local compensation module, a kinematic correction module, and a solution output module. These modules are connected sequentially to form a complete data processing chain. This method solves the problems of interface stiffness distortion and local parasitic oscillations caused by modal truncation, and achieves high-precision prediction of dynamic stress distribution in key parts of the reducer under tilt transition conditions. Attached Figure Description

[0019] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0020] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0021] Figure 1 This is the overall flowchart of the present invention; Figure 2 This is a diagram of the rigid-flexible coupling dynamic simulation system for the tiltrotor reducer of the present invention. Detailed Implementation

[0022] 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.

[0023] Example: A method for constructing a rigid-flexible coupling dynamic model of a tiltrotor gearbox, such as... Figure 1 This includes the following steps: S1: Extract the load spectrum of the tiltrotor reducer under three typical working conditions: hovering, cruise and tilt transition. Perform time-frequency domain analysis on the load spectrum to identify the key frequency components that cause elastic deformation of the shell and transmission shaft system and their corresponding amplitudes. Generate an excitation feature vector to define the deformation contribution of the flexible body and output the excitation feature vector to step S2. S2: Receive the excitation feature vector output from step S1, divide the shell and drive shaft in the three-dimensional solid model of the reducer into substructures based on the excitation feature vector, perform fixed interface modal analysis on each substructure using the Craig-Bampton method, extract the main modes and constraint modes that contribute more than a preset threshold to the key frequency components, discard the high-frequency local modes that contribute less than a preset threshold, generate the reduced flexible body mode set, and output the flexible body mode set to step S3; S3: Receive the flexible body mode set output from step S2, establish the rigid-flexible coupling interface between each rigid body component of the reducer and the flexible body in the multibody dynamics simulation environment, construct the transition unit between the rigid body reference point and the flexible body interface node based on the multi-point constraint algorithm, wherein the internal force-displacement relationship of the transition unit is defined by the modal stress stiffness matrix corresponding to the flexible body mode set, generate an initial interface model containing the basic rigid-flexible coupling relationship, and output the initial interface model to step S4; S4: Receive the initial interface model output from step S3, identify interface stress hotspots with high gradient stress fields at the rigid-flexible coupling interface, extract the flexible body interface node set corresponding to the hotspot, perform sub-model level ultra-refined finite element analysis on the node set, apply typical impact loads and extract the local compliance matrix reflecting local high-frequency deformation information, invert the local compliance matrix and compare the difference with the stiffness component of the transition element in the hotspot region to generate a stiffness deviation matrix for compensating for modal truncation loss; based on the stiffness deviation matrix, implant a constitutive customizable dynamic compensation layer element between the rigid body master node and the flexible body interface slave node. The dynamic compensation layer element exists in the form of a nonlinear spring-damper, and its parameters are obtained by dynamic interpolation of the stiffness deviation matrix combined with the instantaneous load amplitude. Define the discrimination criterion: when an external load acts on the master node, the load gradient is automatically calculated. If the load gradient is lower than the preset threshold, the force-displacement relationship is dominated by the transition element. If the load gradient is higher than the preset threshold, the dynamic compensation layer element is activated in parallel for local correction, generating a rigid-flexible coupling interface correction model with local correction capability, and outputting the interface correction model to step S5. S5: Receive the interface correction model output from step S4, construct the displacement coordination equation in the follower coordinate system at the rigid-flexible coupling interface. The displacement coordination equation not only includes the displacement continuity condition between the rigid body and the flexible body, but also introduces the gyro effect term and the centrifugal stiffening effect term generated by the tilting motion as correction coefficients to correct the bending deformation and torsional deformation of the flexible body inside and outside the tilting plane, generate the complete displacement coordination equation containing kinematic correction, and output the complete displacement coordination equation to step S6. S6: Receive the complete displacement compatibility equations output from step S5, embed the equations into the multibody dynamics simulation solver in the form of a user-defined subroutine, replacing the solver's built-in default rigid-flexible constraint algorithm, and input the excitation feature vectors generated in step S1 as boundary conditions. Solve the rigid-flexible coupled dynamic model after embedding the user-defined subroutine, output the dynamic response of the key parts of the reducer under the tilting transition condition, and verify the effectiveness of the dynamic compensation layer unit in suppressing interface stiffness distortion and local parasitic oscillations based on the output results.

