Gear system dynamics modeling method and device considering basic translation non-inertial system

Abstract

The invention provides a gear system dynamics modeling method and device considering a basic translation non-inertial system, and the method comprises the steps: dividing a gear system into a shaft system substructure and a box body substructure based on a multi-flexible body system dynamics theory, and building the dynamics equations of the shaft system substructure and the box body substructure; performing model order reduction on the box body, retaining a main mode and a constraint mode, and generating a box body order reduction kinetic equation with reduced degree of freedom; establishing a gear shaft dynamical model, and recording a compound motion effect of shaft system acceleration translation and rotation; bearing coupling is achieved through multi-point constraint, and shaft system node bearing force is equivalently distributed to box body bearing hole flexible nodes; establishing a gear meshing coupling model, introducing a gear backlash, a meshing error and time-varying meshing stiffness, and representing nonlinear dynamic characteristics of a gear pair; and coupling the kinetic equations of the shaft system, the box body, the bearing and the gear to form a system overall model, and solving the kinetic response of the system overall model. The engineering application cost can be reduced.

Description

TECHNICAL FIELD

[0001] The embodiment of the application relates to the technical field of mechanical transmission, and particularly relates to a gear system dynamics modeling method and equipment considering a basic translational non-inertial system. BACKGROUND

[0002] With the continuous progress of industrial technology and the improvement of automation level, as a key transmission component, the gear system is increasingly widely applied in the field of mechanical transmission. Especially under high speed, heavy load and complex extreme working conditions, the dynamics performance of the gear system directly affects the stability and reliability of the whole system. Therefore, accurately modeling the gear system to predict its motion characteristics and optimize the design scheme has become a research hotspot in the current engineering field.

[0003] At present, for the dynamics modeling of the gear system, a variety of methods have been proposed and applied. Among them, the modeling method based on the inertial system is the most common one. This kind of method usually assumes that the gear system is in the inertial reference system, and the dynamics equation of the system is established through the mechanical principles such as Newton's law of motion or Lagrange equation. However, in actual application, the gear system is often in a non-inertial reference system, such as a rotating rack or a moving platform. In this case, the non-inertial effects such as inertial force and Coriolis force will have a significant impact on the dynamics behavior of the gear system. The related modeling methods have obvious shortcomings in dealing with non-inertial system effects. On the one hand, these methods often ignore the influence of inertial force on the dynamics of the system, resulting in insufficient model accuracy and being unable to accurately predict the motion characteristics of the gear system. On the other hand, even if the non-inertial system effects are considered, a simplified processing method is often adopted, such as introducing the non-inertial system effects as an additional term into the model, while ignoring the coupling effect with other parts of the system, thereby affecting the accuracy and reliability of the model. Therefore, developing a gear system dynamics modeling method and equipment considering a basic translational non-inertial system can effectively overcome the defects in the related art, and has become a technical problem to be solved in the industry. SUMMARY

[0004] In view of the above problems existing in the prior art, the embodiment of the application provides a gear system dynamics modeling method and equipment considering a basic translational non-inertial system.

[0005] In a first aspect, embodiments of the present application provide a gear system dynamics modeling method considering a basic translational non-inertial system, comprising: based on a multi-flexible-body system dynamics theory, dividing the gear system into an axle system substructure and a box substructure, and respectively establishing dynamics equations thereof; using a fixed interface modal synthesis method to model order reduction of the box, retaining main modes and constraint modes, and generating a box dynamics equation with reduced degrees of freedom; based on a spatial beam theory, establishing a gear axle dynamics model, and taking into account a compound motion effect of translational and rotational acceleration of the axle system; through multi-point constraint MPC, realizing bearing coupling, and equivalently distributing axle system node bearing force to box bearing hole flexible nodes; establishing a gear meshing coupling model, introducing a backlash, a meshing error and a time-varying meshing stiffness, and representing nonlinear dynamic characteristics of a gear pair; coupling dynamics equations of the axle system, the box, the bearing and the gear, forming a system overall model, and using a dimension-increased precise integration algorithm to solve dynamics response of the system overall model.

[0006] In the above method embodiment, the gear system dynamics modeling method considering the basic translational non-inertial system, based on the multi-flexible-body system dynamics theory, divides the gear system into the axle system substructure and the box substructure, and respectively establishes dynamics equations thereof, comprising: establishing a floating coordinate system at a box centroid, taking rigid body translational degrees of freedom and flexible node deformation coordinates as generalized coordinates, deriving a motion equation containing inertial forces and gravity loads based on Lagrange equation, and discretizing the box into solid elements using finite elements.

[0007] In the above method embodiment, the gear system dynamics modeling method considering the basic translational non-inertial system, using the fixed interface modal synthesis method to model order reduction of the box, retaining main modes and constraint modes, and generating a box dynamics equation with reduced degrees of freedom, comprising: dividing box nodes into interface nodes coupled with the outside and internal nodes, extracting fixed interface main modes to describe free vibration of the internal nodes, extracting constraint modes to describe interface node coupled motion, reducing main mode degrees of freedom with three times meshing frequency as a cutoff frequency, and forming a box dynamics equation containing translational degrees of freedom and reduced mode coordinates.

[0008] In the above method embodiment, the gear system dynamics modeling method considering the basic translational non-inertial system, based on the spatial beam theory, establishing a gear axle dynamics model, and taking into account a compound motion effect of translational and rotational acceleration of the axle system, comprising: establishing a floating coordinate system at an axle speed input, taking rigid body translational degrees of freedom, rotational degrees of freedom around an axle line and flexible axle segment deformation coordinates as generalized coordinates, discretizing the axle segment using the spatial beam theory, and using the Lagrange equation to take into account velocity quadratic term additional generalized forces formed by non-inertial system effects of centrifugal inertia force and Coriolis force.

[0009] On the basis of the method embodiment content, the gear system dynamics modeling method considering the basic translational non-inertial system provided in the embodiment of the application, the bearing coupling is realized by MPC, the bearing force of the shaft system node is equivalent distributed to the flexible node of the box bearing hole, including: the generalized coordinate difference of the shaft system bearing node and the box bearing hole node in the inertial coordinate system is defined as the bearing deformation, the bearing force is distributed to the flexible node around the box bearing hole based on the static equivalent principle, and the force and torque balance relationship of the mass center of the virtual rigid body is equivalent.

