Multi-flexible-body coupling dynamics modeling method and device for rotary non-inertial system gear system

Abstract

The invention provides a multi-flexible-body coupling dynamics modeling method and device for a rotary non-inertial system gear system, and the method comprises the steps: dividing the gear system into a shaft system substructure and a box body substructure, and respectively building the kinematic equations of the shaft system substructure and the box body substructure; a generalized coordinate kinetic equation of the box body is obtained, the generalized coordinate kinetic equation comprises fixed-axis rotation coordinates and flexible node coordinates, and the non-inertial system effect of random body rotation is included; a shaft system generalized coordinate kinetic equation is obtained, discretization is carried out, and a composite motion effect is included; performing order reduction on the box body and the shaft system through a state space fixed interface modal synthesis method, retaining interface nodes and mapping internal nodes to a low-order modal space; bearing coupling is achieved through multi-point constraint, and shafting bearing force is equivalently distributed to flexible joints of a box body; establishing a gear meshing coupling model, and loading a gear backlash, a meshing error and time variable stiffness; and all subsystem equations are coupled to form an integral reduced-order model, and a dimension-increasing fine integration algorithm is adopted for solving. The invention provides an efficient and accurate tool for the design of a gear transmission system.

Description

Technical Field

[0001] The embodiments of the present invention relate to the field of dynamics technology of mechanical transmission systems, and in particular to a method and device for multi-flexible-body coupling dynamics modeling of a rotating non-inertial gear system. Background Technology

[0002] With the continuous advancement of industrial technology and the improvement of automation levels, gear systems, as key transmission components, are increasingly widely used in the field of mechanical transmission. Especially under high-speed, heavy-load, and complex extreme conditions, the dynamic performance of gear systems directly affects the stability and reliability of the entire system. Therefore, accurate dynamic modeling of gear systems to predict their motion characteristics and optimize design schemes has become a research hotspot in the current engineering field.

[0003] Currently, various methods have been proposed and applied for dynamic modeling of gear systems. Among them, inertial frame-based modeling methods are the most common. These methods typically assume that the gear system is in an inertial reference frame and establish the system's dynamic equations using mechanical principles such as Newton's laws of motion or Lagrange's equations. However, in practical applications, gear systems are often in non-inertial reference frames, such as rotating frames or moving platforms. In this case, non-inertial effects such as inertial forces and Coriolis forces will significantly affect the dynamic behavior of the gear system. Existing modeling methods have significant shortcomings in handling non-inertial frame effects. On the one hand, these methods often ignore the influence of inertial forces on system dynamics, resulting in insufficient model accuracy and an inability to accurately predict the motion characteristics of the gear system. On the other hand, even when non-inertial frame effects are considered, simplified treatments are often used, such as introducing non-inertial frame effects as additional terms into the model while ignoring their coupling with other parts of the system, thus affecting the accuracy and reliability of the model. Therefore, developing a multi-flexible-body coupled dynamics modeling method and device for rotating non-inertial gear systems can effectively overcome the shortcomings of the aforementioned related technologies, and has become a technical problem that the industry urgently needs to solve. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, embodiments of the present invention provide a method and apparatus for multi-flexible-body coupled dynamic modeling of a rotating non-inertial gear system.

[0005] In a first aspect, embodiments of the present invention provide a multi-flexible-body coupled dynamics modeling method for a rotating non-inertial gear system, comprising: dividing the gear system into a shaft system substructure and a housing substructure, and establishing their kinematic equations based on the multi-flexible-body system dynamics theory; obtaining the generalized coordinate dynamics equation of the housing according to the Lagrange equation, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effect of random body rotation; obtaining the generalized coordinate dynamics equation of the shaft system according to the Lagrange equation, including revolution, rotation, and flexible node coordinates, discretizing according to the spatial beam theory and taking into account the composite motion effect; reducing the order of the housing and shaft system by the state-space fixed interface modal synthesis method, retaining the interface nodes and mapping the internal nodes to the lower-order modal space; realizing bearing coupling through multi-point constraint MPC, and equivalently distributing the shaft system bearing force to the housing flexible nodes; establishing a gear meshing coupling model, loading tooth backlash, meshing error, and time-varying stiffness; coupling the equations of each subsystem to form an overall reduced-order model, and solving it using an augmented-dimensional fine integral algorithm.

[0006] Based on the above method embodiments, the multi-flexible-body coupled dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the generalized coordinate dynamic equation of the box is obtained according to the Lagrange equation, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effect of random body rotation, includes: the generalized coordinate dynamic equation of the box is discretized by finite element solid elements, and the mass matrix includes a coupling term of rotational inertia and deformation inertia.

[0007] Based on the above method embodiments, the multi-flexible-body coupled dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the generalized coordinate dynamic equation of the shaft system is obtained according to the Lagrange equation, including the rotational coordinates of revolution and rotation and the coordinates of flexible nodes, and is discretized according to the spatial beam theory and the composite motion effect is taken into account, includes: the generalized coordinate dynamic equation of the shaft system is discretized based on the spatial beam element, and the mass matrix includes the revolution-rotation-deformation inertia coupling term.

[0008] Based on the above method embodiments, the multi-flexible-body coupled dynamics modeling method for rotating non-inertial gear systems provided in this embodiment of the invention includes the following: reducing the order of the housing and shaft system by using the state-space fixed interface modal synthesis method, retaining interface nodes and mapping internal nodes to a lower-order modal space. The method includes: using the state-space fixed interface modal synthesis method, by extracting the main mode and constraint mode of the fixed interface, mapping the state variables of the internal nodes to a 2n-dimensional modal space, and reducing the degrees of freedom by using three times the meshing frequency as the cutoff frequency.

[0009] Based on the above method embodiments, the multi-flexible-body coupling dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein bearing coupling is achieved through multi-point constraint MPC, and the bearing force of the shaft system is equivalently distributed to the flexible nodes of the housing, includes: the multi-point constraint MPC equates the bearing force to the force and torque of the virtual rigid body center of mass, and distributes it to the flexible nodes of the housing through mass normalization, thereby achieving force-displacement coupling.

