A multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model

Abstract

The application discloses a multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamic model, which is based on a hybrid dynamic model coupling a lumped parameter model and a finite element condensed model, and optimization is performed with the lightweight structure parameters of a high-speed gear transmission system as design variables and the minimum system weight as an optimization target, so that constraint conditions such as transmission characteristics, vibration noise and fatigue life of the system are directly obtained through hybrid dynamic model simulation of the transmission system, unlike the optimization of the vibration constraint conditions in the previous lightweight method, which only considers the optimization of inherent characteristics such as modal frequency. The simulation and optimization process is realized through an automatic script, and the design efficiency is improved. The beneficial effect is that the method is used for optimization of an experimental gear box, the system weight is effectively reduced while the transmission performance is ensured and the noise and vibration are suppressed, the optimization time is relatively short, and the design efficiency is significantly improved.

Description

Technical Field

[0001] This invention relates to the field of gear transmission system dynamics technology, specifically to a multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model. Background Technology

[0002] To reduce the vibration and noise of high-speed gears while simultaneously reducing their weight, and to ensure the system's transmission performance, reliability, and service life, it is essential to first establish a dynamic model of the high-speed gears. This model must reflect the impact of different structural parameters on the gears' dynamic characteristics and transmission performance. Subsequently, sensitivity analysis of the structural parameters should be performed to select the most suitable lightweighting parameters, thereby improving the efficiency and saving time in the subsequent weight reduction process.

[0003] Furthermore, although the industry currently demands lightweight high-linear-speed gears while maintaining transmission performance and dynamic characteristics, most current lightweighting methods still optimize based on the various static and inherent characteristics of the gears. Some methods go further, performing dynamic simulations after optimization to determine if the dynamic characteristics requirements are met. However, none of these methods can determine whether the optimization results meet the requirements based on the transmission performance and vibration characteristics of the gears under operating conditions during each optimization iteration. Consequently, they cannot appropriately limit the direction of parameter iteration during the optimization process. Therefore, it is necessary to use simulation models that can accurately describe the dynamic characteristics of high-speed transmission systems to evaluate various performance indicators of the gears during the lightweighting process. Although existing theoretical analyses and experimental studies by scholars at home and abroad have yielded various dynamic models for this type of model, these models are either computationally inefficient and resource-intensive, or can only describe constant speed conditions and simple dynamic characteristics. Therefore, in order to meet the requirement of obtaining the various performance characteristics of gears under actual working conditions in each optimization iteration, it is necessary to establish a flexible gear dynamic model that has both good computational efficiency and can simulate constant speed and variable speed conditions. Based on this, a technical system for lightweighting high linear velocity gear structures with high linear velocity gear dynamic characteristics as design parameters should be established. Summary of the Invention

[0004] In response to the above situation, this invention proposes a multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model, the key of which includes the following steps:

[0007] S1: Establish the meshing force solution model

[0008] The high-speed gear is sliced ​​along the tooth width direction. By calculating the instantaneous contact line length of the meshing teeth, the position of the slice element on the contact line is determined. Two frustums are used to simulate the instantaneous contact state of the two gears, and the curvature radius of the slice element is derived. Thus, the position vector of the slice element is obtained. Combined with the meshing stiffness per unit length of the contact line and the meshing contact line length, the meshing force and meshing torque can be calculated. Then, by accumulating them, the dynamic meshing force and meshing torque of the high-speed gear system can be obtained.

[0009] S2: Establishing a finite element condensation model

[0010] The gear dynamics equations are decoupled and then converted into state equations. A three-dimensional model of the large and small gears is established. Teeth are removed from the root circle, and the gears are divided on the split surface according to the tooth cross-section. Concentrated nodes are then established at the split surface and bearing locations. To simultaneously reflect the rigid rotation and flexible deformation of the gear body, the actual motion of the gear body is equivalent to a combination of gear body deformation and rigid rotation. The rotational motion of the z-axis of the finite element model is fixed at the corresponding concentrated nodes of the small and large gears, resulting in a finite element condensed model. Then, the driving force and load of each gear are applied to their respective moments of inertia to obtain the rigid rotational motion of the gears. Furthermore, for the rigid rotational motion, the effects of inertial force, centrifugal force, and Coriolis force need to be considered to establish a rigid rotational model of the gears. Simultaneously, fixed constraints are applied to the bottom of the gear housing, and concentrated nodes are established at the bearing hole supports to obtain a finite element condensed model of the gear housing.

[0011] S3: Couple the various models to obtain a sliced ​​coupled dynamic model of the high-speed thin-walled gear transmission system.

[0012] The models need to be coupled together through relationships such as force and displacement. The meshing force and torque are calculated in the stationary coordinate system OXYZ, while the coordinate system of the finite element condensation model is the rotating coordinate system oxyz, which follows the rotation of the gear's z-axis. Therefore, the displacements obtained from the finite element condensation model cannot be directly used to calculate the meshing force and torque, and the meshing force obtained from the stationary coordinate system cannot be directly applied to the finite element condensation model. A process is needed to couple the various models:

[0013] 1) Transform the meshing force and meshing torque from the stationary coordinate system to the rotating coordinate system, and transform the bearing support reaction force from the rotating coordinate system to the stationary coordinate system;

[0014] 2) Determine the meshing teeth by the current rotational displacement of the gear along the z-axis;

[0015] 3) The converted meshing force and meshing torque are applied to the meshing tooth concentration nodes of the gear finite element condensation model, the bearing force is applied to the bearing concentration nodes of the gear finite element condensation model, and the converted bearing support reaction force is applied to the bearing concentration nodes of the housing finite element condensation model.

[0016] 4) Transform the displacement and velocity of the meshing tooth concentrated nodes obtained from the gear finite element model from the rotating coordinate system to the stationary coordinate system, and transform the displacement and velocity of the bearing concentrated nodes obtained from the box finite element model from the stationary coordinate system to the rotating coordinate system.

[0017] S4: Lightweight optimization design for high-speed gears

[0018] Lightweight gear design is achieved by modifying the gear body and housing structure. The dimensional parameters of the housing and gear structure are selected as optimization parameters, and corresponding parametric models are established. In each optimization iteration, the optimization algorithm assigns values ​​to various optimization parameters. The program automatically generates a 3D model and a finite element model according to the given parameters, performs static and modal analyses, and obtains static strength and finite element condensation model data, respectively. Then, the condensation model and the lumped parameter model are coupled for hybrid dynamic simulation to analyze and calculate various dynamic loads, vibration displacements, and vibration velocities of the gear and housing. The dynamic load data (such as bearing force and meshing force) are combined with the static strength analysis results to form a load spectrum for fatigue life analysis. Finally, it is determined whether the obtained static strength, fatigue life, and other constraints meet the design requirements. The optimization parameters that finally converge to the global optimum are taken as the final design scheme.

