Herringbone gear planetary gear train inherent characteristic analysis method considering gear ring flexibility

Abstract

The invention relates to the technical field of mechanical engineering, discloses a herringbone gear planetary gear train inherent characteristic analysis method considering gear ring flexibility, and aims to solve the problem that in the prior art, flexible structure characteristics of an inner gear ring are neglected, so that an analysis result is inaccurate during herringbone gear planetary gear train inherent characteristic analysis. When the inner gear ring is modeled, the inner gear ring is discretized into a plurality of sections of uniformly bent gear ring micro-section units, and the motion differential equation of the inner gear ring is constructed through modeling, so that the flexibility characteristic of the inner gear ring is fully considered when the motion differential equation set of the herringbone gear planetary transmission system is constructed; and a more accurate data basis is provided for subsequent solidity analysis. In addition, the structural characteristics of the herringbone gear are considered, the herringbone gear is divided into the left side and the right side for modeling operation, the accuracy of data needed by calculation is improved, and more practical and more accurate inherent characteristic analysis of the herringbone gear planetary transmission system is achieved.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering technology, and in particular to a method for analyzing the inherent characteristics of herringbone gear planetary gear trains that takes into account the flexibility of the gear ring. Background Technology

[0002] Herringbone planetary gear transmission systems possess numerous advantages, including high overlap ratio, strong load-bearing capacity, compact structure, large transmission ratio, and high efficiency. Therefore, they are widely used in transmission devices in the high-speed, heavy-load applications of aviation and marine industries. To ensure the reliability and stability of herringbone planetary gear transmission systems, analyzing the inherent characteristics of the system is crucial.

[0003] In current technology, the lumped mass method is often used to model herringbone planetary gear transmission systems and then perform inherent characteristic analysis. However, the internal gear ring, as a thin-walled component in the herringbone planetary gear transmission system, has the characteristics of high flexibility and large deformation. It is a key component for the generation and transmission of vibration in the entire system. However, due to its flexibility, it will affect the results when performing inherent characteristic analysis.

[0004] Therefore, it is evident that how to combine the flexible structural features of the internal gear ring to achieve a more realistic and accurate analysis of the inherent characteristics of the herringbone gear planetary transmission system is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that the current technology ignores the flexible structural characteristics of the internal gear ring, resulting in inaccurate analysis results when performing inherent characteristic analysis of herringbone gear planetary transmission systems. Therefore, this invention provides a method for analyzing the inherent characteristics of herringbone gear planetary transmission systems that considers the flexibility of the gear ring, in order to combine the flexible structural characteristics of the internal gear ring and achieve a more realistic and accurate analysis of the inherent characteristics of herringbone gear planetary transmission systems.

[0006] To address the aforementioned technical problems, this invention provides a method for analyzing the inherent characteristics of herringbone gear planetary gear trains that considers the flexibility of the gear ring, including:

[0007] Based on the structural characteristics of the internal gear ring, the internal gear ring is discretized into several uniformly curved gear ring micro-segment units and the dynamics of the internal gear ring are modeled. The dynamics of other components in the herringbone gear planetary transmission system are also modeled.

[0008] Based on dynamic modeling, the stiffness matrix, mass matrix, and damping matrix of each component are determined, and the corresponding differential equations of motion are constructed.

[0009] Based on the relative motion relationships between the components, construct the relative displacement relationships between any two components;

[0010] Based on the relative displacement relationship and the motion differential equations of each component, a system dynamic differential equation set is constructed, and the natural frequency and mode shape of the herringbone gear planetary transmission system are obtained from the system dynamic differential equation set.

[0011] Preferably, the other components of the herringbone gear planetary transmission system include: a planet carrier, a sun gear, and planet gears; both the sun gear and the planet gears are herringbone gears.

[0012] Based on the structural characteristics of the internal gear ring, the internal gear ring is discretized into several uniformly curved micro-segment units, and dynamic modeling of the internal gear ring is performed. Dynamic modeling of other components in the herringbone gear planetary transmission system includes:

[0013] Based on the meshing relationship between each herringbone gear and the internal gear ring, the two gears in each herringbone gear are divided into a left gear and a right gear, with opposite helix angles. The left gear and the right gear are connected by beam elements, and the lumped mass method is applied to the left gear and the right gear for dynamic modeling.

[0014] The lumped mass method was used to perform dynamic modeling of the planetary carrier.

[0015] The internal gear ring is discretized into a ring composed of several uniformly curved Timoshenko beam elements for dynamic modeling. Each Timoshenko beam element constituting the internal gear ring contains two nodes, and each node contains three translational degrees of freedom and one rotational degree of freedom.