[0010] Based on the above method embodiments, the multi-flexible-body coupling dynamics modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the establishment of a gear meshing coupling model and the loading of tooth backlash, meshing error, and time-varying stiffness include: the gear meshing coupling model includes a piecewise function of tooth backlash, a simple harmonic superposition expression of meshing error, and an analytical formula for time-varying meshing stiffness.

[0011] Based on the above method embodiments, the multi-flexible-body coupled dynamics modeling method for rotating non-inertial gear systems provided in this invention embodiment, wherein the equations of each coupled subsystem form an overall reduced-order model, which is solved using an augmented-dimensional refined integration algorithm, includes: the augmented-dimensional refined integration algorithm separating time-varying terms into non-homogeneous terms, realizing time step recursion through the principle of exponential matrix addition, and controlling the error within a certain range. Within the range.

[0012] Secondly, embodiments of the present invention provide a multi-flexible-body coupled dynamics modeling device for a rotating non-inertial gear system, comprising: a first main module for dividing the gear system into a shaft system substructure and a housing substructure, and establishing their kinematic equations based on multi-flexible-body system dynamics theory; a second main module for deriving the generalized coordinate dynamics equations of the housing according to the Lagrange equations, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effects of random body rotation; and a third main module for deriving the generalized coordinate dynamics equations of the shaft system according to the Lagrange equations, including revolution, rotation, and flexible body coordinates. The main modules are as follows: 1) The coordinates of the nodes are discretized according to the spatial beam theory and the combined motion effect is taken into account; 2) The fourth main module is used to reduce the order of the box and shaft system by using the fixed interface modal synthesis method in state space, retaining the interface nodes and mapping the internal nodes to the lower-order modal space; 3) The fifth main module is used to realize bearing coupling by multi-point constraint MPC, and to equivalently distribute the bearing force of the shaft system to the flexible nodes of the box; 4) The sixth main module is used to establish the gear meshing coupling model, and load tooth backlash, meshing error and time-varying stiffness; 5) The seventh main module is used to couple the equations of each subsystem to form an overall reduced-order model, and solve it using an augmented-dimensional fine integral algorithm.

[0013] Thirdly, embodiments of the present invention provide an electronic device, comprising:

[0014] At least one processor, at least one memory, and a communication interface; wherein,

[0015] The processor, memory, and communication interface communicate with each other;

[0016] The memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the multi-body coupling dynamics modeling method for rotating non-inertial gear systems provided by any of the various implementations of the first aspect.

[0017] Fourthly, embodiments of the present invention provide a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a multi-body coupled dynamics modeling method for a rotating non-inertial gear system provided by any of the various implementations of the first aspect.

[0018] The multi-flexible-body coupled dynamics modeling method and device for rotating non-inertial gear systems provided in this invention, through the theory of multi-flexible-body system dynamics, achieves for the first time a deep coupled modeling of non-inertial frame effects with the flexibility of gear shafts, bearings, and housings. This overcomes the limitations of traditional methods that simplify processing or ignore coupling, significantly improving the accuracy of dynamic response prediction under extreme conditions. The use of state-space modal synthesis and dimensionally enhanced refined integral algorithms improves computational efficiency by 3 to 5 times, making it suitable for real-time analysis. Modular substructure partitioning and standardized modeling processes allow for flexible expansion to complex scenarios such as large-scale aircraft maneuvers and automobile start-stop-turning, improving versatility by over 60%. The matrix-based derivation based on the Lagrange equation avoids tedious vector mechanics calculations, improving programming efficiency by 40%, providing an efficient and accurate theoretical tool for the design and optimization of gear transmission systems in high-end equipment. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A schematic diagram of the process for multi-flexible-body coupling dynamics modeling method for rotating non-inertial gear systems provided in an embodiment of the present invention;

[0021] Figure 2 This is a schematic diagram of the structure of the multi-flexible-body coupling dynamics modeling device for a rotating non-inertial gear system provided in an embodiment of the present invention;

[0022] Figure 3 A schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention;

[0023] Figure 4 This is a schematic diagram illustrating the substructure division effect of the transmission system provided in an embodiment of the present invention;

[0024] Figure 5 Any point on the box provided in the embodiment of the present invention Schematic diagram of position coordinates; the superscript j indicates the gearbox body;

[0025] Figure 6 This is a schematic diagram illustrating the effect of dividing the box interface nodes / internal nodes according to an embodiment of the present invention;

[0026] Figure 7 This is a schematic diagram illustrating the effect of shaft system node division provided in an embodiment of the present invention;

[0027] Figure 8 Any point on the shaft system provided in the embodiments of the present invention Schematic diagram of position coordinates;

[0028] Figure 9 This is a schematic diagram of the bearing coupling effect provided in an embodiment of the present invention;

[0029] Figure 10 This is a schematic diagram of the multi-point constraint MPC effect provided in an embodiment of the present invention;

[0030] Figure 11 This is a schematic diagram of the gear coupling effect provided in an embodiment of the present invention. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form feasible technical solutions. Such combinations are not constrained by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. If there are step numbers in the following embodiments, they are only set for ease of explanation and the order between steps is not limited. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0032] This invention provides a method for multi-flexible-body coupled dynamics modeling of a rotating non-inertial gear system, see [link to relevant documentation]. Figure 1 The method includes: dividing the gear system into a shaft system substructure and a housing substructure, and establishing their kinematic equations based on the dynamics theory of multi-flexible-body systems; obtaining the generalized coordinate dynamic equation of the housing according to the Lagrange equation, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effect of random body rotation; obtaining the generalized coordinate dynamic equation of the shaft system according to the Lagrange equation, including revolution, rotation, and flexible node coordinates, discretizing according to the spatial beam theory and taking into account the composite motion effect; reducing the order of the housing and shaft system through the state-space fixed interface modal synthesis method, retaining the interface nodes and mapping the internal nodes to the lower-order modal space; realizing bearing coupling through multi-point constraint MPC, and equivalently distributing the shaft system bearing force to the housing flexible nodes; establishing a gear meshing coupling model, loading tooth backlash, meshing error, and time-varying stiffness; coupling the equations of each subsystem to form an overall reduced-order model, and solving it using an augmented-dimensional fine integral algorithm.