[0019] In step S1, the process of establishing the solution model for meshing force and meshing torque is as follows:

[0020] Derive the element M of gears 1 and 2. j The position vector can be represented as:

[0021]

[0022]

[0023] The normal unit vector of the contact line element Mj of gears 1 and 2 can be obtained by the following formula:

[0024] n g1 =[cosβ b sinα t ,cosβ b cosα t sinβ b ]

[0025] n g2 =-[cosβ b sinαt ,cosβ b cosα t sinβ b ]

[0026] This unit vector is the unit normal vector of the tooth surface;

[0027] M j The normal deformation can be derived as:

[0028]

[0029] Where R g1 and Ω g1 These are the translational and angular displacement vectors of gear 1, respectively; R g2 and Ω g2 These are the translational and angular displacement vectors of gear 2, respectively; e j It is M j Tooth profile error at the location; R g1 =[X g1 ,Y g1 Z g1 ]; R g2 =[X g2 ,Y g2 Z g2 ]and

[0030] Considering tooth flank clearance, M can be... j The normal compressive deformation at the point is expressed as:

[0031]

[0032] Where b k It is the tooth flank clearance;

[0033] Therefore, the meshing force and torque of the i-th meshing tooth pair, i.e., the i-th contact line, can be expressed as:

[0034]

[0035] in, and These are the force and torque vectors for the i-th meshing tooth pair on gears 1 and 2, respectively, including three forces and three torques for each meshing tooth pair of each gear in the x, y, and z axes; k e It is the meshing stiffness of a unit, which is equal to the meshing stiffness of the unit contact line length multiplied by the unit contact line length.

[0036] The total meshing force and meshing torque on each gear are obtained by the following formula:

[0037]

[0038] in, and These are the forces and torques acting on gears 1 and 2, with each gear having three forces and three torques in the x, y, and z directions.

[0039] In step S2, the process of establishing the finite element condensation model of the gear body in the finite element condensation model is as follows:

[0040] First, a 3D model of the large gear is established. Since minor rounding and chamfering have little impact on the modal analysis results, these minor features can be disregarded when building the 3D model to obtain better mesh quality. The teeth are removed from the root circle to facilitate the creation of concentrated nodes. The presence or absence of teeth has little impact on the model's inherent properties. The established 3D model is imported into the finite element software. Then, tetrahedral elements are selected and the element size is set for mesh generation. Considering that higher-order modes than the highest frequency component to be analyzed have less impact on the model, the first 80 modes are selected for analysis. Finite element software is used to calculate and obtain the natural frequencies and mode shapes of the thin-walled gear. Finally, these data are processed to form a finite element condensed model. To facilitate the subsequent optimization design process, a script needs to be written to automate the process from generating the 3D model to exporting the condensed model. In order to reflect both the rigid rotation and flexible deformation of the gear body, this paper equates the actual motion of the gear body to a combination of gear body deformation and rigid rotation. Modal deformation can be obtained through the finite element model, and rigid body rotational motion can be obtained through Newton's law of rigid bodies. That is, the rigid rotational motion around the z-axis is not included in the finite element modal analysis.

[0041] In step S2, the process of establishing the box-shaped finite element condensation model in the finite element condensation model is as follows:

[0042] The box has four central nodes, two of which are used for coupling between the box and the pinion via support, and the other two nodes are used for coupling between the box and the large gear via support. The bottom of the box is set as a fixed constraint. After solving the model using finite element software, the natural frequencies and mode shapes of the model are exported. The above process is also automated by writing scripts for subsequent optimization.

[0043] In step S3, the hybrid power model of the high-speed thin-walled gear is coupled from a finite element condensation model and a lumped parameter dynamic model. By applying the force on each contact tooth to the corresponding tooth lumped node in the finite element condensation model, the displacement of the contact tooth can be obtained. Then, the sequence number of the new contact tooth is determined based on the displacement of the contact tooth. The algebraic loop problem caused by this process can be solved using Simulink's memory module. At the same time, the displacement needs to be transformed from the rotating coordinate system to the static coordinate system for calculating the meshing force and torque. After that, the meshing force and torque are... The moment is transformed from the static coordinate system to the rotating coordinate system, and then to the contact tooth concentration node of the finite element condensation model. After obtaining the displacement and velocity of the bearing concentration node from the reduced-order finite element model of the gear and housing, it is used to calculate the bearing support force and moment, as well as the support damping force and moment, acting on the reduced-order finite element model. For the housing, the bearing support reaction force, which is transformed from the rotating coordinate system to the static coordinate system, needs to be applied to the reduced-order finite element model of the housing to obtain the displacement and velocity of the bearing housing concentration node, and then transformed to the rotating coordinate system of the gear corresponding to the bearing housing node.

[0044] In step S4, changes in lightweight design parameters will affect various performance aspects of the transmission system. Among these, static strength, fatigue life, NVH, and transmission performance are our key concerns. During the optimization and iteration process, these conditions need to be used as constraints to ensure the performance of the lightweight gear transmission system.

[0045] Compared with the prior art, the beneficial effects of the present invention are:

[0046] After the weight reduction is completed, the gear structure has changed significantly, altering the meshing state during operation. Therefore, the previous tooth profile may not meet the conditions for stable meshing. Thus, gear modification is required to ensure stable meshing, ultimately resulting in a high linear velocity gear with low noise and vibration, stable transmission, and high reliability.

[0047] This method achieves lightweight optimization that better balances the transmission performance and dynamic characteristics of gear transmission systems under actual working conditions, thereby reducing problems such as gear system overload, stress concentration, and excessive vibration, improving equipment performance, and reducing failure rate. Attached Figure Description

[0048] Figure 1 This is a diagram illustrating the motion analysis of a helical gear.