[0010] On the basis of the method embodiment content, the gear system dynamics modeling method considering the basic translational non-inertial system provided in the embodiment of the application, the gear meshing coupling model is established, the tooth side gap, meshing error and time-varying meshing stiffness are introduced, and the nonlinear dynamic characteristics of the gear pair are represented, including: in the gear meshing coupling model, the tooth side gap is calculated according to the gear modulus, center distance, pressure angle and machining and installation error, the meshing error is represented by superimposing the simple harmonic function of the accumulated total deviation and the single-tooth tangential deviation of the pitch, and the nonlinear meshing force model is constructed in combination with the time-varying meshing stiffness and the meshing damping.

[0011] On the basis of the method embodiment content, the gear system dynamics modeling method considering the basic translational non-inertial system provided in the embodiment of the application, the dynamics equations of the coupling shaft system, the box, the bearing and the gear are coupled, the system overall model is formed, and the dynamics response of the system overall model is solved by using the dimension-increasing precise integration algorithm, including: the system dynamics equation is converted into a state space form, the linear constant matrix and the time-varying nonlinear term are separated, the time step is segmented and recursively propagated, the matrix addition and the dimension-increasing precise integration are used to solve the exponential matrix, and the calculation efficiency and the accuracy of the coupled system dynamics response are improved.

[0012] In a second aspect, embodiments of the present application provide a device for modeling dynamics of a gear system considering a base translational non-inertial system, comprising: a first main module configured to implement a multi-body system dynamics theory to divide the gear system into a shafting substructure and a housing substructure, and to establish dynamic equations of the shafting substructure and the housing substructure, respectively; a second main module configured to implement a fixed-interface modal synthesis method to model order reduction of the housing, to retain main modes and constraint modes, and to generate a reduced dynamic equation of the housing; a third main module configured to implement a spatial beam theory to establish a dynamic model of a gear shaft, and to consider a combined motion effect of translational and rotational acceleration of the shafting; a fourth main module configured to implement a multi-point constraint (MPC) to realize bearing coupling, and to equivalently distribute shafting node bearing forces to housing bearing hole flexible nodes; a fifth main module configured to implement a gear meshing coupling model, and to introduce a backlash, a meshing error, and a time-varying meshing stiffness to represent nonlinear dynamic characteristics of a gear pair; and a sixth main module configured to couple dynamic equations of the shafting, the housing, the bearing, and the gear, to form a system overall model, and to solve a dynamic response of the system overall model using a dimensionally extended precise integration algorithm.

[0013] In a third aspect, embodiments of the present application provide an electronic device, comprising:

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

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

[0016] the memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the modeling dynamics of the gear system considering the base translational non-inertial system according to any one of the implementation manners of the first aspect.

[0017] In a fourth aspect, embodiments of the present application provide a non-transitory computer-readable storage medium storing computer instructions, and the computer instructions cause a computer to execute the modeling dynamics of the gear system considering the base translational non-inertial system according to any one of the implementation manners of the first aspect.

[0018] The gear system dynamics modeling method and device considering the basic translational non-inertial system provided by the embodiment of the application, by adopting the multi-flexible body theory and fully considering the coupling effect of the basic translational non-inertial effect and the flexibility of the gear shaft, bearing, box and other structures, the dynamic response prediction accuracy under complex working conditions is significantly improved compared with the traditional method; the box model is reduced by the fixed interface modal synthesis method, combined with the dimension increasing precise integration algorithm, the calculation efficiency is greatly improved while the accuracy is ensured, which is suitable for real-time analysis of large coupled systems; the modular substructure division and standardized modeling process make it flexible to adapt to the non-inertial system environment of aircrafts, automobiles, ships and other scenes, and the matrix derivation based on the Lagrange equation is convenient for programming implementation, and reduces the engineering application cost. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor based on these drawings.

[0020] Figure 1 The gear system dynamics modeling method flowchart provided by the embodiment of the application;

[0021] Figure 2 The gear system dynamics modeling device structure schematic diagram provided by the embodiment of the application;

[0022] Figure 3 The physical structure schematic diagram of the electronic device provided by the embodiment of the application;

[0023] Figure 4 The transmission system substructure division effect schematic diagram provided by the embodiment of the application;

[0024] Figure 5 The coordinate schematic diagram of any point on the box floating coordinate system provided by the embodiment of the application;

[0025] Figure 6 The box interface node and internal node division effect schematic diagram provided by the embodiment of the application;

[0026] Figure 7 The shafting node division effect schematic diagram provided by the embodiment of the application;

[0027] Figure 8 The coordinate schematic diagram of any point on the shafting floating coordinate system provided by the embodiment of the application;

[0028] Figure 9A bearing coupling effect schematic diagram provided for the embodiment of the present application;

[0029] Figure 10 A multi-point constraint MPC effect schematic diagram provided for the embodiment of the present application;

[0030] Figure 11 A gear coupling effect schematic diagram provided for the embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application. In addition, the technical features in each embodiment or in a single embodiment provided by the present application can be combined with each other at will to form a feasible technical scheme, and such combination is not restricted by the order of steps and / or structure mode, but must be based on the implementation by those skilled in the art, and when the combination of technical schemes appears contradictory or unimplementable, it should be considered that such combination of technical schemes does not exist and is not within the protection scope required by the present application. If there are step numbers in the following embodiments, they are set only for the convenience of description, and the order between the steps is not limited in any way, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0032] The embodiment of the present application provides a gear system dynamics modeling method considering a basic translational non-inertial system, referring to Figure 1 The method comprises the following steps: based on a multi-flexible body system dynamics theory, a gear system is divided into an axle system substructure and a box substructure, and dynamic equations thereof are respectively established; a fixed interface modal synthesis method is used for model order reduction of the box, main modes and constraint modes are retained, and a box reduced dynamics equation with reduced degrees of freedom is generated; a gear shaft dynamics model is established based on a space beam theory, and the composite motion effect of axle system acceleration translation and rotation is considered; bearing coupling is realized through multi-point constraint MPC, and axle system node bearing force is equivalently distributed to box bearing hole flexible nodes; a gear meshing coupling model is established, and a backlash, a meshing error and a time-varying meshing stiffness are introduced to represent the nonlinear dynamic characteristics of a gear pair; the dynamic equations of the axle system, the box, the bearing and the gear are coupled to form a system overall model, and a dimension-increasing precise integration algorithm is used to solve the dynamic response of the system overall model.