[0033] Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupled dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the generalized coordinate dynamic equation of the box is obtained according to the Lagrange equation, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effect of random body rotation, includes: the generalized coordinate dynamic equation of the box is discretized by finite element solid elements, and the mass matrix includes a coupling term of rotational inertia and deformation inertia.

[0034] Specifically, such as Figure 4 As shown, based on substructure analysis theory, the gear system is divided into a shaft system substructure and a housing substructure. The shaft system substructure includes the input gear shaft, output gear shaft, and other shaft systems. The housing can be further divided into secondary substructures such as an upper housing and a lower housing based on its specific interface connections and assembly relationships. For example... Figure 5 As shown, the floating coordinate system of the machine body The initial position coincides with the inertial coordinate system OXYZ, and the superscript h represents the body. Without loss of generality, let the body rotate about the Z-axis of the inertial coordinate system OXYZ. At this time, the floating coordinate system... of The axis coincides with the Z-axis of the inertial coordinate system OXYZ, and the floating coordinate system... of , Rotate about the X and Y axes of the inertial coordinate system OXYZ respectively. horn.

[0035] The gear transmission system is mounted and fixed on the machine body, and rotates along the machine body around a fixed axis. A floating coordinate system for the machine body is established at the center of mass of the machine body. The superscript j denotes the gearbox housing. Without loss of generality, let the gearbox housing coordinate system... of axis, axis, The axes are respectively related to the floating coordinate system of the machine body. of axis, axis, The axes are parallel. Floating coordinate system for the box. The position vector of the origin in the inertial coordinate system OXYZ is , In the floating coordinate system of the box The projection in the plane is Then the floating coordinate system of the box. The position coordinate components of the origin in the inertial coordinate system OXYZ are:

[0036] (1)

[0037] in, for The length of the mold, for and The initial included angle. for Projection onto the Z-axis of the inertial coordinate system. Taking the derivative with respect to time, we get:

[0038] (2)

[0039] (2) In the formula,

[0040] (3)

[0041] The value is shown in (3). The value is shown in (3), which is the angular velocity of the box; the superscript T indicates transpose. Based on the dynamics theory of multi-flexible body systems, the box is discretized by finite element method and divided into n e Individual units A flexible node, any point on the box. The state coordinates in the inertial coordinate system OXYZ are:

[0042] (4)

[0043] in, For any point on the box Position coordinates in the inertial coordinate system OXYZ For any point on the box Velocity coordinates in the inertial coordinate system OXYZ; Let Z be the rotation transformation matrix of the box about the Z-axis of the inertial coordinate system OXYZ, and its value is:

[0044] (5)

[0045] for Point relative to the box's floating coordinate system The position coordinate vector is decomposed into fixed coordinate vectors. With the deformed coordinate vector after finite element discretization ; Let element k be in the floating coordinate system of the box. The unit shape function under, Let the displacement vector of the flexible body node of the box be denoted as . For the rotation transformation matrix, the rotation angle The derivative matrix of . For the box-shaped floating coordinate system The derivative of the position vector of the origin in the inertial coordinate system OXYZ with respect to time. Let be the time derivative of the rotation transformation matrix of the box about the Z-axis of the inertial coordinate system OXYZ. The value is shown in (3). The value is shown in (3), which is the angular velocity of the box.

[0046] Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupled dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the generalized coordinate dynamic equation of the shaft system is obtained according to the Lagrange equation, including the rotational coordinates of revolution and rotation and the coordinates of flexible nodes, and is discretized according to the spatial beam theory and the composite motion effect is taken into account, including: the generalized coordinate dynamic equation of the shaft system is discretized based on the spatial beam element, and the mass matrix includes the revolution-rotation-deformation inertia coupling term.

[0047] Specifically, the kinetic and potential energy of the box can be obtained from equation (4), and then substituted into the Lagrange equations for the box in its free state to obtain the generalized coordinate dynamic equations of the box:

[0048] (6)

[0049] Here is the mass matrix of the box.

[0050] To augment the stiffness matrix of the box,

[0051] For terms related to the square of velocity,

[0052] This refers to the generalized gravitational load acting on the box.

[0053] Let be the generalized coordinate matrix of the box in the inertial coordinate system OXYZ. for The second derivative with respect to time. Its value is:

[0054] (7)

[0055] The values ​​of each sub-block are:

[0056] (8)

[0057] , , These represent the 1st, 2nd, and mth flexible nodes of the box, respectively, with each node containing three degrees of freedom in three directions. for The second derivative with respect to time. The value of each sub-block is the value of the second derivative with respect to time of each sub-block in formulas (7) and (8).

[0058] Let be the mass matrix of the box, whose value is the superposition of the mass matrices of each element, i.e.:

[0059] (9)

[0060] in, Let n be the mass matrix of the k-th box element. e Indicates the number of box units.

[0061] Each sub-block is the superposition of the corresponding sub-blocks in each unit mass matrix, that is:

[0062] (10)

[0063] Let a be the ab sub-block of the k-th unit mass matrix, where a and b alternately take θ and f, respectively.

[0064] The values ​​of each sub-block in the unit mass matrix k are:

[0065] (11)

[0066] in, For the unit density, V jk Let E be the volume of the k-th unit of the box. jT For E j The transpose of E j The value of is shown in formula (3).

[0067] The augmented stiffness matrix for the box is:

[0068] (12)

[0069] This is the superposition of the stiffness matrices of all elements in the box, i.e.:

[0070] (13)

[0071] That is, the floating coordinate system of the box. The stiffness matrix of the lower k element.

[0072] The term related to the square of the velocity is equivalent to the centrifugal inertial force and the Coriolis force, that is:

[0073] (14)

[0074] Let be the time derivative of the generalized coordinate matrix of the box in the inertial coordinate system OXYZ. Let be the time derivative of the box mass matrix in the inertial coordinate system OXYZ. The values ​​for each sub-block are:

[0075] (15.a)

[0076] (15.b)

[0077] in,

[0078] (16.a)

[0079] (16.b)

[0080] (16.c)

[0081] (16.d)

[0082] , The first and second rows of the k-element shape functions are shown, with the superscript T indicating transpose. Let k be any point on the flexible body floating coordinate system. The i-th element of the fixed coordinate vector.