[0016] Preferably, the equations of motion for the internal gear ring include:

[0017] Determine the nodal coordinates of each Timoshenko beam element of the internal gear ring in the local coordinate system;

[0018] The stiffness matrix and mass matrix are determined based on the horizontal and torsional displacements of the nodes in the local coordinate system.

[0019] The stiffness matrix and mass matrix in the local coordinate system are transformed into matrices in the coordinate system of the internal gear ring, and then into stiffness matrix and mass matrix in the overall coordinate system of the herringbone gear planetary transmission system.

[0020] The damping matrix is ​​determined based on the stiffness matrix and the mass matrix;

[0021] The kinematic differential equations of the internal gear ring are constructed based on the stiffness matrix, mass matrix, and damping matrix.

[0022] Preferably, the step of constructing the relative displacement relationship between any two components based on the relative motion relationship between each component includes:

[0023] By projecting the displacements of the sun gear and planet gears toward the direction of the meshing line, the relative displacements between the sun gear and planet gears can be obtained.

[0024] Projecting the displacements of the internal gear ring and planetary gears towards the direction of the meshing line yields the relative displacement between the internal gear ring and the planetary gears.

[0025] The relative displacement of the planet carrier with respect to the planet gears is obtained by projecting the planet gears onto the planet gear support direction.

[0026] Preferably, obtaining the natural frequencies and mode shapes of the herringbone gear planetary transmission system based on the system dynamics differential equations includes:

[0027] The stiffness matrix and mass matrix are determined based on the system dynamics differential equations, which are then used to determine the characteristic equations required to solve the inherent characteristics of the herringbone gear planetary transmission system.

[0028] Solve the characteristic equation to obtain the natural frequencies and mode shapes in the inherent properties.

[0029] Preferably, the stiffness matrix of the internal gear ring in the local coordinate system is:

[0030] ;

[0031] The mass matrix of the internal gear ring in the local coordinate system is:

[0032] ;

[0033] The elastic modulus of the material. For the material shear elasticity model, Let be the cross-sectional area of ​​the element. The length of a beam is a unit. In order to be in Moment of inertia of the cross section in the coordinate plane As a correction factor, For material density, It is the polar moment of inertia. Here is the stiffness matrix of the internal gear ring in the local coordinate system. This is the mass matrix of the internal gear ring in the local coordinate system.

[0034] Preferably, the kinematic differential equation of the internal gear ring is:

[0035] ;

[0036] The mass matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The damping matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The stiffness matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. Let be the generalized coordinate vector of the internal gear ring. for The first partial derivative with respect to time, for Second-order partial derivative with respect to time.

[0037] Preferred,

[0038] The relationship between the local coordinate system and the global coordinate system of the herringbone gear planetary transmission system is as follows:

[0039]

[0040] or ;

[0041] In local coordinate system Global coordinate system of shaft and herringbone gear planetary transmission system The included angle, Let be the inner diameter of the internal gear ring. Let be the distance from the midpoint of the left gear to the midpoint of the right gear, and let be the local coordinate system. The global coordinate system of the herringbone gear planetary transmission system is .

[0042] Preferably, the stiffness matrix and mass matrix after transforming from the local coordinate system to the global coordinate system of the herringbone gear planetary transmission system are:

[0043] ;

[0044] in, , ,

[0045]

[0046] or .

[0047] Preferably, the system dynamics differential equations include:

[0048] ;

[0049] in, The mass matrix of a herringbone gear planetary transmission system The stiffness matrix of a herringbone gear planetary transmission system The first of the herringbone gear planetary transmission system First natural frequency, The first of the herringbone gear planetary transmission system The mode shape corresponding to the first natural frequency.

[0050] This invention provides a method for analyzing the inherent characteristics of herringbone gear planetary transmission systems that considers the flexibility of the gear ring. Compared to current technologies that neglect the flexible structural characteristics of the internal gear ring, leading to inaccurate analysis results, this invention discretizes the internal gear ring into several uniformly curved micro-segments during modeling. By constructing the motion differential equations of the internal gear ring through modeling, the flexibility of the internal gear ring is fully considered when assembling the motion differential equations of the herringbone gear planetary transmission system, providing a more accurate data foundation for subsequent fixed-structure analysis. Furthermore, this invention also considers the structural characteristics of the herringbone gear, dividing it into left and right sides for modeling and calculation, improving the accuracy of the calculated data and achieving a more realistic and accurate analysis of the inherent characteristics of the herringbone gear planetary transmission system. Attached Figure Description

[0051] To more clearly illustrate the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart illustrating an inherent characteristic analysis method for a herringbone gear planetary gear train considering the flexibility of the gear ring, provided in an embodiment of the present invention;