[0033] Specifically, as Figure 4As shown, based on the substructure analysis theory, the gear system is divided into an axle system substructure and a box substructure. The axle system substructure includes an input gear axle, an output gear axle and the like, and the box can be further divided into an upper box and a lower box according to the specific interface connection and assembly relationship.

[0034] Based on the content of the above method embodiment, as an optional embodiment, the gear system dynamics modeling method considering the base translational non-inertial system provided in the embodiment of the application divides the gear system into an axle system substructure and a box substructure based on the multi-flexible body system dynamics theory, and establishes the dynamics equations thereof respectively, including: establishing a floating coordinate system at the centroid of the box, taking the rigid translational degrees of freedom and the flexible node deformation coordinates as generalized coordinates, deriving the motion equation containing the inertial force and the gravity load based on the Lagrange equation, and discretizing the box into solid elements by using the finite element method.

[0035] Specifically, as shown in the figure, Figure 5 a floating coordinate system o j x j y j z j of the box is established at the centroid position of the box. j Without loss of generality, the x j axis, the y j axis and the z j axis are parallel to the X axis, the Y axis and the Z axis of the inertial coordinate system OXYZ respectively. Based on the multi-flexible body system dynamics theory, the box is discretized into n f solid elements by using the finite element method, and the box is in an accelerated translational state. The position coordinates and velocity coordinates of any point P j in the inertial coordinate system OXYZ are expressed as

[0036]

[0037] wherein R j is the position coordinates of the floating coordinate system o j x j y j z j of the box in the inertial coordinate system OXYZ, u jk is the position coordinates of the point P j in the floating coordinate system o j x j y j z j of the box, which is divided into fixed coordinates and deformation coordinates . Wherein N jk is the element k in the floating coordinate system o j x j y j of the box.z j the unit shape function under the local coordinate system of the element, is the flexible node coordinate of the box. N jk is the value

[0038]

[0039] In the above formula, S jk is the shape function under the local coordinate system of the element, and the solid element can use tetrahedral elements or hexahedral elements, etc. T1 jk is the transformation matrix of the element displacement vector from the local coordinate system of the element to the floating coordinate system o j x j y j z j of the box, is the transformation matrix of the element node displacement vector from the local coordinate system of the element to the floating coordinate system o j x j y j z j of the box. L jk is a Boolean indication matrix, which represents the numbering of the element displacement vector in the floating coordinate system o j x j y j z j of the box, which completes the alignment of the element shape function in the overall shape function. The kinetic energy of the box is represented as

[0040]

[0041] where ρ j is the density of the box, q j is the generalized coordinate matrix of the box under the inertial coordinate system OXYZ, and its value is

[0042]

[0043] The value of each sub-block is

[0044]

[0045] M j is the mass matrix of the box, and its value is the superposition of the mass matrices of each element, that is,

[0046]

[0047] M jk is the mass matrix of the kth element of the box. Where each sub-block is the superposition of each corresponding sub-block in each element mass matrix, that is,

[0048]

[0049] where a and b are alternately taken as R and f, respectively.

[0050] The value of each sub-block of the unit mass matrix k is

[0051]

[0052] where m jk is the k unit mass. Substitute (3) into the Lagrange equation of the box, i.e.

[0053]

[0054] where,

[0055]

[0056] where -K j q j is the generalized force corresponding to the elastic deformation of the box, K j is the augmented stiffness matrix of the box, i.e.

[0057]

[0058] is the superposition of the stiffness matrices of all the units of the box, i.e.

[0059]

[0060] is the floating coordinate system o j x j y j z j of the box.

[0061] is the generalized gravity load acting on the box. Without loss of generality, let the gravity be applied in the negative direction of the Y axis of the inertial coordinate system OXYZ, and its value is

[0062]

[0063] where, is the second row of N jk

[0064] Solving (9), the dynamic equation of the box in the generalized coordinates is obtained as

[0065]

[0066] ​As an optional embodiment, the gear system dynamics modeling method considering the base translational non-inertial system provided in the embodiment of the application adopts the fixed interface modal synthesis method to reduce the model order of the box, retains the main modal and constraint modal, and generates the box reduced dynamics equation with reduced degrees of freedom, which includes: dividing the box nodes into interface nodes coupled with the outside world and internal nodes, extracting the fixed interface main modal to describe the free vibration of the internal nodes, extracting the constraint modal to describe the interface node dependent motion, reducing the degrees of freedom of the main modal with three times the meshing frequency as the cutoff frequency, and forming the box dynamics equation containing translational degrees of freedom and reduced modal coordinates.

[0067] Specifically, due to the large number of finite element discrete units, efficient analysis is difficult, and the reduced order processing is required. Based on the fixed interface modal synthesis method theory, according to the relationship between the nodes and the outside world, the flexible nodes are divided into interface nodes Internal nodes and internal nodes, the interface nodes are the part of energy exchange with the outside world, which are bearing nodes in this example, and are further subdivided into bearing interface nodes 1 bearing interface nodes 2 bearing interface nodes 3 bearing interface nodes 4 as shown. At this time, the displacement vector matrix of the box flexible substructure j is represented as Figure 6

[0068]

[0069] wherein,

[0070]

[0071] Therefore, the box dynamics equation expression is rewritten as

[0072]

[0073] According to the kinematic principle, the motion of the internal nodes of the box can be expressed as the sum of the relative motion when the interface is fixed and the dependent motion with the interface. When the interface is fixed, the free vibration equation of the box is

[0074]

[0075] Solving obtains the regularized main modal r=1…3n f . That is

[0076]

[0077] ω r is the rth order natural frequency. The ​The fixed-interface principal modes are obtained, and the internal node displacements are

[0078]

[0079] The modal displacement coordinates are defined. Thus, the internal node is transformed from the physical space to the modal space.