[0083] The generalized gravitational load acting on the box has the following value:

[0084] (17)

[0085] In the formula, for The second element, for The second line, for The second line. g is the acceleration due to gravity.

[0086] Therefore, the dynamic equations of the box can be expressed as:

[0087] (18.a)

[0088] (18.b)

[0089] in, , , Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupled dynamics modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the state space fixed interface modal synthesis method is used to reduce the order of the housing and shaft system, retain the interface nodes and map the internal nodes to the lower-order modal space, includes: the state space fixed interface modal synthesis method, by extracting the fixed interface principal mode and constraint mode, mapping the internal node state variables to a 2n-dimensional modal space, and reducing the degrees of freedom with three times the meshing frequency as the cutoff frequency.

[0090] For details, please refer to [link / reference]. Figure 6 Due to the large number of discrete elements in the finite element method, efficient analysis is difficult, necessitating a reduction in the order of the elements. Using the traditional fixed-interface modal synthesis method, the modes of the substructure must first be determined. However, the modes of the rotating substructure are time-varying, requiring modal synthesis and order reduction of the rotating body using state-space theory. Firstly, based on the interaction between the nodes and the external environment, the flexible nodes... Divided into interface nodes Internal nodes The system consists of two parts. The interface nodes are the parts that exchange energy with the outside world. In this example, they are all bearing nodes, and are further subdivided into bearing interface nodes 1 according to their location. Bearing interface node 2 Bearing interface node 3 Bearing interface node 4 At this point, the displacement vector matrix of the flexible substructure j of the box is expressed as:

[0091] (19)

[0092] in,

[0093] (20)

[0094] Therefore, the equation of motion for the box is rewritten as:

[0095] (twenty one)

[0096] in, , , , , , Based on the state-space decoupling method, 2(3n) is introduced. j +1) dimensional state vector,

[0097] (twenty two)

[0098] , ,

[0099] The dynamic state-space equation of the box is:

[0100] (twenty three)

[0101] in,

[0102] (24.a)

[0103] , , , , , , ,

[0104] (24.b)

[0105]

[0106] (24.c)

[0107]

[0108] (24.d)

[0109]

[0110] According to basic kinematic principles, the motion of the nodes inside the box can be expressed as the sum of the relative motion when the interface is fixed and the motion caused by the interface. When the interface is fixed, The equation for free vibration in the state space of the box is obtained as follows:

[0111] (25)

[0112] Solving equation (25) yields each characteristic frequency. A corresponding pair of regularized mode vectors , (r = 1,2,…,3) ),make:

[0113] (26)

[0114]

[0115] The orthogonality relation is then expressed as:

[0116] (27)

[0117] Let be the r-th natural frequency. The cutoff frequency is defined as three times the meshing frequency, retaining the first l-th dominant modes, called . , To reduce the principal mode by fixing the interface of the box, the state vector of the internal nodes is now:

[0118] (28)

[0119]

[0120] , For modal coordinates, This transforms the internal nodes from physical space to a reduced-order modal space.

[0121] Constrained modes Defined as:

[0122] (29)

[0123] The internal node state vector generated due to the movement along with the interface is:

[0124] (30)

[0125] Therefore, the state vector expression for the motion of the internal nodes is:

[0126] (31)

[0127] The above equation shows that the principal mode and the constraint mode of the fixed interface constitute a complete mode set. This leads to the transformation equation with a greatly reduced number of degrees of freedom:

[0128] (32)

[0129] I is the identity matrix.

[0130] Substitute into (23) and multiply by the left. ,have to:

[0131] (33)

[0132] In the formula,

[0133] (34), blank spaces are all 0 elements.

[0134] Equation (33) is the reduced-order dynamic state space equation for the rotating box.

[0135] Based on the geometry of the shaft system, the shaft system is divided into: There are 1 shaft segment, totaling 10 shaft segments. There are several nodes. Nodes must be installed at locations where there is energy exchange with the outside world or changes in geometric dimensions, such as... Figure 7 As shown. Floating coordinate system of axes. Set at the speed input node, such as Figure 8 As shown, with the axial direction as The coordinates of any point P on axis segment k in the inertial coordinate system OXYZ are:

[0136] (35)

[0137] Let P be the coordinates of any point P on axis segment k. Let P be the velocity coordinate of any point P on axis segment k.

[0138] in, It is an axis coordinate system The coordinate transformation matrix to the inertial coordinate system OXYZ has the following value:

[0139] (36)

[0140] in The rotation angle of the shaft system about its central axis.

[0141] Axis coordinate system The position coordinates of the origin in the inertial coordinate system OXYZ Let be the relative distance between the axis coordinate system and the box coordinate system, and its components are expressed as:

[0142] (37)

[0143] The coordinates of any point on element k relative to the origin of the floating coordinate system are divided into fixed coordinates. and deformation amount The components of a fixed coordinate system are expressed as follows:

[0144] (38)

[0145] For the shaft system deformation coordinates, for right The derivative matrix, For shaft speed, For the k-th axis segment in the axis coordinate system The unit shape function under the given conditions has the value of . The shape function in the unit coordinate system. The element displacement vector moves from the element coordinate system to the axis system in a floating coordinate system. The transformation matrix, The element nodal displacement vector is a floating coordinate system from the element coordinate system to the axis system. The transformation matrix. This is a Boolean indicator matrix, representing the element displacement vector in the floating coordinate system of the axis. The number in the middle.

[0146] Each discrete axis segment is modeled using a spatial beam, with a floating coordinate system for the axis system. The flexible deformation node of the lower beam node i is represented as:

[0147] (39)

[0148] The element shape function matrix in the element's local coordinate system is represented as follows:

[0149] (40)

[0150] in,

[0151] (41)

[0152] (42)

[0153] In the formula, x is the coordinate of any point on axis segment k, and l is the length of the axis segment; EI zz EI yy Floating coordinate system of axis z s Direction and y s Directional bending stiffness, where G is the shear modulus, A is the cross-sectional area, and κ is the shear correction factor, has the following value for a thin-walled circular tube:

[0154] (43)

[0155] μ is Poisson's ratio.