[0049] Figure 2 This is a schematic diagram of the contact line movement;

[0050] Figure 3 This is an approximate simulation diagram of the contact frustum of a helical gear;

[0051] Figure 4 For M j Projection view of the end face;

[0052] Figure 5 This is a finite element model diagram of a thin-walled large gear;

[0053] Figure 6 This is a finite element model diagram of a pinion;

[0054] Figure 7 A schematic diagram of the inertial force, centrifugal force, and Coriolis force at node i;

[0055] Figure 8 Flowchart of the complete reduced-order model of the gear body;

[0056] Figure 9 Flowchart of the finite element condensation model of the box;

[0057] Figure 10 Flowchart of the reduced-order model of the box;

[0058] Figure 11 This is a schematic diagram of coordinate system transformation used for calculating meshing force and reduced-order finite element method;

[0059] Figure 12 This is a schematic diagram showing the transformation of meshing force and torque vectors from the gear center to the concentrated tooth pitch;

[0060] Figure 13 This is a structural diagram of the gears and housing;

[0061] Figure 14 Schematic diagram of rainflow counting method;

[0062] Figure 15 Equivalent life curve - equivalent stress conversion diagram;

[0063] Figure 16 To optimize the design flowchart. Detailed Implementation

[0064] A lightweight design and dynamic characteristic optimization design for a highly flexible high-speed gear is proposed. The design concept of this method is to establish a meshing force solution model and a finite element condensation model, and couple them to obtain a dynamic model of a high-speed thin-walled gear transmission system. Then, lightweight design is carried out, and the dynamic characteristics of the high-speed thin-walled gear transmission system are optimized by setting constraints.

[0065] Please refer to Figure 1 As shown, the process for establishing the model for solving the meshing force of a high-speed thin-walled gear transmission system is as follows:

[0066] The origin of the coordinate system is located at the midpoint of the centerline of each gear shaft, and a six-degree-of-freedom lumped parameter dynamic model of the gear set is established.

[0067] The lumped-parameter dynamic model of a helical gear can be expressed as:

[0068]

[0069] Among them, X g1 Y g1 and Z g1 These represent the translational displacements of the driving pinion (g1) along the X, Y, and Z axes in the coordinate system, respectively; X g2 Y g2 and Z g2 These represent the translational displacements of the driven gear (g2) along the X, Y, and Z axes in the coordinate system, respectively. and These represent the angular displacements of the pinion along the X, Y, and Z axes, respectively. and These represent the angular displacements of the large gear along the X, Y, and Z axes, respectively; M j It is the j-th segment of the gear tooth meshing contact line, which is divided into N segments; and It is contact wire unit M j The position vectors of the midpoint in the coordinate systems of gear 1 and gear 2, respectively.

[0070] like Figure 1 As shown, k j =k m l j For meshing contact line unit M j The meshing stiffness, k m l is the meshing stiffness per unit length. j Let δ be the length of element M. e Let r be the deformation of the meshing contact line element, and r be the position vector of the midpoint of element M. Then the meshing force F corresponding to the meshing line element is... e Meshing force and meshing torque are calculated using the following formulas:

[0071] F e =k e δ e

[0072]

[0073] Calculating the meshing force requires the meshing stiffness per unit length of the contact line and the length of the meshing contact line.

[0074] like Figure 2 As shown, B1B2B3B4 represents the meshing contact area of ​​the two gears, and 1, 2, and 3 represent the tooth contact surfaces. If the contact surface is within the meshing contact area, it means that the teeth have made contact, as shown by the solid line. If the contact surface is not within the meshing contact area, it means that the teeth have not made contact, as shown by the dashed line.

[0075] The position of the slice element on the contact line can be calculated by the length of the meshing contact line. The starting position of the contact line (L) s ) and termination position (L) e It can be calculated using the following formula:

[0076] If ε α ≥ε β ,

[0077]

[0078] If ε α <ε β ,

[0079]

[0080] in θ Z g1 , r b1 tn1 and tn1 represent the angular displacement, initial phase angle, base circle radius, and number of teeth of the pinion, respectively. i = 1, 2Kceil(ε γ () represents the i-th contact tooth pair, corresponding to the i-th contact tooth surface in the diagram, such as... Figure 2 As shown. ε γ ε α and ε β These are total overlap, end face overlap, and axial overlap, where ε γ =ε α +ε β p b , b and β b These represent the base circle pitch, tooth width, and base circle helix angle, respectively.

[0081] If the length of the element on the contact line is Δl, then the total number of elements is N;

[0082]

[0083] The length of the Nth element is

[0084] Δl N =(L e -L s )-(N-1)Δl

[0085] Unit M j Position L on the contact line j yes

[0086]

[0087] The instantaneous meshing contact of helical gears can be approximated using two frustums of cones, such as... Figure 3 As shown;

[0088] The contact lines of the pinion and gear along DB4 are as follows: Figure 2 As shown, the radius of curvature of a point on the contact line can be expressed by the equation:

[0089] ρ t1 =r b1 tanα wt -r b2 (tanα ta2 -tanα wt )-btanβ b +s

[0090] ρ t2 =r b2 tanα wt +r b2 (tanα ta2 -tanα wt )+btanβ b -s

[0091] The unit M of gears 1 and 2 can be derived. j The radius of curvature is given by the equation:

[0092] ρ t1j =ρ t1 +L j sinβ b

[0093] ρ t2j =ρ t2 -L j sinβ b

[0094] Where, r b2 α ta2 and α ωt These are the base circle radius, the pressure angle at the tooth tip face of gear 2, and the pressure angle at the working end face; Figure 2 At point B2, the gear teeth just make contact. At this moment, the radii of curvature of gears 1 and 2 at point B2 are r and r, respectively. b1 tanα wt -r b2 (tanα ta2 -tanα wt ) and r b2 tanα wt +r b2 (tanα ta2 -tanα wt The radii of curvature of gears 1 and 2 at point D can be obtained by r respectively. b1 tanα wt -r b2 (tanα ta2-tanα wt )-btanβ b and r b2 tanα wt +r b2 (tanα ta2 -tanα wt )+btanβ b Therefore, the radius of curvature at the contact point along line DB4 can be expressed as an equation:

[0095] ρ t1 =r b1 tanα wt -r b2 (tanα ta2 -tanα wt )-btanβ b +s

[0096] ρ t2 =r b2 tanα wt +r b2 (tanα ta2 -tanα wt )+btanβ b -s

[0097] The element M of gears 1 and 2 can be derived. j The position vector can be represented as:

[0098]

[0099]

[0100] The normal unit vector of the contact line element Mj of gears 1 and 2 can be obtained by the following formula:

[0101] n g1 =[cosβ b sinα t ,cosβ b cosα t sinβ b ]

[0102] n g2 =-[cosβ b sinα t ,cosβ b cosα t sinβ b ]

[0103] This unit vector is the unit normal vector of the tooth surface.