[0024] The load spectrum extraction in step S1 further includes: obtaining time history load data of the input shaft, output shaft, and shell connection of the reducer under three typical operating conditions: hovering, cruise, and tilt transition, from the full-aircraft flight test data of the tiltrotor. The time history load data includes torque, axial force, radial force, and bending moment; performing a fast Fourier transform on the time history load data to obtain the load spectrum diagram under each operating condition; identifying frequency components with amplitudes exceeding 20% ​​of the reference amplitude in the load spectrum diagram as key frequency components, where the reference amplitude is the arithmetic mean of the amplitudes of all frequency components under each operating condition; extracting the amplitude and phase information corresponding to the key frequency components; constructing the real and imaginary parts of the excitation feature vector according to the operating condition category; and combining the excitation feature vectors of the three operating conditions into a multidimensional excitation feature matrix, which is output to step S2 as the input of the modal truncation criterion.

[0025] The determination of the preset threshold in step S2 further includes: receiving the multidimensional excitation feature matrix output in step S1, performing principal component analysis on the multidimensional excitation feature matrix, and extracting the principal components with a cumulative contribution rate of more than 95% as the main excitation directions; for the fixed interface modal analysis results of each substructure, calculating the modal participation factor of each retained principal mode and constraint mode, the modal participation factor is defined as the absolute value of the product of the mode shape and the direction cosine of the main excitation direction; arranging the modal participation factors in descending order, calculating the cumulative participation factor, the modal order corresponding to the first time the cumulative participation factor reaches 0.95 is the cutoff order of the retained mode, and the minimum modal participation factor value corresponding to this order is the preset threshold; discarding all high-order local modes below the preset threshold, retaining modes higher than or equal to the preset threshold, generating a reduced flexible body modal set, and outputting the flexible body modal set to step S3.

[0026] The construction of the transition element in step S3 further includes: selecting a set of master nodes on the flexible body interface, with the master nodes located at the center of the bearing seat, the projection position of the gear meshing point, and the flange connecting the shell and the support arm; establishing rigid beam elements between the rigid body reference point and each master node, with the length direction of the rigid beam elements perpendicular to the flexible body interface; establishing displacement coordination relationships between the nodes of the rigid beam elements on the flexible body interface and the surrounding slave nodes through a multi-point constraint algorithm, with the displacement coordination relationships implemented using the Lagrange multiplier method, and the constraint equations being that the three translational degrees of freedom of each slave node are equal to the translational degrees of freedom of the master node plus the entrainment displacement caused by the rotational degrees of freedom of the master node; applying forces and moments from the rigid body to the rigid body reference point of the rigid beam element, with the forces and moments distributed to each slave node through the constraint equations, thereby forming the transition element, and the stiffness characteristics of the transition element being calculated by the modal stress stiffness matrix of each mode in the flexible body modal set output in step S2 using the modal superposition method.

[0027] Step S4, the identification of stress hotspot regions, further includes: receiving the initial interface model output from step S3; applying the tilt transition load from the excitation feature vector output from step S1 to the initial interface model; performing preliminary rigid-flexible coupling dynamic simulation; extracting the Mises stress time history of each node on the flexible body interface; calculating the root mean square stress value of each node during the entire tilt transition time history; spatially interpolating the root mean square stress values ​​in the flexible body interface region to generate a stress distribution cloud map; identifying continuous regions in the stress distribution cloud map where the root mean square stress value is greater than 1.5 times the global root mean square stress average value, and marking these regions as high gradient stress field hotspot regions; extracting the node numbers and coordinates of all flexible body interface nodes covered by the hotspot regions to form an interface stress hotspot node set, and outputting the node set to the sub-model analysis step.