[0080] The unit displacement is applied to each interface degree of freedom in turn (the remaining interface degrees of freedom are kept fixed), and the static equilibrium relationship is obtained

[0081]

[0082] wherein is called the constraint mode. The above formula is the dependent motion of the internal node on the interface, and thus the expression of the internal node motion is

[0083]

[0084] The above formula shows that the fixed-interface principal modes and the constraint mode constitute a complete modal set. The triple meshing frequency is defined as the cutoff frequency, the first l-order principal modes are reserved, and the transformation formula with a greatly reduced degree of freedom is obtained

[0085]

[0086] The first l-order principal modes are reserved, and in the formula, l is much smaller than 3n f .

[0087] (23) is substituted into (17), and left multiplied by (Φ j ) T , and the following is obtained

[0088]

[0089] In the formula,

[0090]

[0091] (24) is the dynamic reduced-order equation of the box in the accelerated translational state, and is combined and expressed as

[0092]

[0093] Based on the above method embodiments, as an optional embodiment, the gear system dynamics modeling method considering the basic translational non-inertial frame provided in this embodiment of the invention, wherein the gear shaft dynamics model is established based on the spatial beam theory, taking into account the combined motion effect of the shaft system's accelerated translation and rotation, includes: establishing a floating coordinate system at the shaft system speed input, using the rigid body translational degrees of freedom, rotational degrees of freedom around the axis, and flexible shaft segment deformation coordinates as generalized coordinates, discretizing the shaft segment using the spatial beam theory, and using the Lagrange equation to take into account the velocity quadratic term of the non-inertial frame effect formed by the centrifugal inertial force and the Coriolis force as an additional generalized force.

[0094] Specifically, based on the geometry of the shaft system, the shaft system is divided into n s There are n axis segments in total. s +1 node. Nodes are required at locations where there is energy exchange with the outside world, or where there are geometric changes, such as... Figure 7 As shown. A floating coordinate system o is established at the input speed node. s x s y s z s Each discrete axis segment is modeled using a spatial beam, let x s The direction is axial, and any point P on the axis segment k s The position in the inertial coordinate system OXYZ is as follows: Figure 8 As shown, the specific expressions for its position coordinates and velocity coordinates are as follows:

[0095]

[0096] Among them, R s =R j +u js For the axis coordinate system o s x s y s z s The position coordinates of the origin in the inertial coordinate system OXYZ, where u js For the axis coordinate system o s x s y s z s With box coordinate system o j x j y j z j The relative distance, the components are expressed as

[0097]

[0098] A s =A sθ A sR It is an axis coordinate system o s x s ys z s Coordinate transformation matrix to the inertial coordinate system OXYZ, A sR is the shaft coordinate system o s x s y s z s Initial transformation matrix between the shaft coordinate system o sθ and the inertial coordinate system OXYZ, A s x s y s z s Rotation transformation matrix between the shaft coordinate system o

[0099]

[0100] where θ is the rotation angle of the shaft coordinate system around the central axis, is A s the derivative matrix of θ, is the shaft coordinate system

[0101] Rotational speed. u sk is the position coordinate of point P s in the shaft coordinate system o s x s y s z s , which is divided into fixed coordinates and deformation coordinates , where the components of the fixed coordinates are expressed as

[0102]

[0103] N sk is the unit shape function of the k-th shaft segment in the shaft coordinate system, which has the same form as equation (2), i.e.

[0104]

[0105] Similarly, T1 sk is the transformation matrix of the unit displacement vector from the unit local coordinate system to the shaft coordinate system o s x s y s z s , A is the transformation matrix of the unit node displacement vector from the unit local coordinate system to the shaft coordinate system o s x s y s z s . L jk is a Boolean indication matrix, which represents the unit displacement vector in the shaft coordinate system os x s y s z s the unit shape functions are completed in the global shape functions.

[0106] Let the coordinate axes of the local coordinate system of the unit shape functions be parallel to the corresponding coordinate axes of the axis system coordinate system, then the transformation matrix between the unit coordinate system and the axis system coordinate system o s x s y s z s are all unit matrices.

[0107] S sk is the unit shape function matrix in the local coordinate system of the unit, which is expressed as

[0108]

[0109] wherein,

[0110]

[0111] In the formula, x is the coordinate of any point on the axis segment k, l is the length of the axis segment; E is the elastic modulus, G is the shear modulus, A is the cross-sectional area, k is the shear correction coefficient, and for a thin-walled circular tube, the value is

[0112] κ=(1+μ) / (2+μ) (35)

[0113] μ is the Poisson's ratio.

[0114] is the coordinate of the flexible node of the axis system. Since each discrete axis segment is modeled by a spatial beam, the value is

[0115]

[0116] wherein the value of the i-th node coordinate is

[0117]

[0118] The kinetic energy of the axis system is obtained from equation (27) as

[0119]

[0120] wherein ρ s is the density of the axis system, q s is the generalized coordinate matrix of the axis system in the inertial coordinate system OXYZ, and the value is

[0121]

[0122] The value of each sub-block is

[0123]

[0124] M s is the mass matrix of the shafting,

[0125]

[0126] M sk is the mass matrix of the kth element of the shafting. Where each sub-block is the superposition of the corresponding sub-blocks in each element mass matrix, i.e.

[0127]

[0128] where a, b are alternatively R, θ, f.

[0129] The value of each sub-block of the element mass matrix k is

[0130]

[0131]

[0132] where represents the ith row of N sk

[0133] Similarly, substituting equation (38) into the Lagrange equation of the shafting, i.e.

[0134]

[0135] where

[0136]

[0137] where -K s q s is the generalized force corresponding to the elastic deformation of the shafting, K s is the augmented stiffness matrix of the shafting, i.e.

[0138]

[0139] The value of is

[0140] is the generalized gravity load acting on the shafting, whose value is

[0141]

[0142] Solving equation (44) gives the dynamic equation of the shafting in free state as

[0143] ​

[0144] For the term related to the square of the speed, it is equivalent to the centrifugal inertia force and the Coriolis force, i.e.