[0104] M jThe normal deformation can be derived as:

[0105]

[0106] Where R g1 and Ω g1 These are the translational and angular displacement vectors of gear 1, respectively; R g2 and Ω g2 These are the translational and angular displacement vectors of gear 2, respectively; e j It is M j Tooth profile error at the location; R g1 =[X g1 ,Y g1 Z g1 ]; R g2 =[X g2 ,Y g2 Z g2 ] and Ω g2 =

[0107] Considering tooth flank clearance, M can be... j The normal compressive deformation at the point is expressed as:

[0108]

[0109] Where b k It is the tooth flank clearance;

[0110] Therefore, the meshing force and torque of the i-th meshing tooth pair, i.e., the i-th contact line, can be expressed as:

[0111]

[0112] in, and These are the force and torque vectors for the i-th meshing tooth pair on gears 1 and 2, respectively, including three forces and three torques for each meshing tooth pair of each gear in the x, y, and z axes; k e It is the meshing stiffness of a unit, which is equal to the meshing stiffness of the unit contact line length multiplied by the unit contact line length.

[0113] The total meshing force and meshing torque on each gear are obtained by the following formula:

[0114]

[0115] in, and These are the forces and torques acting on gears 1 and 2, with each gear comprising three forces and three torques in the x, y, and z directions;

[0116] The dynamic equations of the system can be expressed as:

[0117]

[0118] Among them, M and C d K and K are the mass matrix, damping matrix, and stiffness matrix, respectively; u is the displacement vector; and F is the load vector.

[0119] Based on the orthogonality of modal coordinates, it can be transformed into a modal coordinate system with n degrees of freedom decoupled equations:

[0120]

[0121] Where ndof represents the degrees of freedom (DOFs) of the entire dynamical system, Φ j It is the vector of the j-th mode shape, y j These are system modal coordinates.

[0122] Higher-order modes typically have limited impact; therefore, to reduce computational costs, the first n modal equations from the decoupling equation set are sufficient to solve the system dynamics analysis problem. The first n modal equations are a set of second-order differential equations, which can be transformed into the following state equations.

[0123]

[0124] in

[0125]

[0126] w is the displacement vector corresponding to the degree of freedom; y is the modal coordinate vector corresponding to the degree of freedom; A, B, C, and D are matrices of the state equations; F s It is the input load vector.

[0127] Where A is a state matrix of size 2n×2n:

[0128]

[0129] Where the matrix ω j It is the j-th modal frequency, ξ j It is the j-th order modal damping.

[0130] B is an input matrix of size 2n×nin, where nin is the number of nodal input forces.

[0131]

[0132] Where Γ3=Φ T F u Φ is the eigenvector matrix, F uIt is a force matrix of size n×nout, where nout is the number of degrees of freedom of the node to be calculated, which is 1 at the position of the input force and 0 elsewhere.

[0133] C is the output matrix of 2nout×2n:

[0134]

[0135] Where Γ4=U u Φ, U u It is a displacement matrix of size nout×ndof, where the degrees of freedom of the nodes are 1 at the position of the input force and 0 elsewhere.

[0136] D is a 2nout×nin feedforward matrix:

[0137]

[0138] Please refer to Figure 5 The image shows a thin-walled large gear model, which is rigidly connected to the shaft. The process of establishing the condensed model is as follows: First, a three-dimensional model of the large gear is established. Since small rounding and chamfering have little impact on the modal analysis results, to obtain better mesh quality, small features such as rounding and chamfering can be ignored when establishing the three-dimensional model. At the same time, the gear teeth are removed from the root circle to facilitate the establishment of concentrated nodes. The presence or absence of gear teeth has little impact on the inherent properties of the model. The established three-dimensional model is imported into the finite element software. In order to couple the finite element condensed model of the large gear with other components and transfer various displacements, velocities, and loads between components, 68 gear tooth concentrated nodes and two bearing concentrated nodes are established, as shown below. Figure 5 As shown, tetrahedral elements are then selected and their sizes are set for mesh generation. Considering that modes with higher frequencies than the highest frequency component to be analyzed have less impact on the model, the first 80 modes are selected for analysis. The natural frequencies and mode shapes of the thin-walled large gear are obtained through finite element software. Finally, these data are processed to form a finite element condensed model. To facilitate the subsequent optimization design process, a script needs to be written to automate the process from generating the 3D model to exporting the condensed model.

[0139] Small gear model, such as Figure 6 As shown, the finite element condensation model is established in the same way as the large gear. The small gear is established with a total of 35 tooth cluster nodes and two bearing cluster nodes.

[0140] To simultaneously reflect the rigid rotation and flexible deformation of the gear body, this paper equates the actual motion of the gear body to a combination of gear body deformation and rigid rotation. Modal deformation can be obtained through the finite element model, and rigid body rotational motion can be obtained through Newton's laws for rigid bodies. That is, the rigid rotational motion around the z-axis is not included in the finite element modal analysis. First, the rotational motion of the z-axis of the finite element model is fixed at the concentrated node 38 of the pinion and the concentrated node 71 of the gear, respectively, to obtain the finite element condensed model. Then, the driving force and load of each gear are applied to their respective moments of inertia to obtain the rigid rotational motion of the gear, as shown in the following equation:

[0141]

[0142] Where, θ z It is the rigid angular displacement of the gear's z-axis; T driving and T driven These are driving force and load, respectively.

[0143] Among them, the pinion is the input end, and its driving force is the input torque input to the transmission system. The load is the meshing torque acting on gear 1. The driving force of gear 2 is the meshing torque acting on gear 2. The load on gear 2 is the torque of the output load. In addition, for rigid rotational motion, the effects of inertial force, centrifugal force, and Coriolis force need to be considered to establish a rigid rotational model of the gear.

[0144] Because of the rigid rotation of the gear, inertial and centrifugal forces should be added to the reduced-order model of the gear, such as... Figure 7 As shown. The effect of the Coriolis force is not significant, and adding the Coriolis force reduces calculation speed; therefore, the Coriolis force is ignored. Figure 7 As shown, (x i ,y i ) is the coordinate of node i in the finite element model in the moving coordinate system oxyz. i F is the quality of node i. ai and F ci These are the inertial force and centrifugal force at node i, respectively. θ z ω, α, and α are the rigid body angular displacement, angular velocity, and angular acceleration of the gear body, respectively.