[0028] The sub-model-level ultra-refined finite element analysis in step S4 further includes: receiving the interface stress hotspot node set output from step S5; extracting a local geometric model containing the hotspot node set and at least three layers of surrounding element regions from the original three-dimensional solid model of the reducer; re-meshing the local geometric model, setting the element size to 1 / 5 of the original global mesh size, and performing secondary refinement at stress concentration locations to ensure that the minimum element size does not exceed 0.1 mm; applying displacement boundary conditions to the local geometric model, the displacement boundary conditions being taken from the displacement time history of the hotspot region boundary nodes at the corresponding time in the preliminary rigid-flexible coupling dynamic simulation; applying dynamic loads at the corresponding time on the internal nodes of the local geometric model, the dynamic loads including gear meshing force, bearing force, and inertial force; solving the transient dynamic equations of the local geometric model, extracting the displacement response of each master node in the hotspot node set, and constructing a displacement response matrix; inverting the displacement response matrix to obtain the local compliance matrix, which reflects the true local deformation characteristics of the hotspot region under a high gradient stress field.

[0029] The parameter determination of the dynamic compensation layer unit in step S4 further includes: extracting the stiffness matrix blocks corresponding to the master nodes in the hot spot region from the transition unit generated in step S3. These blocks have a dimension of 6×6 and represent the modal stiffness contribution of the master nodes in their six degrees of freedom. The local stiffness matrix is ​​obtained by inverting the local flexibility matrix output in step S6; this local stiffness matrix also has a dimension of 6×6. The difference between the local stiffness matrix and the modal stiffness matrix blocks is calculated to obtain the stiffness deviation matrix. Eigenvalue decomposition is performed on the stiffness deviation matrix to extract its principal eigenvalues ​​and corresponding eigenvectors. The principal eigenvalues ​​represent the magnitude of stiffness loss caused by modal truncation, and the eigenvectors represent the dominant direction of stiffness loss. Using the principal eigenvalues ​​as the initial stiffness coefficients of the dynamic compensation layer unit and the eigenvectors as direction weights, a nonlinear spring-damper model is established. The force-displacement relationship of the nonlinear spring-damper model provides a basis for aircraft dynamics modeling and simulation technology.F = k · x + c · dx / dt Among them, aircraft dynamics modeling and simulation technology k Aircraft dynamics modeling and simulation techniques utilize nonlinear functions resulting from the initial stiffness coefficient multiplied by directional weights. c The aircraft dynamics modeling and simulation technology uses a damping coefficient, which is taken as 0.1 times the critical damping ratio; nonlinear spring-damper is implanted in parallel into the transition unit to form a dynamic compensation layer unit.

[0030] The load gradient calculation of the discrimination criterion in step S4 further includes: In each simulation integration step, reading the instantaneous load vector F of the rigid body acting on the master node, where the load vector contains three force and three moment components; calculating the Euclidean norm |F| of the load vector F; defining a spherical neighborhood with a radius of 10 mm centered on the master node, statistically analyzing the coordinates of all slave nodes within the neighborhood, and calculating the distance vector from the slave nodes to the master node; projecting the load vector F onto the radial direction of each slave node to obtain the radial load components of each slave node; calculating the spatial rate of change of the radial load components within the neighborhood, i.e., the difference between the maximum and minimum values ​​of the radial load components divided by the distance from the master node to the farthest slave node, to obtain the load gradient value. G ; Performance modeling and simulation technology for aircraft dynamics based on load gradient values G Aircraft dynamics modeling and simulation technology and preset threshold aircraft dynamics modeling and simulation technology G A comparison of aircraft dynamics modeling and simulation technologies, and a comparison of aircraft dynamics modeling and simulation technologies with preset thresholds. G The value of 0 in the aircraft dynamics modeling and simulation technology is 1.2 times the maximum slope of the load spectrum under the tilt transition condition in step S1; if the aircraft dynamics modeling and simulation technology G < G If the value is 0, the load gradient is determined to be below the threshold, and only the transition unit is activated; if the aircraft dynamics modeling and simulation technology... G ≥ G If the value is 0, the load gradient is determined to be higher than the threshold, and the dynamic compensation layer unit is activated in parallel for local correction.