[0156] In its free state, the shaft system is subjected to gravity and is in a state of combined motion, rotating around its axis and revolving with the box. Its dynamic equation is:

[0157] (44)

[0158] in Let X be the generalized coordinate matrix of the axis system in the inertial coordinate system OXYZ, and its values ​​are:

[0159] (45) for The second derivative with respect to time.

[0160] The degrees of freedom of the flexible nodes in the shaft system are:

[0161] (46)

[0162] The mass matrix of the shaft system.

[0163] (47)

[0164] n s This represents the number of shaft segment elements. Each sub-block is the superposition of the corresponding sub-blocks in the mass matrix of each element, i.e.:

[0165] (48)

[0166] Where a and b take turns , f.

[0167] The values ​​of each sub-block in the unit mass matrix k are:

[0168] Moment of inertia of the shaft system:

[0169] (49.a)

[0170] Inertial coupling between the revolution and rotation of the shaft system:

[0171] (49.b)

[0172] Inertial coupling of shaft system revolution and deformation:

[0173] (49.c)

[0174] Moment of inertia of the shaft system:

[0175] (49.d)

[0176] Shaft rotation and deformation inertia coupling:

[0177] (49.e)

[0178] Relative deformation inertia of flexible bodies:

[0179] (49.f)

[0180] in, , V sk Let be the volume of the k-th element in the axis system. , , They represent The first, second, and third lines.

[0181] Here is the augmented stiffness matrix of the shaft system, i.e.:

[0182] (50)

[0183] The value is:

[0184] (51)

[0185] The term related to the square of the velocity is equivalent to the centrifugal inertial force and the Coriolis force, that is:

[0186] (52) The superscript · indicates the derivative with respect to time.

[0187] The values ​​of each sub-block are:

[0188] (53.a)

[0189] (53.b)

[0190] (53.c)

[0191] in,

[0192] (54.a)

[0193] (54.b)

[0194] (54.c)

[0195] (54.d)

[0196] (54.e)

[0197] (54.f)

[0198] (54g)

[0199] (54.h)

[0200] The generalized gravity load acting on the shaft system has the following value:

[0201] (55)

[0202] in for The second line.

[0203] This yields the dynamic equations of the shaft system under the combined motion state of rotation around the axis and revolution with the box.

[0204] Similarly, the flexible nodes are divided into interface nodes and internal nodes. Interface nodes include gear nodes and bearing nodes, while the remaining flexible nodes are classified as internal nodes. Using the same state-space decoupling method, 2[6(n s +1)+2] dimensional state vector,

[0205] (56)

[0206]

[0207] in For the gear node on shaft s, Let be a bearing node on shaft system s. Then the dynamic state-space equation of the shaft system is:

[0208] (57)

[0209] in,

[0210] (58.a)

[0211] (58.b)

[0212] (58.c)

[0213] (58.d)

[0214] Using the state-space fixed-interface modal synthesis method, the reduced-order state-space dynamic equations of the shaft system are obtained:

[0215] (59)

[0216] in,

[0217] (60)

[0218] The internal node degrees of freedom are greatly reduced by using modal coordinates and omitting higher-order modes.

[0219] Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupling dynamic modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein bearing coupling is achieved through multi-point constraint MPC, and the bearing force of the shaft system is equivalently distributed to the flexible nodes of the housing, includes: the multi-point constraint MPC equates the bearing force to the force and torque of the virtual rigid body center of mass, and distributes it to the flexible nodes of the housing through mass normalization, thereby achieving force-displacement coupling.

[0220] Specifically, such as Figure 9 As shown, the shaft system is coupled to the housing via bearings. Therefore, a local coordinate system is established at the bearing positions on the shaft system. The generalized coordinates of the bearing nodes in the shaft system in the inertial coordinate system OXYZ are: The values ​​of its items are:

[0221] (61)

[0222] in, For the bearing nodes of the shaft system relative to the shaft system coordinate system Translation coordinates of the origin Let be the rotational coordinates of the bearing node i in the shaft system. Similarly, establish a local coordinate system for the bearing node at the geometric center of the bearing bore in the housing. Its generalized coordinates in the inertial coordinate system OXYZ are: The values ​​for each item are:

[0223] (62)

[0224] in, For the bearing nodes of the housing relative to the housing coordinate system Translation coordinates of the origin Let be the rotational coordinate of bearing node i in the housing. The deformation of the bearing in the inertial coordinate system OXYZ can be expressed as the difference between the generalized coordinates of the shaft bearing node and the generalized coordinates of the housing bearing node, i.e.:

[0225] (63)

[0226] The bearing stiffness is:

[0227] (64)

[0228] The bearing force in the inertial coordinate system OXYZ is:

[0229] (65)

[0230] in,

[0231] (66)

[0232] The bearing force acting on shaft element s is:

[0233] (67)

[0234] like Figure 10 As shown, in order to transfer the bearing force on the bearing node of the housing to the housing, according to the MPC constraint principle, the bearing force is distributed to the bearing hole according to the static equivalent relationship. The deformation coordinate vector of each bearing-coupled flexible node is the interface node of the housing. The bearing is coupled to a flexible node and then equated to a virtual rigid body, the center of mass of which experiences a force of... The torque is Under the action of the center-of-mass force and torque, the acceleration of the center of mass and the angular acceleration about the center of mass of a rigid body in the inertial coordinate system are respectively:

[0235] (68)

[0236] in The normalized quality of the k-th flexible node is, i.e. . Let the moment of inertia of the rigid body be... Let be the distance from the k-th flexible node to the bearing node of the housing. If the flexible node is attached to the rigid body and moves with the rigid body, then the acceleration of the k-th flexible node is:

[0237] (69)

[0238] In the formula Let be the coordinate matrix of the angular acceleration at the center of mass, and its value is:

[0239] (70)

[0240] Let the position coordinates of the k-th flexible node relative to the bearing node of the housing be given by the component expression:

[0241] (71)

[0242] but Expanded representation:

[0243] (72)

[0244] The force on the kth flexible node is:

[0245] (73)

[0246] Therefore, the bearing force on the housing can be expressed as:

[0247] (74)

[0248] In the formula, The value is:

[0249] (75)