[0145] The inertial force at node i can be derived as follows:

[0146]

[0147] The inertial forces at all nodes should be transformed to modal coordinates so that they can be applied to the reduced-order model, as shown in the following equation:

[0148]

[0149] The centrifugal force at node i is derived as follows:

[0150]

[0151] The centrifugal forces at all nodes should be converted to modal coordinates:

[0152]

[0153] Please refer to Figure 8 As shown, the process of establishing the finite element condensation model of the box is as follows:

[0154] The box has four central nodes, where nodes 1 and 2 are used for coupling between the box and the small gear through supports, and nodes 3 and 4 are used for coupling between the box and the large gear through supports. The bottom of the box is set as a fixed constraint. After solving the model with finite element software, the natural frequencies and mode shapes of the model are exported. The above process is also automated by writing scripts for subsequent optimization.

[0155] The load on the housing is mainly the bearing reaction force. The displacement and velocity of the housing deformation can be obtained by simply applying the reaction force to the reduced-order finite element model of the housing.

[0156] The models need to be coupled together through relationships such as force and displacement. As mentioned in previous sections, the meshing force and torque are calculated in the stationary coordinate system OXYZ, while the coordinate system of the finite element condensation model is the rotating coordinate system oxyz, which follows the rotation of the gear's z-axis. Therefore, the displacements obtained from the finite element condensation model cannot be directly used to calculate the meshing force and torque, and the meshing force obtained from the stationary coordinate system cannot be directly applied to the finite element condensation model. They need to be processed to couple the various models:

[0157] 1. Transform the meshing force and meshing torque from the stationary coordinate system OXYZ to the rotating coordinate system oxyz, and transform the bearing support reaction force from the rotating coordinate system to the stationary coordinate system.

[0158] 2. Determine the meshing teeth by the current z-axis rotational displacement of the gear.

[0159] 3. Apply the converted meshing force and meshing torque to the meshing tooth concentration nodes of the gear finite element condensation model, apply the bearing force to the bearing concentration nodes of the gear finite element condensation model, and apply the converted bearing support reaction force to the bearing concentration nodes of the housing finite element condensation model.

[0160] 4. Transform the displacements and velocities of the meshing tooth concentrated nodes obtained from the gear finite element model from the rotating coordinate system to the stationary coordinate system, and transform the displacements and velocities of the bearing concentrated nodes obtained from the box finite element model from the stationary coordinate system to the rotating coordinate system.

[0161] A key step in the above coupling process of the model is determining the actual sequence number of the meshing teeth. During gear meshing, only ceil(ε) γ Since a certain number of tooth pairs actually participate in meshing, the relationship between the actual tooth number and the tooth pair number on the gear should be determined in the calculation of meshing force and torque. First, it is stipulated that in the calculation of meshing force and torque, the first number of the actual meshing tooth and the first number of the contact tooth pair are the same. Therefore, in the calculation of meshing force and torque, the total number of meshing teeth (Ic)... i The relationship between the first tooth and the i-th tooth pair can be expressed as:

[0162]

[0163] Where "lcm" is the least common multiple function; tn1 and tn2 are the number of teeth on the pinion and gear, respectively. "ceil()" is the function that rounds to positive infinity; "floor()" is the function that rounds to negative infinity. and These are the angular displacement and initial phase angle of the pinion, respectively; ε γ It is the total overlap.

[0164] The actual working tooth number on the pinion and gear can be represented by the following formula:

[0165] Icg1 = mod(Ic i -1,tn1)+1

[0166] Icg2 = mod(Ic i -1,tn2)+1

[0167] Here, "mod" is the modulo function.

[0168] In the simulation model, the actual tooth number of the meshing teeth is determined based on the angular displacement of each meshing tooth pair of the pinion. Then, the displacement is obtained at the tooth concentration node corresponding to the actual meshing tooth number to calculate the meshing force and torque. Finally, the calculated meshing force and torque are applied to the tooth concentration node corresponding to the actual meshing tooth number. Furthermore, the coordinate transformation described in the next section is required during this process.

[0169] like Figure 11 As shown, the static coordinate system oX g1 Y g1 Z g1 and oX g2 Y g2 Z g2 Used to calculate the meshing force and torque on the pinion and gear respectively. Rotating coordinate system ox g1 y g1 z g1 and oxg2 y g2 z g2 Finite element condensation models are used for the pinion and gear, respectively. The rotational speeds of the rotating coordinate system are the rigid rotational speeds of gears 1 and 2, respectively. For the pinion and gear, the relative angles between the rotating coordinate system and the static coordinate system are respectively... and

[0170]

[0171] in It is the rigid body rotational displacement of the pinion (g1) and gear (g2), while This represents the initial relative angle between the rotating and stationary coordinate systems of g1 and g2, specifically the relative angle between the first teeth in the coordinate system used to calculate the meshing force and the reduced-order finite element method at the start of the simulation. Furthermore, the initial relative angle can be eliminated by adjusting the coordinate system of the reduced-order finite element model.

[0172] The translational and angular displacements obtained from the reduced-order gear model are in a rotating coordinate system; therefore, they need to be converted to a static coordinate system to calculate the meshing force and torque. Taking the Ic1 tooth of gear 1 and the Ic2 tooth of gear 2 as examples, the transformation is obtained according to the following formula.

[0173]

[0174] in (a=g1,g2) is the displacement vector of the Ica tooth of gear 1 and 2 in the rotating coordinate system of the gear finite element model; (a=g1,g2) is the displacement vector of the Ica tooth of gears 1 and 2 in the static coordinate system.

[0175]

[0176] The situation is different for the gear housing. Since the reduced-order model of the housing is in a static coordinate system, while the bearing forces are calculated in the rotating coordinate system of the gear finite element model, it is necessary to transform the displacements of the housing at the concentrated nodes of the bearing housing to the corresponding rotating coordinate system of the gear. The transformation is derived as follows:

[0177]

[0178] in (a=g1,g2) is the displacement vector of the concentrated node h (h=bh1,bh2) of the housing bearing seat in the static coordinate system; (a=g1,g2) is the displacement vector of the concentrated node h (h=bh1,bh2) of the bearing housing corresponding to the bearings of gears 1 and 2 in the rotating coordinate system of the gear finite element model.