[0145]

[0146] The value of each sub-block is

[0147]

[0148] In the formula, is The matrix obtained by taking the partial derivative of the rotation angle θ.

[0149] Based on the content of the above method embodiment, as an optional embodiment, the gear system dynamics modeling method considering the basis prismatic non-inertial system provided in the embodiment of the application, the bearing coupling is realized by MPC, and the bearing force of the shafting node is equivalent to the flexible node of the box bearing hole, including: defining the generalized coordinate difference of the shafting bearing node and the box bearing hole node in the inertial coordinate system as the bearing deformation, and based on the static equivalent principle, the bearing force is distributed to the flexible node around the box bearing hole, and the force and torque balance relationship of the mass center of the virtual rigid body is equivalent.

[0150] Specifically, as shown in Figure 9 , the shafting and the box are coupled through bearings. Therefore, a local coordinate system is established at the bearing position on the shafting. The generalized coordinates of the shafting bearing node in the inertial coordinate system OXYZ are

[0151]

[0152] Wherein, is the prismatic coordinate of the shafting bearing node relative to the shafting floating coordinate system o s x s y s z s origin, is the rotation coordinate of the shafting bearing node i direction relative to the inertial coordinate system OXYZ. Similarly, a local coordinate system is established at the geometric center of the box bearing hole. That is, the box bearing node jbo, whose generalized coordinates in the inertial coordinate system OXYZ are The values of each term are

[0153]

[0154] Similarly, is the prismatic coordinate of the box bearing node relative to the box floating coordinate system o j xj y j z j translation coordinates of the origin, is the rotation coordinate of the bearing node i of the box in the inertial coordinate system OXYZ. The deformation of the bearing in the inertial coordinate system OXYZ can be expressed as the generalized coordinates of the bearing node of the shaft system and the difference between the generalized coordinates of the bearing node of the box , that is,

[0155]

[0156] The bearing stiffness is

[0157]

[0158] The bearing force in the inertial coordinate system is

[0159]

[0160] wherein

[0161]

[0162] The bearing force received by the shaft system unit s is

[0163]

[0164] As shown in Figure 10 , in order to transmit the bearing force received by the bearing node of the box to the box, according to the MPC constraint principle, the bearing force is distributed to the nb bearing coupling flexible nodes on the bearing hole according to the static equivalent relationship , that is, the box reserved interface node, so as to equivalently connect the bearing coupling flexible node and the virtual rigid body, and the force acting on the center of mass of the rigid body is The torque acting on the center of mass is Under the action of the center of mass force and the torque, the acceleration of the center of mass of the rigid body and the angular acceleration around the center of mass in the inertial coordinate system are respectively

[0165]

[0166] wherein is the normalized mass of the kth flexible node, that is is the moment of inertia of the rigid body, is the distance from the kth flexible node to the bearing hole node. The flexible node attached to the rigid body moves with the rigid body, and the acceleration of the kth flexible node is

[0167]

[0168] In the formula is the coordinate matrix of the angular acceleration of the centroid, and its value is

[0169]

[0170] is the position coordinate of the kth flexible node relative to the bearing hole node of the box, and the component expression is

[0171]

[0172] Then is expanded as

[0173]

[0174] The force borne by the kth flexible node is

[0175]

[0176] Therefore, the bearing force borne by the box is

[0177]

[0178] In the formula, k T The value is

[0179]

[0180] Therefore, the bearing coupling unit dynamics equation is

[0181]

[0182] F b is the external force matrix corresponding to the degrees of freedom participating in coupling.

[0183] Based on the content of the above method embodiment, as an optional embodiment, the gear system dynamics modeling method considering the base prismatic non-inertial system provided in the embodiment of the application, the gear meshing coupling model is established, the backlash, the meshing error and the time-varying meshing stiffness are introduced, and the nonlinear dynamic characteristics of the gear pair are represented, including: in the gear meshing coupling model, the backlash is calculated according to the gear modulus, the center distance, the pressure angle and the machining and installation error, the meshing error is represented by superimposing the simple harmonic function of the accumulated total deviation of the pitch and the tangential deviation of a single tooth, and the time-varying meshing stiffness and the meshing damping are combined to construct the nonlinear meshing force model.

[0184] Specifically, as shown in Figure 11 , a local coordinate system o m x m y m z m is established at the gear meshing point of the shaft system, and the generalized coordinates thereof in the inertial coordinate system are

[0185]

[0186] wherein,

[0187]

[0188] The generalized coordinates of the gear pair are

[0189]

[0190] i = 1, 2 respectively correspond to the driving wheel and the driven wheel.

[0191] The relative vibration displacement of the gear pair in the direction of the meshing line can be expressed as

[0192] δ m = V m q m (71)

[0193] wherein V m is a projection vector column of the generalized coordinate displacement converted to the direction of the meshing line, and the value is

[0194]

[0195] In the formula, r b1 , r b2 respectively represent the base circle radii of the driving wheel and the driven wheel, α is the face pressure angle, and β b is the helix angle.

[0196] Considering the influence of the gear meshing error and the tooth side gap, the actual relative elastic deformation of the gear pair is

[0197]

[0198] wherein e n is the gear meshing error, and b is the tooth side gap. The total deviation of the pitch accumulation and the tangential deviation of a single tooth are fitted as a superposition of a simple harmonic function to obtain the gear meshing error e n .

[0199] e n = F p1 sin (ω s1 t) + F p2 sin (ω s2 t) + 0.5 (f′ i1 + f′ i2 ) sin (ω m t) (74)

[0200] wherein F p is the total deviation tolerance of the pitch accumulation, and f i is the tangential deviation of a single tooth.is the single-tooth tangential tolerance, and the subscripts 1 and 2 represent the driving gear and the driven gear, respectively; ω s is the gear rotation frequency, and ω m is the gear meshing frequency.