[0250] Therefore, the dynamic equation of the bearing coupling unit is:

[0251] (76)

[0252] That is, (76) the coupling between the housing and the shaft system was completed. Among them... , , These represent the mass matrix, gyroscope matrix, and stiffness matrix blocks corresponding to the positions of the box after order reduction. , , These represent the mass matrix, gyroscope matrix, and stiffness matrix blocks corresponding to the positions of the reduced-order axis system, respectively. This is the external force matrix corresponding to the degrees of freedom involved in the coupling. The inertia of the virtual rigid body has the following value:

[0253] (77)

[0254] like Figure 11 As shown, a local coordinate system is established at the gear meshing point of the shaft system. Its generalized coordinates in the inertial coordinate system are:

[0255] (78)

[0256] in,

[0257] (79)

[0258] The components are represented as ;

[0259] Let be the position coordinates of the gear meshing point from the origin of the floating coordinate system of the shaft system. Then the generalized coordinates of the gear meshing unit are:

[0260] (80)

[0261] In the formula, 1 and 2 correspond to the driving wheel and the driven wheel, respectively.

[0262] The relative vibration displacement of the gear meshing unit in the direction of the meshing line can be expressed as:

[0263] (81)

[0264] in This is the projection vector array that transforms the generalized coordinate displacement towards the direction of the meshing line, and its values ​​are:

[0265] (82)

[0266] In the formula, , These represent the base circle radii of the driving and driven wheels, respectively. The end face pressure angle, γ is the helix angle. γ1 and γ2 are the initial installation position angles of the driving and driven wheels, respectively.

[0267] Taking into account the effects of gear meshing error and tooth flank clearance, the actual relative elastic deformation of the gear pair is:

[0268] (83)

[0269] in, Let b be the tooth meshing error, and b be the tooth flank clearance. The tooth meshing error is obtained by fitting the accumulated total pitch deviation and the single-tooth tangential deviation as a simple harmonic function and superimposing them. for:

[0270] (84)

[0271] in, This is the total cumulative deviation tolerance of the tooth pitch. For single-tooth tangential tolerance, the subscripts 1 and 2 indicate the driving and driven gears, respectively. For gear frequency, This refers to the gear meshing frequency.

[0272] Tooth flank clearance is:

[0273] (85)

[0274] Where m is the gear module and a is the center distance. The pressure angle; and These represent the tooth thickness deviations of the driving and driven gears, respectively. Indicates center distance deviation. This indicates the amount of compensation for the reduction in backlash caused by machining and installation errors in the gear pair. min b represents the minimum tooth flank clearance. max This indicates the maximum tooth flank clearance.

[0275] Based on the force state at the gear node, the differential equation of gear coupling motion is obtained, namely:

[0276] (86)

[0277] in,

[0278] (87)

[0279] These represent the gear inertia matrix and the load matrix, respectively. Blank spaces represent zero elements. For the translational mass of the gear, Let j represent the moment of inertia of gear i about axis j. This represents the load torque. Where i = 1, 2, and j = x, y, z.

[0280] For the time-varying overall meshing stiffness of helical gears, This provides damping for the helical gear meshing. Thus, equation (87) completes the shaft system. With shaft system The coupling.

[0281] Coupled with equations (33), (59), (76), and (87), a reduced-order model of the gear-shaft-bearing-box system is formed, yielding the coupled dynamic equations of the system in the 2n-dimensional state space:

[0282] (88)

[0283] in,

[0284] (89)

[0285] Let i be the state vector of shaft system i that takes into account factors such as error and backlash. It includes a gear meshing damping array. Torque matrix A matrix in the state space.

[0286] Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupling dynamics modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the establishment of a gear meshing coupling model and the loading of tooth backlash, meshing error, and time-varying stiffness include: the gear meshing coupling model includes a piecewise function of tooth backlash, a simple harmonic superposition expression of meshing error, and an analytical formula for time-varying meshing stiffness.

[0287] Based on the above method embodiments, as an optional embodiment, the multi-flexible-body coupled dynamics modeling method for rotating non-inertial gear systems provided in this embodiment of the invention, wherein the equations of each coupled subsystem form an overall reduced-order model, and the solution is obtained using an augmented-dimensional refined integration algorithm, including: the augmented-dimensional refined integration algorithm separates the time-varying terms into non-homogeneous terms, and realizes time step recursion through the principle of exponential matrix addition, with the error controlled within... Within the range.

[0288] Specifically, by separating the constant matrix of equation (88) and subsuming the time-varying terms into the non-homogeneous terms, we obtain:

[0289] (90)

[0290] In formula (71) , It is a linear constant coefficient matrix. Let be all nonlinear time-varying terms. Based on the dimension-enhanced fine integration algorithm, equation (90) is transformed into:

[0291] (91)

[0292] In the formula,

[0293] (92)

[0294] (93)

[0295] Let the time step be Δt, in a very small time interval Within tk=kΔt, the H matrix changes very little and can be considered a constant matrix, resulting in the following recursive formula:

[0296] (94)

[0297] Exponential matrix Solve using precise integration, that is, by using the addition principle, let ,

[0298] (95)

[0299] Let m = 2N, expand The first five terms yield:

[0300] (96)

[0301] but , The statement for generating the method is:

[0302] (97)

[0303] Then after N multiplications For larger matrices, this significantly reduces rounding errors during calculation.

[0304] The multi-flexible-body coupled dynamics modeling method for rotating non-inertial gear systems provided in this invention, through the theory of multi-flexible-body system dynamics, achieves for the first time a deep coupled modeling of non-inertial frame effects with the flexibility of gear shafts, bearings, and housings. This overcomes the limitations of traditional methods that simplify processing or ignore coupling, significantly improving the accuracy of dynamic response prediction under extreme conditions. Employing state-space modal synthesis and dimensionality-enhanced refined integral algorithms, computational efficiency is improved by 3 to 5 times, making it suitable for real-time analysis. Modular substructure partitioning and standardized modeling processes allow for flexible extension to complex scenarios such as large-scale aircraft maneuvers and automobile start-stop-turning, improving versatility by over 60%. The matrix-based derivation based on the Lagrange equation avoids tedious vector mechanics calculations, improving programming efficiency by 40%, providing an efficient and accurate theoretical tool for the design and optimization of gear transmission systems in high-end equipment.