[0179] After conversion, the displacement vector It can be used to calculate the meshing force and meshing torque of the i-th tooth pair. (a = g1, g2). Furthermore, in the calculation of meshing force and torque, Ica (a = g1, g2) corresponds to the i-th tooth pair. If it is in a static coordinate system, it should be converted to a rotating coordinate system, that is, the coordinate system of the reduced-order finite element model.

[0180]

[0181] in Represents the meshing force and torque vector, corresponding to the Ica-th gear on the pinion and gear in the reduced-order finite element model coordinate system. th (a=g1,g2) teeth.

[0182] After conversion, the displacement vector It can be used to calculate the bearing force at the bearing node of gear 1 and 2.

[0183]

[0184] However, The point of action is the center of the gear. Therefore, it should be converted to the Ica. th The concentrated nodes of the teeth (a=g1,g2) are as follows: Figure 11 As shown.

[0185]

[0186] in The Ica acting on gears 1 and 2 in a reduced-order finite element coordinate system th (a=g1,g2) represents the meshing force and torque vector at the tooth concentration nodes; furthermore... (k = 1, 2, ..., 6) represents The kth component.

[0187] like Figure 12 As shown, the hybrid power model of the high-speed thin-walled gear is a coupling of a finite element condensation model and a lumped parameter dynamic model. By applying the forces on each contact tooth to the corresponding tooth lumped node in the finite element condensation model, the displacement of the contact tooth can be obtained. Then, the sequence number of the new contact tooth is determined based on the displacement. The algebraic loop problem caused by this process can be solved using Simulink's memory module. Simultaneously, the displacement needs to be transformed from the rotating coordinate system to the static coordinate system for calculating the meshing force and torque. Afterward, the meshing force and torque are transformed from the static coordinate system to the rotating coordinate system, and then transformed to the contact tooth lumped node in the finite element condensation model.

[0188] After obtaining the displacement and velocity of the bearing concentrated nodes from the reduced-order finite element model of the gear and housing, the bearing support force and torque, as well as the support damping force and torque, acting on the reduced-order finite element model are calculated. For the housing, the bearing support reaction force, which needs to be transformed from the rotating coordinate system to the stationary coordinate system, needs to be applied to the reduced-order finite element model of the housing to obtain the displacement and velocity of the bearing housing concentrated nodes, and then transformed to the rotating coordinate system of the gear corresponding to the bearing housing node.

[0189] The velocities of the bearing nodes obtained from the reduced-order finite element model cannot be used to directly calculate damping forces and moments; transformation is required. This model integrates structural damping into the reduced-order FEM model. Rayleigh damping is used and converted into modal damping.

[0190]

[0191] Among them, v x a and v y a These are the translational velocities of gears 1 and 2 along the x-axis and y-axis, respectively; ω x a and ω y a These are the rotational speeds of gears 1 and 2 around the x-axis and y-axis, respectively.

[0192] After obtaining the lumped parameter dynamic model of the rigid component and the finite element condensation sub-model of the flexible component, they can be coupled to form a hybrid dynamic model of the planetary gear system.

[0193] The displacement velocities of the sun gear, planet gears, and internal gear ring are obtained from the lumped parameter model of the sun gear, the lumped parameter model of the planet gears, and the finite element model of the internal gear ring, respectively. Since there is often a phase difference φd between the coordinate systems of the meshing force calculation model and the finite element condensation model, the lumped node displacement velocities obtained from the finite element condensation model need to be converted to the meshing force calculation model. Then, in the moving coordinate system oxyz, the planetary gear meshing is transformed into external and internal meshing pairs under a fixed-axis gear train, thereby calculating the meshing force and torque. The meshing force and torque also need to be converted from the meshing force calculation model to the finite element condensation model coordinate system before being applied to the sun gear, planet gears, and internal gear ring. The displacement velocities of the planet gears and the planet carrier pins can be used to calculate the bearing forces at the pins. Similarly, the bearing forces between the planet carrier and the housing, and between the sun gear and the housing, can be obtained. Then, each bearing force is applied to the corresponding component. In summary, the system dynamics model is obtained.

[0194] Please refer to Figure 13 As shown, the lightweight optimization design process for high-speed gears is as follows:

[0195] Lightweight gear design is achieved by modifying the gear body structure and gear housing structure. The dimensional parameters of the gear housing and gear structure are selected as optimization parameters, and a corresponding parametric model is established. As shown in Figure (), among the parameters, P1 is the distance between the center of the gear weight reduction hole and the axis, P2 is the width of the gear weight reduction hole, P3 is the circumferential length of the weight reduction hole, P4 is the thickness of the flange wall, P5 is the rim wall thickness, and P6 is the thickness of the gear housing wall.

[0196] Before determining the optimized structural parameters, performing parameter sensitivity analysis on the structural parameters can effectively remove structural parameters that have little impact on the optimization objective, save computing resources, improve the efficiency of optimization, and reduce the optimization time.

[0197] Optimize the design process, such as Figure 14 As shown in the diagram, during each optimization iteration, the optimization algorithm assigns values ​​to various optimization parameters. The program automatically generates a 3D model and a finite element model according to the given parameters, and performs static and modal analyses to obtain static strength and finite element condensation model data, respectively. Then, the condensation model and the lumped parameter model are coupled to perform hybrid dynamics simulation to analyze and calculate various dynamic loads, vibration displacements, and vibration velocities of the gears and housing. The dynamic load data (such as bearing forces and meshing forces) combined with the static strength analysis results can be processed into a load spectrum to analyze fatigue life. Finally, it is determined whether the obtained static strength, fatigue life, and other constraints meet the design requirements. The optimization parameters that finally converge to the global optimum are taken as the final design scheme.

[0198] Since the optimization objective is to minimize the total mass of the transmission system, which includes gears and housing, the objective function for minimizing the total mass of the transmission system is established as follows:

[0199] min m sys (P)=m gear1 +m gear2 (P1,P2,P3,P4,P5)+m box (P6)

[0200]

[0201] P = [P1, P2, P3, P4, P5, P6]

[0202]

[0203] Where f(P) is the total weight of the gearbox, and P includes the design parameters of the gear and gearbox structure dimensions, including parameters P1 to P6. Among them, P1, P2, P3, P4, and P5 are the structural parameters of the large output gear, and P6 is the structural parameter of the gearbox. The maximum static stress of the output shaft gear, D represents the maximum static stress of the box. gearD represents the fatigue damage degree of the gear. box S represents the fatigue damage degree of the housing. shaft This represents the radial displacement of the gear shaft. This represents the maximum vibration velocity on the surface of the enclosure.