[0201] is the side clearance of the gear

[0202]

[0203] where m is the gear modulus, and a is the center distance; |E sni1 | and |E sni2 | respectively represent the under-thickness deviation of the driving gear and the driven gear, and f a represents the center distance deviation, and J n represents the compensation amount of the side clearance reduction caused by the machining and installation errors of the gear pair.

[0204] According to the force state of the gear node, the gear coupling motion differential equation is obtained, that is,

[0205]

[0206] where,

[0207]

[0208] respectively represent the inertia matrix and the load matrix. m i is the translational mass, I ij represents the rotational inertia around the j-axis, T i represents the load torque. Here, i = 1, 2, and j = x, y, z.

[0209] k m is the time-varying comprehensive meshing stiffness of the helical gear, c m is the meshing damping of the helical gear.

[0210] Based on the content of the above method embodiments, as an optional embodiment, the gear system dynamics modeling method considering the basic translational non-inertial system provided in the embodiments of the present application, the dynamics equations of the coupling shaft system, the box, the bearing and the gear form a system overall model, and the dynamics response of the system overall model is solved by using the increased dimension fine integration algorithm, which comprises: converting the system dynamics equation into a state space form, separating the linear constant coefficient matrix and the time-varying nonlinear term, recursively propagating through time steps, solving the exponential matrix by using matrix addition and increased dimension fine integration, and improving the calculation efficiency and accuracy of the dynamics response of the coupling system.

[0211] Specifically, the coupling equations (26), (49), (67) and (76) form a gear-shaft system-bearing-casing overall model, and the system coupling dynamics equation is

[0212]

[0213] in,

[0214]

[0215] F is the generalized coordinate system i that takes into account factors such as error and backlash. m For the torque matrix f m The array in the global coordinate system.

[0216] Based on the dimension-enhanced fine integration algorithm, the constant matrix of equation (78) is separated, and the time-varying terms are assigned to the non-homogeneous terms, resulting in...

[0217]

[0218] In formula (80) F is a linear constant coefficient matrix. n (q,t) represents all nonlinear time-varying terms. According to the augmented-dimensional refined integration method, equation (80) is transformed into...

[0219]

[0220] In the formula,

[0221]

[0222] Let the time step be Δt, in a very small time interval [t k ,t k+1 ], t k Within the range of kΔt, the H matrix changes very little and can be considered a constant matrix, resulting in the recursive formula:

[0223] X[(k+1)Δt]=exp(H k Δt)X(kΔt) (84)

[0224] Exponential matrix exp(H k Δt) is solved using the increased-dimensional precise integration method, that is, by using the addition principle, let

[0225]

[0226] Let m = 2 N Expand exp(H k The first five terms of τ) yield...

[0227] exp(H k τ)=I n +H k τ+(H k τ 2 ) 2 / 2! +(H k τ 2 )3 / 3!+(H k τ 2 ) 4 / 4!=I n +T a (86)

[0228] then T a The statement of the generation method is

[0229]

[0230] then T after N multiplications a is a larger matrix, which significantly reduces the rounding error in the calculation process.

[0231] The gear system dynamics modeling method considering the basic translational non-inertial system provided by the embodiment of the application significantly improves the dynamic response prediction accuracy under complex working conditions compared with the traditional method by adopting the multi-flexible body theory and fully considering the coupling effect of the basic translational non-inertial effect and the flexibility of the gear shaft, bearing, box and other structures; the box model is reduced by the fixed interface modal synthesis method, and the calculation efficiency is greatly improved while ensuring the accuracy by combining the dimension-increasing precise integration algorithm, which is suitable for real-time analysis of large coupled systems; the modular substructure division and standardized modeling process enable it to be flexibly adapted to the non-inertial system environment of aircraft, automobile, ship and other scenes, and the matrix derivation based on the Lagrange equation facilitates programming implementation and reduces the engineering application cost.

[0232] The implementation basis of each embodiment of the application is that the processing is realized by the programmed processing of the device with the processor function. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the application can be packaged into various modules. Based on this actual situation, on the basis of each embodiment described above, the embodiment of the application provides a gear system dynamics modeling device considering the basic translational non-inertial system, which is used to execute the gear system dynamics modeling method considering the basic translational non-inertial system in the above method embodiment. Referring to Figure 2The device comprises: a first main module for dividing a gear system into an axle system substructure and a box substructure based on a flexible body system dynamics theory, and respectively establishing dynamics equations thereof; a second main module for implementing model reduction of the box by using a fixed interface modal synthesis method, retaining main modes and constraint modes, and generating a box dynamics equation with reduced degrees of freedom; a third main module for implementing establishment of a gear axle dynamics model based on a space beam theory, and taking into account the composite motion effect of axle system acceleration translation and rotation; a fourth main module for implementing bearing coupling by using a multi-point constraint MPC, and equivalently distributing axle system node bearing force to box bearing hole flexible nodes; a fifth main module for implementing establishment of a gear meshing coupling model, introducing gear side clearance, meshing error and time-varying meshing stiffness, and representing nonlinear dynamic characteristics of a gear pair; and a sixth main module for implementing coupling of dynamics equations of the axle system, the box, the bearing and the gear, forming a system overall model, and solving a dynamics response of the system overall model by using a dimension-increasing precise integration algorithm.

[0233] The device for gear system dynamics modeling considering a basic translation non-inertial system provided in the embodiment of the application adopts Figure 2 the several modules in the device, and significantly improves the dynamic response prediction precision under complex working conditions compared with traditional methods by using the flexible body theory and fully considering the coupling effect of the basic translation non-inertial effect and the flexibility of the gear axle, the bearing and the box; the box model is reduced by using the fixed interface modal synthesis method, and the dimension-increasing precise integration algorithm is combined to greatly improve the calculation efficiency while ensuring the precision, and the device is suitable for real-time analysis of large coupled systems; the modularized substructure division and the standardized modeling process enable the device to be flexibly adapted to multi-scene non-inertial system environments such as aircrafts, automobiles and ships, and the matrix derivation based on the Lagrange equation facilitates programming implementation and reduces engineering application costs.