[0031] The calculation of the gyroscopic effect term and the centrifugal stiffening effect term in step S5 further includes: extracting the tilt angular velocity (ω) and tilt angular acceleration (ω) from the excitation eigenvectors output in step S1. α The tilt angular velocity (ω) of the aircraft dynamics modeling and simulation technology is a vector, containing angular velocity components around the three body axes of the aircraft. In the servo coordinate system, the motion equations of any infinitesimal element on the flexible body are established, and a gyroscopic torque term (M) is introduced. gyro =-2ωv, where v is the relative velocity vector of the infinitesimal element in the following coordinate system; a centrifugal stiffening effect term is introduced. K cf = pAω 2 r Among them, aircraft dynamics modeling and simulation technology r Aircraft dynamics modeling and simulation technology is used for material density. A Aircraft dynamics modeling and simulation technology uses infinitesimal cross-sectional area as a unit, while ω represents the magnitude of angular velocity. r The aircraft dynamics modeling and simulation technology is based on the distance from the infinitesimal element to the rotation axis. The gyroscopic torque term and the centrifugal stiffening effect term are added as additional load vectors to the right-hand side of the displacement compatibility equation. At the same time, the derivative of the gyroscopic torque term with respect to displacement is added as an additional stiffness matrix to the left-hand coefficient matrix of the displacement compatibility equation, forming a modified displacement compatibility equation. This equation describes the dynamic displacement compatibility relationship between a rigid body and a flexible body under tilting motion.

[0032] like Figure 2 As shown, a rigid-flexible coupling dynamic simulation system for a tiltrotor gearbox applying the above method is also provided, comprising: The load spectrum analysis module is used to obtain the load spectrum of the tiltrotor reducer under typical operating conditions, perform time-frequency domain analysis on the load spectrum, and generate an excitation feature vector to define the deformation contribution of the flexible body. The modal reduction module, connected to the load spectrum analysis module, is used to receive excitation feature vectors, perform substructure division and modal analysis on the shell and drive shaft in the three-dimensional solid model of the reducer based on the excitation feature vectors, extract the modes that contribute to the excitation feature vectors more than a preset threshold, and generate the reduced flexible body mode set. The interface construction module, connected to the modal reduction module, is used to receive the flexible body modal set, establish the rigid-flexible coupling interface between the rigid body and the flexible body in the multibody dynamics simulation environment, and build transition units on the interface to generate an initial interface model containing the basic rigid-flexible coupling relationship. The local compensation module, connected to the interface construction module, is used to receive the initial interface model, identify hot spots of high gradient stress field in the initial interface model, perform sub-model ultra-refinement analysis on the hot spots, extract the local flexibility matrix and compare the difference with the stiffness components of the transition unit to generate a stiffness deviation matrix, and implant dynamic compensation layer units in the hot spots based on the stiffness deviation matrix to generate a rigid-flexible coupling interface correction model with local correction capability. The kinematic correction module, connected to the local compensation module, is used to receive the rigid-flexible coupling interface correction model, apply boundary conditions under the tilting transition condition to the model, including tilting angular velocity and tilting angular acceleration, and introduce gyro effect terms and centrifugal stiffening effect terms as correction coefficients to generate a complete displacement compatibility equation containing kinematic corrections. The solution output module, connected to the kinematic correction module, is used to receive the complete displacement compatibility equation, embed the complete displacement compatibility equation into the multibody dynamics simulation solver for numerical solution, and output the dynamic response of key parts of the reducer under tilting transition conditions.