[0053] Figure 2 A structural diagram of an NGW planetary gear reducer system provided in an embodiment of the present invention;

[0054] Figure 3 A schematic diagram of a discrete flexible internal gear ring provided in an embodiment of the present invention;

[0055] Figure 4 A schematic diagram of a beam element model provided in an embodiment of the present invention;

[0056] Figure 5 This is a schematic diagram of the discretization process of an internal gear ring provided in an embodiment of the present invention;

[0057] Figure 6 A schematic diagram showing the relative positional relationship between the sun gear and planet gears in an engaged state, provided for an embodiment of the present invention;

[0058] Figure 7 This is a schematic diagram showing the relative positional relationship between the internal gear ring and the planetary gear in a meshing state, provided for an embodiment of the present invention.

[0059] Figure 8A schematic diagram showing the relative positional relationship between the planet carrier and the planet gears in an engaged state, provided for an embodiment of the present invention;

[0060] Figure 9 This is a simplified schematic diagram of the sun gear and planetary gears in a dynamic model provided for an embodiment of the present invention. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the protection scope of the present invention.

[0062] The core of this invention is to provide a method for analyzing the inherent characteristics of herringbone gear planetary transmission systems that takes into account the flexibility of the gear ring. This method combines the flexible structural features of the internal gear ring to achieve a more realistic and accurate analysis of the inherent characteristics of the herringbone gear planetary transmission system.

[0063] To enable those skilled in the art to better understand the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0064] Figure 1 A flowchart illustrating an inherent characteristic analysis method for a herringbone gear planetary gear train considering the flexibility of the gear ring, as provided in this embodiment of the invention, is shown below. Figure 1 As shown, the method includes:

[0065] S10: Based on the structural characteristics of the internal gear ring, the internal gear ring is discretized into several uniformly curved gear ring micro-segment units and the dynamics model of the internal gear ring is performed. The dynamics model of other components in the herringbone gear planetary transmission system is also performed.

[0066] S11: Based on dynamic modeling, confirm the stiffness matrix, mass matrix, and damping matrix of each component, and construct the corresponding differential equations of motion;

[0067] S12: Based on the relative motion relationships between the components, construct the relative displacement relationships between any two components;

[0068] S13: Construct a system of dynamic differential equations based on the relative displacement relationship and the motion differential equations of each component, and obtain the natural frequency and mode shape of the herringbone gear planetary transmission system based on the system of dynamic differential equations.

[0069] The inherent characteristic analysis method for herringbone gear planetary transmission systems considering gear ring flexibility provided by this invention is used to analyze the inherent characteristics of herringbone gear planetary transmission systems, specifically by calculating the natural frequencies and mode shapes of the herringbone gear planetary transmission system. In specific implementations, the execution entity of this method can be a herringbone gear planetary transmission system inherent characteristic analysis device. This device may specifically include a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the herringbone gear planetary transmission system inherent characteristic analysis method considering gear ring flexibility provided in the above embodiments. In some embodiments, the herringbone gear planetary transmission system inherent characteristic analysis device may also include a display, touch screen, or other human-computer interaction device. In specific implementations, the herringbone gear planetary transmission system inherent characteristic analysis device provided in this embodiment may include, but is not limited to, smartphones, tablets, laptops, or desktop computers.

[0070] Of course, it is understood that if the methods in the above embodiments are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the technical solution of the present invention can be embodied in the form of a software product, which is stored in a storage medium and executes all or part of the steps of the methods described in the various embodiments of the present invention.

[0071] In step S10, the various components of the herringbone gear planetary transmission system are first modeled. A herringbone gear planetary transmission system typically includes four parts: a sun gear, planet gears, an internal gear ring, and a planet carrier. Therefore, these four parts can be modeled during the modeling process. Of course, in some specific embodiments, depending on the structure of the herringbone gear planetary transmission system, it can be divided into more or fewer components. This invention fully considers the flexibility of the internal gear ring, discretizing it into several uniformly curved micro-segment units based on its structural characteristics, and then performing dynamic modeling of the internal gear ring. This invention provides a specific modeling method, using an NGW planetary gear reducer as an example for dynamic modeling. Figure 2 This is a structural diagram of an NGW planetary gear reducer system provided in an embodiment of the present invention. , and The numbers represent the number of teeth on the sun gear, planet gears, and internal gear ring, respectively, and H represents the planet carrier. The main components of the system include the sun gear, planet gears, internal gear ring, and planet carrier, with power input through the sun gear and output through the planet carrier. Then, in step S11, the stiffness matrix, mass matrix, and damping matrix of each component can be determined based on dynamic modeling, and the corresponding differential equations of motion can be constructed. Because the internal gear ring is discretized into multiple elements in this invention, the stiffness matrix and mass matrix of each element can be obtained in detail, thus providing an accurate data foundation for subsequent calculations.