[0234] It should be noted that the device in the device embodiment provided in the application can be used to implement the methods in the method embodiments provided in the application, and the difference is only that corresponding function modules are arranged, the principle is basically the same as that of the above-mentioned device embodiments provided in the application, as long as the person skilled in the art improves the device in the above-mentioned device embodiments on the basis of the above-mentioned device embodiments, refers to the specific technical solutions in other method embodiments, obtains corresponding technical means by combining technical features, and the technical solutions formed by these technical means, on the premise of ensuring the practicability of the technical solutions, the device in the above-mentioned device embodiments can be improved to obtain corresponding device embodiments, which are used to implement the methods in other method embodiments. For example:

[0235] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling dynamics of a gear system considering a basic translational non-inertial system provided in the embodiment of the present application further comprises: a first sub-module, configured to divide the gear system into an axle system substructure and a box substructure based on the multi-flexible body system dynamics theory, and to establish dynamic equations thereof respectively, including: establishing a floating coordinate system at the center of mass of the box, taking rigid body translational degrees of freedom and flexible node deformation coordinates as generalized coordinates, deriving a motion equation containing inertial forces and gravity loads based on the Lagrange equation, and discretizing the box into solid elements by using the finite element method.

[0236] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling dynamics of a gear system considering a basic translational non-inertial system provided in the embodiment of the present application further comprises: a second sub-module, configured to implement model reduction of the box by using the fixed interface modal synthesis method, to retain main modes and constraint modes, and to generate a reduced dynamic equation of the box with reduced degrees of freedom, including: dividing the nodes of the box into interface nodes coupled with the outside world and internal nodes, extracting fixed interface main modes to describe the free vibration of the internal nodes, extracting constraint modes to describe the coupled motion of the interface nodes, reducing the degrees of freedom of the main modes with three times the meshing frequency as the cutoff frequency, and forming a box dynamic equation containing translational degrees of freedom and reduced mode coordinates.

[0237] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling dynamics of a gear system considering a basic translational non-inertial system provided in the embodiment of the present application further comprises: a third sub-module, configured to implement the establishment of a gear shaft dynamic model based on the spatial beam theory, taking into account the combined motion effect of the translational and rotational acceleration of the axle system, including: establishing a floating coordinate system at the input of the rotational speed of the axle system, taking rigid body translational degrees of freedom, rotational degrees of freedom around the axis, and flexible shaft segment deformation coordinates as generalized coordinates, discretizing the shaft segment by using the spatial beam theory, and using the Lagrange equation to take into account the velocity quadratic term additional generalized force formed by the non-inertial system effect of the centrifugal inertia force and the Coriolis force.

[0238] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling dynamics of a gear system considering a basic translational non-inertial system provided in the embodiment of the present application further comprises: a fourth sub-module, configured to implement bearing coupling by using the multi-point constraint (MPC), and to equivalently distribute the bearing force of the axle system node to the flexible nodes of the box bearing hole, including: defining the difference between the generalized coordinates of the axle system bearing node and the box bearing hole node in the inertial coordinate system as the bearing deformation, and equivalently distributing the bearing force to the flexible nodes around the box bearing hole based on the static equivalent principle, and equivalently balancing the force and torque at the center of mass of the virtual rigid body.

[0239] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling gear system dynamics in consideration of basic translational non-inertial system provided in the embodiment of the application further comprises: a fifth sub-module for implementing the establishment of the gear meshing coupling model, introducing the backlash, meshing error and time-varying meshing stiffness, and representing the nonlinear dynamic characteristics of the gear pair, comprising: in the gear meshing coupling model, the backlash is calculated according to the gear modulus, center distance, pressure angle and machining and installation error, the meshing error is represented by superimposing the simple harmonic function of the accumulated total deviation of the gear pitch and the single-tooth tangential deviation, and the nonlinear meshing force model is constructed in combination with the time-varying meshing stiffness and meshing damping.

[0240] Based on the content of the above device embodiment, as an optional embodiment, the device for modeling gear system dynamics in consideration of basic translational non-inertial system provided in the embodiment of the application further comprises: a sixth sub-module for implementing the dynamic equations of the coupling shaft system, the box, the bearing and the gear, forming the overall system model, and solving the dynamic response of the overall system model by using the extended precision integration algorithm, comprising: converting the system dynamic equations into the state space form, separating the linear constant coefficient matrix and the time-varying nonlinear term, segmenting and recursively propagating through the time step, solving the exponential matrix by using the matrix addition and the extended precision integration, and improving the calculation efficiency and accuracy of the dynamic response of the coupled system.

[0241] The method of the embodiment of the application is implemented by relying on an electronic device, and therefore it is necessary to introduce the related electronic device. For this purpose, the embodiment of the application provides an electronic device, as shown in the accompanying drawings, which comprises 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 complete the communication among each other through the communications bus. The at least one processor can call the logical instructions in the at least one memory to execute all or part of the steps of the method provided in the foregoing various method embodiments. Figure 3

[0242] ​In addition, the logic instructions in the at least one memory described above can be implemented in the form of a software function unit and sold or used as an independent product, and can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various method embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various program code storage media.

[0243] The device embodiments described above are only schematic, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., can be located in one place, or can be distributed on multiple network units. Part or all of the modules can be selected according to actual needs to achieve the purpose of the present embodiment. Those skilled in the art can understand and implement without creative labor.

[0244] From the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be realized by means of software and the necessary general hardware platform, and of course can also be realized by hardware. Based on such understanding, the above technical solutions essentially or the part that contributes to the prior art can be embodied in the form of a software product. The computer software product can be stored in a computer readable storage medium, such as a ROM / RAM, a magnetic disk, an optical disk, etc., and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0245] The computer program product of the present application can be a computer program implemented on one or more various apparatuses, e.g., general purpose computers or dedicated computers. According to one embodiment, the computer program product is tangibly embodied (fixed in a tangible medium of expression) in a non-transitory computer-readable medium of a server, a client, or of any device (for example, RAM containing the program as it is being executed, ROM, EEPROM, compact disk, digital tape, etc.). According to another embodiment, the computer program product is tangibly embodied (fixed in a tangible medium of expression) in a transmission medium, transmitted by a device or a

[0246] It should be noted that the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. Any "one", "another", or "at least one" preceding any statement are intended to encompass one or more individuals. Any "couple", "coupled", or "couples" between different elements, signifies either a direct or an indirect coupling, which can be permanent or replaceable at any time.