[0305] The implementation of the various embodiments of this invention is based on programmed processing through a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of this invention can be encapsulated into various modules. Based on this reality, and building upon the above embodiments, this invention provides a multi-flexible-body coupled dynamics modeling device for a rotating non-inertial gear system. This device is used to execute the multi-flexible-body coupled dynamics modeling method for a rotating non-inertial gear system in the above method embodiments. See also... Figure 2The device comprises: a first main module for dividing the gear system into a shaft system substructure and a housing substructure, and establishing their kinematic equations based on the dynamics theory of multi-flexible-body systems; a second main module for deriving the generalized coordinate dynamic equations of the housing according to the Lagrange equations, including fixed-axis rotation coordinates and flexible node coordinates, and taking into account the non-inertial frame effects of random body rotation; and a third main module for deriving the generalized coordinate dynamic equations of the shaft system according to the Lagrange equations, including revolution, rotation, and flexible node coordinates, discretizing them according to the spatial beam theory and taking into account... The main modules are as follows: The fourth module is used to reduce the order of the housing and shaft system using the fixed-interface modal synthesis method in state space, preserving interface nodes and mapping internal nodes to a lower-order modal space; the fifth module is used to achieve bearing coupling through multi-point constraint MPC, effectively distributing the shaft bearing force to the flexible nodes of the housing; the sixth module is used to establish a gear meshing coupling model, loading tooth backlash, meshing error, and time-varying stiffness; and the seventh module is used to couple the equations of each subsystem to form an overall reduced-order model, which is then solved using an augmented-dimensional fine integral algorithm.

[0306] The multi-flexible-body coupling dynamics modeling device for rotating non-inertial gear systems provided in this embodiment of the invention employs... Figure 2 Several modules within the system, through the theory of multi-flexible body system dynamics, achieve for the first time a deep coupling modeling of non-inertial frame effects with the flexibility of gear shafts, bearings, and housings. This overcomes the limitations of traditional methods that simplify processing or ignore coupling, significantly improving the accuracy of dynamic response prediction under extreme conditions. The use of state-space modal synthesis and dimension-enhanced refined integral algorithms improves computational efficiency by 3 to 5 times, making it suitable for real-time analysis. Modular substructure partitioning and standardized modeling processes allow for flexible expansion to complex scenarios such as large-scale aircraft maneuvers and car start-stop-turn, improving versatility by over 60%. The matrix-based derivation based on the Lagrange equation avoids tedious vector mechanics calculations, improving programming efficiency by 40%, providing an efficient and accurate theoretical tool for the design and optimization of gear transmission systems in high-end equipment.

[0307] It should be noted that the apparatus in the device embodiments provided by the present invention can be used not only to implement the methods in the above method embodiments, but also to implement the methods in other method embodiments provided by the present invention. The difference lies only in the setting of corresponding functional modules. Its principle is basically the same as that of the above device embodiments provided by the present invention. As long as those skilled in the art, based on the above device embodiments and referring to the specific technical solutions in other method embodiments, obtain corresponding technical means and technical solutions composed of these technical means by combining technical features, and improve the apparatus in the above device embodiments while ensuring the practicality of the technical solutions, they can obtain corresponding device-type embodiments for implementing the methods in other method-type embodiments. For example:

[0308] Based on the above-described device embodiments, as an optional embodiment, the rotating non-inertial gear system multi-flexible body coupling dynamics modeling device provided in this embodiment of the invention further includes: a first sub-module, used to implement the generalized coordinate dynamic equation of the box obtained according to the Lagrange equation, which includes fixed-axis rotation coordinates and flexible node coordinates, and takes into account the non-inertial frame effect of random body rotation, including: the generalized coordinate dynamic equation of the box is discretized by finite element solid elements, and the mass matrix includes a coupling term of rotational inertia and deformation inertia.

[0309] Based on the above-described device embodiments, as an optional embodiment, the rotating non-inertial gear system multi-flexible-body coupled dynamics modeling device provided in this embodiment of the invention further includes: a second sub-module, used to implement the generalized coordinate dynamic equation of the shaft system obtained according to the Lagrange equation, which includes the revolution, rotation, and flexible node coordinates, and is discretized according to the spatial beam theory and incorporates the composite motion effect, including: the generalized coordinate dynamic equation of the shaft system is discretized based on the spatial beam element, and the mass matrix includes the revolution-rotation-deformation inertia coupling term.

[0310] Based on the above-described device embodiments, as an optional embodiment, the rotating non-inertial gear system multi-flexible body coupling dynamics modeling device provided in this embodiment of the invention further includes: a third sub-module, used to implement the reduction of the gearbox and shaft system by the state-space fixed interface modal synthesis method, retaining interface nodes and mapping internal nodes to a lower-order modal space, including: the state-space fixed interface modal synthesis method, by extracting the fixed interface principal mode and constraint mode, mapping the internal node state variables to a 2n-dimensional modal space, and reducing the degrees of freedom with three times the meshing frequency as the cutoff frequency.

[0311] Based on the above-described device embodiments, as an optional embodiment, the rotating non-inertial gear system multi-flexible body coupling dynamics modeling device provided in this embodiment of the invention further includes: a fourth sub-module, used to realize the bearing coupling through multi-point constraint MPC, and to equivalently distribute the shaft bearing force to the housing flexible node, including: the multi-point constraint MPC equivalently converts the bearing force into the force and torque of the virtual rigid body center of mass, and distributes it to the housing flexible node through mass normalization to realize force-displacement coupling.

[0312] Based on the above-described device embodiments, as an optional embodiment, the rotating non-inertial gear system multi-flexible-body coupling dynamics modeling device provided in this embodiment of the invention further includes: a fifth sub-module, used to implement the establishment of the gear meshing coupling model, loading tooth backlash, meshing error, and time-varying stiffness, including: the gear meshing coupling model includes a piecewise function of tooth backlash, a simple harmonic superposition expression of meshing error, and an analytical formula for time-varying meshing stiffness.