[0033] The foregoing describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a rigid-flexible coupled dynamic model of a tiltrotor reducer, characterized in that, Includes the following steps: S1: Obtain the load spectrum of the tiltrotor reducer under typical operating conditions, perform time-frequency domain analysis on the load spectrum, and generate an excitation feature vector to define the deformation contribution of the flexible body. S2: Based on the excitation feature vector, perform substructure division and modal analysis on the housing and transmission shaft in the three-dimensional solid model of the reducer, extract the modes that contribute to the excitation feature vector more than a preset threshold, and generate a reduced flexible body mode set. S3: Based on the flexible body mode set, establish a rigid-flexible coupling interface between a rigid body and a flexible body in a multibody dynamics simulation environment, and construct a transition unit on the interface to generate an initial interface model containing the basic rigid-flexible coupling relationship. S4: Identify hotspot regions of high gradient stress field in the initial interface model, perform sub-model ultra-refinement analysis on the hotspot regions, extract the local flexibility matrix and compare the difference with the stiffness components of the transition unit to generate a stiffness deviation matrix, and implant dynamic compensation layer units in the hotspot regions based on the stiffness deviation matrix to generate a rigid-flexible coupling interface correction model with local correction capability. S5: Apply boundary conditions under the tilting transition condition to the rigid-flexible coupling interface correction model, including tilting angular velocity and tilting angular acceleration, and introduce gyro effect term and centrifugal stiffening effect term as correction coefficients to generate a complete displacement compatibility equation containing kinematic correction. S6: Embed the complete displacement coordination equation into the multibody dynamics simulation solver for numerical solution, and output the dynamic response of the key parts of the reducer under tilting transition conditions.

2. A rigid-flexible coupling dynamic simulation system for a tiltrotor reducer, characterized in that, include: The load spectrum analysis module is used to obtain the load spectrum of the tiltrotor reducer under typical operating conditions, perform time-frequency domain analysis on the load spectrum, and generate an excitation feature vector to define the deformation contribution of the flexible body. The modal reduction module, connected to the load spectrum analysis module, is used to receive the excitation feature vector, perform substructure division and modal analysis on the housing and transmission shaft in the three-dimensional solid model of the reducer based on the excitation feature vector, extract the modes that contribute to the excitation feature vector more than a preset threshold, and generate a reduced flexible body modal set. The interface construction module, connected to the modal reduction module, is used to receive the flexible body modal set, establish a rigid-flexible coupling interface between the rigid body and the flexible body in the multibody dynamics simulation environment, and construct transition units on the interface to generate an initial interface model containing basic rigid-flexible coupling relationships. The local compensation module, connected to the interface construction module, is used to receive the initial interface model, identify hotspot regions of high gradient stress field in the initial interface model, perform sub-model ultra-refinement analysis on the hotspot regions, extract the local flexibility matrix and compare the difference with the stiffness components of the transition unit to generate a stiffness deviation matrix, and implant dynamic compensation layer units in the hotspot regions based on the stiffness deviation matrix to generate a rigid-flexible coupling interface correction model with local correction capability. The kinematic correction module, connected to the local compensation module, is used to receive the rigid-flexible coupling interface correction model, apply boundary conditions under the tilting transition condition to the model, including tilting angular velocity and tilting angular acceleration, and introduce gyro effect terms and centrifugal stiffening effect terms as correction coefficients to generate a complete displacement compatibility equation containing kinematic corrections. The solution output module, connected to the kinematic correction module, is used to receive the complete displacement coordination equation, embed the complete displacement coordination equation into the multibody dynamics simulation solver for numerical solution, and output the dynamic response of the key parts of the reducer under tilting transition conditions.

3. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The acquisition of the load spectrum in step S1 further includes: acquiring time history load data of the input shaft, output shaft, and housing connection of the reducer under three typical operating conditions: hovering, cruise, and tilt transition, from the full-aircraft flight test data of the tiltrotor. The time history load data includes torque, axial force, radial force, and bending moment. A fast Fourier transform is performed on the time history load data to obtain the load spectrum diagram for each operating condition. Frequency components with amplitudes exceeding 20% ​​of a reference amplitude are identified as key frequency components in the load spectrum diagram. The reference amplitude is the arithmetic mean of the amplitudes of all frequency components under each operating condition. The amplitude and phase information corresponding to the key frequency components are extracted, and the real and imaginary parts of the excitation feature vectors are constructed according to the operating condition category. The excitation feature vectors of the three operating conditions are combined into a multidimensional excitation feature matrix.

4. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The determination of the preset threshold in step S2 further includes: receiving the multidimensional excitation feature matrix output in step S1, performing principal component analysis on the multidimensional excitation feature matrix, and extracting the principal components with a cumulative contribution rate exceeding 95% as the main excitation directions; for the fixed interface modal analysis results of each substructure, calculating the modal participation factor of each retained principal mode and constraint mode, wherein the modal participation factor is defined as the absolute value of the product of the mode shape and the direction cosine of the main excitation direction; arranging the modal participation factors in descending order, calculating the cumulative participation factor, and the modal order corresponding to the first time the cumulative participation factor reaches 0.95 is the cutoff order of the retained mode, and the minimum modal participation factor value corresponding to this order is the preset threshold; discarding all higher-order local modes below the preset threshold, retaining modes higher than or equal to the preset threshold, and generating a reduced flexible body modal set.

5. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The construction of the transition unit in step S3 further includes: selecting a set of master nodes on the flexible body interface, the master nodes being located at the center of the bearing seat, the projection position of the gear meshing point, and the flange connecting the housing and the support arm; establishing a rigid beam element between the rigid body reference point and each of the master nodes, the length direction of the rigid beam element being perpendicular to the flexible body interface; establishing displacement coordination relationships between the nodes of the rigid beam element on the flexible body interface and the surrounding slave nodes through a multi-point constraint algorithm, the displacement coordination relationships being implemented using the Lagrange multiplier method, the constraint equations being that the three translational degrees of freedom of each slave node are equal to the translational degrees of freedom of the master node plus the entrainment displacement caused by the rotational degrees of freedom of the master node; applying forces and moments from the rigid body to the rigid body reference point of the rigid beam element, the forces and moments being distributed to each slave node through the constraint equations, thereby forming a transition unit, the stiffness characteristics of the transition unit being calculated by the modal stress stiffness matrix of each mode in the flexible body modal set output in step S2 using the modal superposition method.

6. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The identification of high-gradient stress field hotspot regions in step S4 further includes: receiving the initial interface model output from step S3; applying the tilt transition load from the excitation feature vector output from step S1 to the initial interface model; performing preliminary rigid-flexible coupling dynamic simulation; extracting the von Mises stress time history of each node on the flexible body interface; calculating the root mean square stress value of each node during the entire tilt transition time history; spatially interpolating the root mean square stress value in the flexible body interface region to generate a stress distribution cloud map; identifying continuous regions in the stress distribution cloud map where the root mean square stress value is greater than 1.5 times the global root mean square stress average value, and marking these regions as high-gradient stress field hotspot regions; extracting the node numbers and coordinates of all flexible body interface nodes covered by the hotspot regions to form an interface stress hotspot node set.

7. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The sub-model ultra-refinement analysis in step S4 further includes: receiving the interface stress hotspot node set output in step S6; extracting a local geometric model containing the hotspot node set and at least three layers of surrounding unit regions from the original three-dimensional solid model of the reducer; re-meshing the local geometric model, setting the unit size to one-fifth of the original global mesh size, and performing secondary refinement at stress concentration locations to ensure that the minimum unit size does not exceed 0.1 mm; applying displacement boundary conditions to the local geometric model, the displacement boundary conditions being taken from the displacement time history of the hotspot region boundary nodes at the corresponding time in the preliminary rigid-flexible coupling dynamic simulation; applying dynamic loads at the corresponding time to the internal nodes of the local geometric model, the dynamic loads including gear meshing force, bearing force, and inertial force; solving the transient dynamic equations of the local geometric model, extracting the displacement response of each master node in the hotspot node set, and constructing a displacement response matrix; and inverting the displacement response matrix to obtain the local compliance matrix.

8. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The parameter determination of the dynamic compensation layer unit in step S4 further includes: extracting stiffness matrix blocks corresponding to the master nodes in the hotspot region from the transition unit generated in step S3. These blocks have a dimension of 6×6 and represent the modal stiffness contributions of the master nodes across their six degrees of freedom. The local stiffness matrix is ​​obtained by inverting the local flexibility matrix output in step S7; this local stiffness matrix also has a dimension of 6×6. The difference between the local stiffness matrix and the modal stiffness matrix blocks is calculated to obtain the stiffness deviation matrix. ΔK A nonlinear spring-damper model is established, wherein the force-displacement relationship of the nonlinear spring-damper is as follows: F= kx+c(dx / dt) , where is the nonlinear function resulting from the initial stiffness coefficient multiplied by the direction weight. c The damping coefficient is taken as 0.1 times the critical damping ratio; the nonlinear spring-damper is implanted in parallel into the transition unit to form a dynamic compensation layer unit.

9. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The activation criterion for the dynamic compensation layer unit in step S4 further includes: within each simulation integration step, reading the instantaneous load vector F of the rigid body acting on the master node, the load vector containing three force and three moment components; calculating the Euclidean norm Fi of the load vector F; defining a spherical neighborhood with a radius of 10 mm centered on the master node, statistically analyzing the coordinates of all slave nodes within the neighborhood, and calculating the distance vector from the slave nodes to the master node; projecting the load vector F onto the radial direction of each slave node to obtain the radial load component of each slave node; calculating the spatial rate of change of the radial load component within the neighborhood, i.e., the difference between the maximum and minimum values ​​of the radial load component divided by the distance from the master node to the farthest slave node, to obtain the load gradient value. G The load gradient value G With preset threshold G 0 The preset threshold is compared. G 0 The value is taken as 1.2 times the maximum slope of the load spectrum under the tilting transition condition in step S1; if G < G 0 If the load gradient is below the threshold, only the transition unit is activated; if G≥G 0 If the load gradient is higher than the threshold, the dynamic compensation layer unit is activated in parallel for local correction.

10. The method for constructing a rigid-flexible coupling dynamic model of a tiltrotor reducer according to claim 1, characterized in that: The calculation of the gyroscopic effect term and the centrifugal stiffening effect term in step S5 further includes: extracting the tilt angular velocity under the tilt transition condition from the excitation feature vector output in step S1. ω and tilt angular acceleration α The tilt angular velocity ω The vector contains angular velocity components about the three body axes of the aircraft; in the servo coordinate system, the motion equations of any infinitesimal element on the flexible body are established, and the gyroscopic torque term M is introduced. gyro =-2 ωv ,in v Let be the relative velocity vector of the infinitesimal element in the moving coordinate system; introduce a centrifugal stiffening effect term. K cf = ρAω 2 r ,in ρ For material density, A Let the cross-sectional area of ​​the infinitesimal element be... ω =ǀ ω ǀ represents the magnitude of angular velocity. r The distance from the infinitesimal element to the rotation axis is given. The gyroscopic torque term and the centrifugal stiffening effect term are added as additional load vectors to the right-hand side of the displacement compatibility equation. At the same time, the derivative of the gyroscopic torque term with respect to displacement is added as an additional stiffness matrix to the left-hand coefficient matrix of the displacement compatibility equation, forming a modified displacement compatibility equation. This equation describes the dynamic displacement compatibility relationship between a rigid body and a flexible body under tilting motion.

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