[0247] Finally, it should be noted that the above-mentioned embodiments are merely used to illustrate the technical solutions of the present application, instead of limiting the technical solutions of the present application; although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that the technical solutions recorded in the above-mentioned embodiments can be modified or equivalent replacements can be made to some of the technical features; the modifications or replacements 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 application.

Claims

1. A method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame, characterized in that, include: Based on the dynamics theory of multi-flexible body systems, the gear system is divided into shaft substructure and housing substructure, and their dynamic equations are established respectively. The fixed interface modal synthesis method is used to reduce the order of the box model, retaining the principal and constraint modes, and generating the reduced-order dynamic equations of the box with reduced degrees of freedom; a gear shaft dynamic model is established based on the spatial beam theory, taking into account the combined motion effects of the shaft system's accelerated translation and rotation. Bearing coupling is achieved through multi-point constraint MPC, and the bearing force of the shaft system nodes is equivalently distributed to the flexible nodes of the bearing holes in the housing. A gear meshing coupling model is established, and tooth backlash, meshing error and time-varying meshing stiffness are introduced to characterize the nonlinear dynamic characteristics of the gear pair. The dynamic equations of the shaft system, housing, bearing and gear are coupled to form the overall system model, and the dynamic response of the overall system model is solved by the dimension-enhanced fine integral algorithm.

2. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 1, characterized in that, The aforementioned theory of dynamics of multi-flexible-body systems divides the gear system into a shaft substructure and a housing substructure, and establishes their respective dynamic equations, including: establishing a floating coordinate system at the center of mass of the housing, using the rigid body translational degrees of freedom and the flexible node deformation coordinates as generalized coordinates, deriving the motion equations including inertial forces and gravitational loads based on the Lagrange equation, and using the finite element discrete housing as the solid element.

3. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 2, characterized in that, The method of using fixed interface modal synthesis to reduce the order of the box model, retaining the principal modes and constraint modes, and generating reduced-order box dynamic equations with reduced degrees of freedom, includes: dividing the box nodes into interface nodes coupled with the outside world and internal nodes; extracting the fixed interface principal modes to describe the free vibration of the internal nodes; extracting the constraint modes to describe the entrainment motion of the interface nodes; reducing the degrees of freedom of the principal modes with three times the meshing frequency as the cutoff frequency; and forming box dynamic equations that include translational degrees of freedom and reduced-order modal coordinates.

4. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 3, characterized in that, The aforementioned gear shaft dynamics model based on spatial beam theory, which takes into account the combined motion effects of shaft acceleration translation and rotation, includes: establishing a floating coordinate system at the shaft rotation speed input, using the rigid body translational degrees of freedom, rotational degrees of freedom around the axis, and deformation coordinates of the flexible shaft segment as generalized coordinates, discretizing the shaft segment using spatial beam theory, and using the Lagrange equation to incorporate the velocity quadratic term of the non-inertial system effect formed by centrifugal inertial force and Coriolis force as an additional generalized force.

5. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 4, characterized in that, The method of achieving bearing coupling through multi-point constraint MPC and equivalently distributing the bearing force of the shaft system node to the flexible node of the housing bearing hole includes: defining the generalized coordinate difference between the shaft system bearing node and the housing bearing hole node in the inertial coordinate system as the bearing deformation amount; distributing the bearing force to the flexible node around the housing bearing hole based on the static equivalence principle, which is equivalent to the balance relationship between the mass center force and the torque of a virtual rigid body.

6. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 5, characterized in that, The establishment of the gear meshing coupling model, which introduces tooth backlash, meshing error, and time-varying meshing stiffness to characterize the nonlinear dynamic characteristics of the gear pair, includes: in the gear meshing coupling model, tooth backlash is calculated based on gear module, center distance, pressure angle, and machining and installation errors; meshing error is characterized by the superposition of the total accumulated deviation of tooth pitch and the simple harmonic function of the single tooth tangential deviation; and a nonlinear meshing force model is constructed by combining time-varying meshing stiffness and meshing damping.

7. The method for dynamic modeling of a gear system considering a fundamental translational non-inertial frame of reference as described in claim 6, characterized in that, The dynamic equations of the coupled shaft system, housing, bearings, and gears form a system-wide model. The dynamic response of the system-wide model is solved using an augmented-dimensional fine integration algorithm. This includes: converting the system dynamic equations into state-space form, separating the linear constant coefficient matrix from the time-varying nonlinear terms, recursively solving the exponential matrix using time step recursion, and solving the exponential matrix using matrix addition and augmented-dimensional fine integration to improve the computational efficiency and accuracy of the coupled system's dynamic response.

8. A dynamic modeling device for a gear system considering a fundamental translational non-inertial frame of reference, characterized in that, include: The first main module is used to implement the dynamic equations of the gear system, which is divided into shaft substructure and housing substructure based on the dynamics theory of multi-flexible body system. The second main module is used to reduce the model order of the housing using the fixed interface modal synthesis method, retaining the principal and constraint modes, and generating reduced-degree-of-freedom dynamic equations for the housing. The third main module is used to establish a gear shaft dynamic model based on spatial beam theory, taking into account the combined motion effects of shaft acceleration translation and rotation. The fourth main module is used to achieve bearing coupling through multi-point constraint MPC, effectively distributing the bearing forces at shaft nodes to the flexible nodes of the housing bearing holes. The fifth main module is used to establish a gear meshing coupling model, introducing tooth flank clearance, meshing error, and time-varying meshing stiffness to characterize the nonlinear dynamic characteristics of the gear pair. The sixth main module is used to realize the dynamic equations of the coupled shaft system, housing, bearings, and gears, forming an overall system model, and using an augmented-dimensional refined integral algorithm to solve the dynamic response of the overall system model.

9. An electronic device, characterized in that, include: 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 that can be executed by the processor, which invokes the program instructions to perform the method described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions that cause the computer to perform the method described in any one of claims 1 to 7.

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