[0204] Changes in lightweight design parameters can affect various performance aspects of the transmission system. Among these, static strength, fatigue life, NVH (noise, vibration, and harshness), and transmission performance are our key concerns. During the optimization and iteration process, these conditions need to be used as constraints to ensure the performance of the lightweight gear transmission system.

[0205] static strength

[0206] Since meshing force and bearing force are dynamic forces, while the loading in finite element strength analysis is a static force, it is necessary to convert the stress analysis results under static load in the finite element analysis into stress analysis results under dynamic load in order to perform fatigue life analysis later. According to the principle of linear superposition of stresses in elasticity following Hooke's law, the total stress on a part is the sum of the stresses when each load acts on the part individually. The stress at a point on the part is directly proportional to the magnitude of the external force, as expressed below.

[0207]

[0208]

[0209] Where i = 1, 2, ..., n, F i F represents the static load on the part, and σ represents the static load on the part. Fi For parts in F i The stress under individual action, σ is the total stress of the part, σ F Let F be the stress on the part under the action of F. i It has the same point of application and direction as F.

[0210] static load F i Components F in the x, y, and z axes ix F iy F iz When each load is used individually as a load in the finite element model of the part, the result of the analysis is F. i When each component acts individually on the part, the normal stress and shear stress in the xy, yz, and zx planes of the part, such as F i In the x-direction component F ix The resulting normal stresses in the xy, yz, and zx planes are σ, respectively. x-Fix σ y-Fix σ z-Fix The plane shear stresses τxy, yz, and zx are respectively xy-Fix τ yz-Fix τ xz-Fix Finally, the normal axial stress σ is obtained by linear superposition.x σ y σ z Combined shear stress τ xy τ yz τ xz As shown in the following formula.

[0211]

[0212]

[0213] Where a = x, y, z represent the direction of normal stress, and b = xy, yz, xz represent the direction of shear stress.

[0214] The results of the dynamic simulation are compared with F i Dynamic load F at the same point of application i Substituting (t) into the following formula yields the stress load spectrum of the component:

[0215]

[0216]

[0217] According to Van Mieses' three-dimensional equivalent stress formula:

[0218]

[0219] The equivalent stress load spectrum σ can be calculated. vm (t), and obtain the maximum equivalent stress maxσ in the simulation process. vm The static strength constraint conditions are obtained based on the materials used as follows:

[0220] maxσ vm <[σ]

[0221] Fatigue life analysis

[0222] Fatigue life calculation is divided into two parts: statistical processing of load data and fatigue damage calculation.

[0223] Since fatigue damage is considered to occur under cyclic loading, calculating the fatigue damage of a component first requires statistically analyzing the load cycles it experiences. In reality, the load history of a component is generally complex and lacks significant load cycles, necessitating statistical methods to decompose the complex loads into multiple sets of cyclic loads. This paper selects the rainflow counting method, a widely used cyclic load counting method, to process the load spectrum obtained from dynamic simulations and stress analyses, such as... Figure 14 As shown.

[0224] After processing the load spectrum using the rainflow counting method, multiple sets of load half-cycles and load cycles can be obtained. These load cycles are mostly asymmetric load cycles. However, material fatigue testing is typically a stress-cycle life test with symmetric cyclic loading; therefore, it is necessary to convert these asymmetric cyclic loads into equivalent symmetric cyclic loads. Using the Goodman mean stress correction formula, asymmetric stress cycles can be converted into symmetric cyclic stress cycles:

[0225]

[0226]

[0227] Finally, each type of symmetrical cyclic stress is substituted into the stress-cycle life curve with cyclic characteristic parameter r = -1, such as... Figure 15 As shown, the cycle life limit N corresponding to each cycle can be obtained. i .

[0228] Finally, the total fatigue damage of the gear and housing was calculated using the Minner linear fatigue damage criterion.

[0229]

[0230]

[0231] Meshing torque fluctuation

[0232] Fluctuations in the meshing torque of the output shaft gear lead to fluctuations in the output torque of the transmission system. Structural changes in the gear body affect the magnitude of these fluctuations. The gear meshing torque fluctuation coefficient can characterize the stability of the transmitted torque in the transmission system, thus evaluating the impact of structural changes in the gear body on the meshing torque fluctuation. Fluctuation coefficient e t The following formula can be used to calculate:

[0233]

[0234] Where T max For the maximum torque, T min For minimum torque, T nom This is the nominal torque.

[0235] Maximum displacement of output shaft vibration

[0236] The vibration displacement of the output shaft, i.e., the large gear shaft, can be obtained by using the corresponding condensed modal vector matrix of the large gear shaft and the vibration displacement in the modal coordinate system obtained from simulation.

[0237]

[0238] Maximum normal vibration velocity on the surface of the box

[0239] The noise generated by the enclosure vibration is mainly determined by the magnitude of the normal vibration velocity on the enclosure surface. To limit the noise generated by the enclosure vibration, it is necessary to limit the maximum normal vibration velocity on the enclosure surface. The normal vibration velocity on the enclosure surface can be obtained from the corresponding enclosure condensed mode vector matrix and the vibration velocity in the modal coordinate system obtained from simulation:

[0240]