[0313] Based on the above-described device embodiments, as an optional embodiment, the multi-flexible-body coupled dynamics modeling device for rotating non-inertial gear systems provided in this embodiment of the invention further includes: a sixth submodule, used to realize the formation of an overall reduced-order model from the equations of the coupled subsystems, and to solve it using an augmented-dimensional refined integration algorithm, including: the augmented-dimensional refined integration algorithm separating time-varying terms into non-homogeneous terms, and using the principle of exponential matrix addition to achieve time step recursion, with the error controlled within... Within the range.

[0314] The method in this embodiment of the invention is implemented using an electronic device; therefore, it is necessary to introduce the relevant electronic device. For this purpose, this embodiment of the invention provides an electronic device, such as... Figure 3 As shown, the electronic device includes at least one processor, a communications interface, at least one memory, and a communications bus, wherein the at least one processor, the communications interface, and the at least one memory communicate with each other via the communications bus. The at least one processor can invoke logical instructions stored in the at least one memory to execute all or part of the steps of the methods provided in the foregoing method embodiments.

[0315] Furthermore, when the logical instructions in at least one of the aforementioned memories can be implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various method embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0316] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0317] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0318] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Based on this understanding, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, or sometimes in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0319] It should be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. Any expressions such as "predetermined threshold," "preset threshold," etc., without specifying a particular value, can be determined by those skilled in the art through simple experimentation or appropriate adjustments.

[0320] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling the dynamics of a multi-body coupling of a rotating non-inertial system gear train, the method comprising: The gear system is divided into a shafting substructure and a box substructure, kinematic equations of which are respectively established based on the multi-body system dynamics theory; a generalized coordinate dynamics equation of the box is obtained according to the Lagrange equation, and contains fixed-axis rotation coordinates and flexible node coordinates, and the non-inertial system effect of random body rotation is taken into account; a generalized coordinate dynamics equation of the shafting is obtained according to the Lagrange equation, and contains revolution, rotation and flexible node coordinates, and is discretized according to the spatial beam theory and the composite motion effect is taken into account; the box and the shafting are reduced by the state space fixed interface modal synthesis method, the interface nodes are reserved and the internal nodes are mapped to the low-order modal space; the bearing coupling is realized by the multi-point constraint MPC, and the bearing force of the shafting is equivalently distributed to the flexible nodes of the box; a gear meshing coupling model is established, and the tooth side gap, the meshing error and the time-varying stiffness are loaded; the overall reduced model is formed by coupling the equations of each subsystem, and the augmented precise integration algorithm is used for solving. The generalized coordinate dynamics equation of the box obtained according to the Lagrange equation contains fixed-axis rotation coordinates and flexible node coordinates, and the non-inertial system effect of random body rotation is taken into account, including: the generalized coordinate dynamics equation of the box is discretized by a finite element solid element, and the mass matrix contains rotation inertia and deformation inertia coupling terms.

2. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 1, wherein, The generalized coordinate dynamics equation of the shafting obtained according to the Lagrange equation contains revolution, rotation and flexible node coordinates, and is discretized according to the spatial beam theory and the composite motion effect is taken into account, including: the generalized coordinate dynamics equation of the shafting is discretized based on the spatial beam element, and the mass matrix contains revolution-rotation-deformation inertia coupling terms.

3. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 2, wherein, The box and the shafting are reduced by the state space fixed interface modal synthesis method, the interface nodes are reserved and the internal nodes are mapped to the low-order modal space, including: the state space fixed interface modal synthesis method is used to extract the fixed interface main modal and the constraint modal, map the internal node state variables to the 2n-dimensional modal space, and reduce the degrees of freedom with the triple meshing frequency as the cutoff frequency.

4. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 3, wherein, The bearing coupling is realized by the multi-point constraint MPC, and the bearing force of the shafting is equivalently distributed to the flexible nodes of the box, including: the multi-point constraint MPC equivalently distributes the bearing force to the virtual rigid body mass center force and torque, and distributes it to the flexible nodes of the box through mass normalization, realizing force-displacement coupling.

5. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 4, wherein, The gear meshing coupling model is established, and the tooth side gap, the meshing error and the time-varying stiffness are loaded, including: the gear meshing coupling model contains a tooth side gap segmented function, a meshing error simple harmonic superposition expression and a time-varying meshing stiffness analytical formula.

6. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 5, wherein, The overall reduced model is formed by coupling the equations of each subsystem, and the augmented precise integration algorithm is used for solving, including: the augmented precise integration algorithm separates the time-varying terms into non-homogeneous terms, and realizes time step recursion through the exponential matrix addition principle.

7. The rotational non-inertial system gear system multi-body coupling dynamics modeling method of claim 6, wherein, The first main module is used to realize that the gear system is divided into a shafting substructure and a box substructure, and kinematic equations of which are respectively established based on the multi-body system dynamics theory.

8. A device for modeling the dynamics of a multi-body coupling of a rotating non-inertial system gear system, characterized by, ​ ​ The second main module is used for realizing a generalized coordinate dynamic equation of the box obtained according to Lagrange equation, and contains fixed-axis rotation coordinates and flexible node coordinates, and the non-inertial system effect of random body rotation is taken into account; the third main module is used for realizing a generalized coordinate dynamic equation of the shaft system obtained according to Lagrange equation, and contains revolution and rotation coordinates and flexible node coordinates, and is discretized according to the space beam theory and the composite motion effect is taken into account; the fourth main module is used for realizing order reduction of the box and the shaft system through a state space fixed interface modal synthesis method, retaining interface nodes and mapping internal nodes to a low-order modal space; the fifth main module is used for realizing bearing coupling through multi-point constraint MPC, and equivalent distribution of bearing forces of the shaft system to flexible nodes of the box; the sixth main module is used for realizing establishment of a gear meshing coupling model, and loading of a gear side gap, a meshing error and time-varying stiffness; the seventh main module is used for realizing formation of an overall order reduction model by coupling equations of each subsystem, and solving by using an augmented dimension fine integration algorithm.

9. An electronic device, comprising: Comprise: At least one processor, at least one memory and a communication interface; wherein, The processor, memory and communication interface communicate with each other; The memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the method of any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium stores computer instructions, and the computer instructions cause the computer to execute the method of any one of claims 1 to 7.

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