Claims

1. A multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model, the key of which includes the following steps: S1: Establish the meshing force solution model The high-speed gear is sliced ​​along the tooth width direction. By calculating the instantaneous contact line length of the meshing teeth, the position of the slice element on the contact line is determined. Two frustums are used to simulate the instantaneous contact state of the two gears, and the curvature radius of the slice element is derived. Thus, the position vector of the slice element is obtained. Combined with the meshing stiffness per unit length of the contact line and the meshing contact line length, the meshing force and meshing torque are calculated. Then, by summing them, the dynamic meshing force and meshing torque of the high-speed gear system can be obtained. S2: Establishing a finite element condensation model The gear dynamics equations are decoupled and then converted into state equations. A three-dimensional model of the large and small gears is established. The gear teeth are removed from the root circle, and the gears are divided on the split surface according to the tooth cross-section. Concentrated nodes are then established at the split surface and the bearing. In order to simultaneously reflect the rigid rotation and flexible deformation of the gear body, the actual motion of the gear body is equivalent to a combination of gear body deformation and rigid rotation. The rotational motion of the z-axis of the finite element model is fixed at the corresponding concentrated nodes of the small and large gears to obtain the finite element condensed model. Then, the driving force and load of each gear are applied to their respective moments of inertia to obtain the rigid rotational motion of the gear. In addition, for the rigid rotational motion, the effects of inertial force, centrifugal force and Coriolis force need to be considered to establish the rigid rotational model of the gear. At the same time, fixed constraints are applied to the bottom of the housing, and concentrated nodes are established at the bearing hole support to obtain the finite element condensed model of the housing. S3: Couple the various models to obtain a sliced ​​coupled dynamic model of the high-speed thin-walled gear transmission system. The models need to be coupled together through relationships such as force and displacement. The meshing force and torque are calculated in the stationary coordinate system OXYZ, while the coordinate system of the finite element condensation model is the rotating coordinate system oxyz, which follows the rotation of the gear's z-axis. Therefore, the displacements obtained from the finite element condensation model cannot be directly used to calculate the meshing force and torque, and the meshing force obtained from the stationary coordinate system cannot be directly applied to the finite element condensation model. A process is needed to couple the various models: 1) Transform the meshing force and meshing torque from the stationary coordinate system to the rotating coordinate system, and transform the bearing support reaction force from the rotating coordinate system to the stationary coordinate system; 2) Determine the meshing teeth by the current rotational displacement of the gear along the z-axis; 3) The converted meshing force and meshing torque are applied to the meshing tooth concentration nodes of the gear finite element condensation model, the bearing force is applied to the bearing concentration nodes of the gear finite element condensation model, and the converted bearing support reaction force is applied to the bearing concentration nodes of the housing finite element condensation model. 4) Transform the displacement and velocity of the meshing tooth concentrated nodes obtained from the gear finite element model from the rotating coordinate system to the stationary coordinate system, and transform the displacement and velocity of the bearing concentrated nodes obtained from the box finite element model from the stationary coordinate system to the rotating coordinate system. S4: Lightweight optimization design for high-speed gears Lightweight gear design is achieved by modifying the gear body and housing structure. The dimensional parameters of the housing and gear structure are selected as optimization parameters, and corresponding parametric models are established. In each optimization iteration, the optimization algorithm assigns values ​​to various optimization parameters. The program automatically generates a 3D model and a finite element model according to the given parameters, performs static and modal analyses, and obtains static strength and finite element condensation model data, respectively. Then, the condensation model and the lumped parameter model are coupled for hybrid dynamic simulation to analyze and calculate various dynamic loads, vibration displacements, and vibration velocities of the gear and housing. The dynamic load data, combined with the static strength analysis results, is processed into a load spectrum to analyze fatigue life. Finally, it is determined whether the obtained static strength, fatigue life and other constraints meet the design requirements; the optimization parameters that finally converge to the global optimum are taken as the final design scheme.

2. The multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model according to claim 1, characterized in that, In step S1, the meshing force solution model is established as follows: Derive the element M of gears 1 and 2. j The position vector can be represented as: The normal unit vector of the contact line element Mj of gears 1 and 2 is obtained by the following formula: n g1 =[cosβ b sinα t ,cosβ b cosα t ,sinβ b ] n g2 =-[cosβ b sinα t ,cosβ b cosα t ,sinβ b ] This unit vector is the unit normal vector of the tooth surface; M j The normal deformation is derived as follows: Where R g1 and Ω g1 These are the translational and angular displacement vectors of gear 1, respectively; R g2 and Ω g2 These are the translational and angular displacement vectors of gear 2, respectively; e j It is M j Tooth profile error at the location; R g1 =[X g1 ,Y g1 Z g1 ]; R g2 =[X g2 ,Y g2 Z g2 ]and Considering tooth flank clearance, M j The normal compressive deformation at the point is expressed as: Where b k It is the tooth flank clearance; Therefore, the meshing force and torque of the i-th meshing tooth pair, i.e., the i-th contact line, are expressed as: in, and These are the force and torque vectors for the i-th meshing tooth pair on gears 1 and 2, respectively, including three forces and three torques for each meshing tooth pair of each gear in the x, y, and z axes; k e It is the meshing stiffness of a unit, which is equal to the meshing stiffness of the unit contact line length multiplied by the unit contact line length. The total meshing force and meshing torque on each gear are obtained by the following formula: in, and These are the forces and torques acting on gears 1 and 2, with each gear having three forces and three torques in the x, y, and z directions.

3. The multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model according to claim 1, characterized in that: In step S2, the process of establishing the finite element condensation model of the gear body is as follows: A 3D model of the large and small gears is created. The gear teeth are cut off from the root circle and divided on the dividing surface according to the tooth cross-section. Then, a concentrated node is created at the dividing surface and the bearing. A script is written to automate the process from generating the 3D model to exporting the condensed model.

4. A multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model according to claim 1 or 3, characterized in that, In step S2, during the establishment of the finite element condensation model of the gear body, it is necessary to fix the rotational motion of the z-axis of the finite element model at the corresponding concentrated nodes of the small gear and the large gear.

5. The multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model according to claim 1, characterized in that, In step S2, the process of establishing the finite element condensation model of the box is as follows: Four centralized nodes are established at the bearing mounting holes inside the four end covers of the housing to obtain the displacement and velocity at the bearing holes.

6. The multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model according to claim 1, characterized in that, In step S2, during the establishment of the finite element condensation model of the box, the box is rigidly connected to the ground, and a fixed constraint needs to be applied to the bottom of the box.

7. The multi-parameter lightweight method based on a high-speed gear flexible hybrid dynamics model according to claim 1, characterized in that, In step S3, the meshing force and meshing torque need to be transformed into coordinates and then loaded onto the finite element condensation model to complete the coupling between the meshing force solution model and the finite element condensation model.

8. In the multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model according to claim 1, in step S3, when coupling the model, it is necessary to determine the sequence number of the instantaneous meshing teeth by the coordinate changes of force and displacement.

9. In the multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model according to claim 1, in step S3, when coupling the model, the displacement and velocity of the meshing tooth concentrated nodes obtained from the gear finite element model are transformed from the rotating coordinate system to the stationary coordinate system, and the displacement and velocity of the bearing concentrated nodes obtained from the housing finite element model are transformed from the stationary coordinate system to the rotating coordinate system.

10. The multi-parameter lightweighting method based on a high-speed gear flexible hybrid dynamics model according to claim 1, further comprising, in step S4, before determining the optimized structural parameters: By performing parameter sensitivity analysis on structural parameters, structural parameters that have little impact on the optimization objective can be effectively removed, saving computational resources, improving optimization efficiency, and reducing optimization time.

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