[0072] Furthermore, this invention also considers the influence of the structural characteristics of the herringbone gear model in the system on the analysis results, and constructs a more detailed model of the herringbone gear model. Taking the NGW planetary gear reducer system as an example, in the herringbone gear planetary transmission system, both the sun gear and planet gears adopt a herringbone gear model, while the internal meshing is performed by two internal gear rings with the same parameters but opposite helix directions meshing with the planet gears. Therefore, when performing dynamic modeling of the sun gear and planet gears with the herringbone gear structure, the following method can be adopted: divide the herringbone gear into a left gear and a right gear, with opposite helix angles, and connect them using beam elements. Considering the interaction between the left and right gears, each gear is considered to have four degrees of freedom, namely along... Directional movement and rotation Torsional vibration of the shaft. Accordingly, each Timoshenko beam element constituting the internal gear ring contains two nodes, each node containing three translational degrees of freedom and one rotational degree of freedom.

[0073] It is understandable that in a herringbone planetary transmission system, there are two internal gear rings that mesh internally with the left and right sides of the planet gears, respectively. Therefore, to account for the flexibility of the gear rings, both the left and right internal gear rings need to be discretized. The herringbone gear includes a sun gear and planet gears. In this invention, based on the external meshing between the sun gear and planet gears, and the internal meshing between the planet gears and the internal gear rings, the herringbone gear is divided into a left gear and a right gear. The helix angles of the left and right gears are opposite, and the left and right gears are connected by beam elements. This embodiment refines the structure of the herringbone gear, modeling each refined structure separately. Compared to modeling the herringbone gear as a whole, this embodiment applies the lumped mass method to the dynamic modeling of the left and right gears separately, providing more accurate data when calculating the stiffness and mass matrices. The dynamic modeling of the planet carrier is also performed using the lumped mass method, accounting for two translational degrees of freedom. , and a torsional degree of freedom ( , indicating the planetary frame.

[0074] Figure 3This is a schematic diagram of a discretized flexible internal gear ring provided in an embodiment of the present invention. Because in the herringbone planetary transmission system that incorporates the flexibility of the gear ring, when modeling and analyzing the dynamics of the sun gear and planet gears, in addition to the original two translational degrees of freedom and one rotational degree of freedom, the interaction between the left and right gears is considered, introducing an axial degree of freedom. Therefore, when discretizing the flexible internal gear ring, each beam element constituting the internal gear ring contains two nodes, and each node includes three translational degrees of freedom (…). (direction) and one rotational degree of freedom (around) Therefore, when constructing the motion differential equations of the internal gear ring, it is first necessary to determine the nodal coordinates of each Timoshenko beam element of the internal gear ring in the local coordinate system. Then, the stiffness matrix and mass matrix are determined based on the horizontal and torsional displacements of the nodes in the local coordinate system. In order to realize the overall construction of the internal gear ring and adapt the construction of the differential equations of the entire system, the stiffness matrix and mass matrix in the local coordinate system need to be transformed into matrices in the coordinate system of the internal gear ring, and then into the stiffness matrix and mass matrix in the overall coordinate system of the herringbone gear planetary transmission system. The damping matrix is ​​determined based on the stiffness matrix and mass matrix. The motion differential equations of the internal gear ring are constructed based on the stiffness matrix, mass matrix, and damping matrix.

[0075] Figure 4 This is a schematic diagram of a beam element model provided in an embodiment of the present invention. In the local coordinate system of the internal gear ring, the nodal coordinates are represented as follows:

[0076] ;

[0077] in These represent the nodes of the Timoshenko beam element. Displacement in the local coordinate system It is a node Torsional displacement in the local coordinate system. In this invention, the local coordinate system refers to the coordinate system for each beam element assembly. Based on relevant knowledge of elasticity mechanics, the stiffness matrix and mass matrix of the beam elements divided into gear rings in their respective local coordinate systems can be obtained, as well as the stiffness matrix of the internal gear ring in the local coordinate system. for:

[0078] ;

[0079] Internal gear mass matrix in local coordinate system for:

[0080] ;

[0081] In the formula, The elastic modulus of the material. For the material shear elasticity model, Let be the cross-sectional area of ​​the element. The length of a beam is a unit. In order to be in Moment of inertia of the cross section in the coordinate plane As a correction factor, For material density, It is the polar moment of inertia.

[0082] Since there are two meshing internal gear rings in the system, and the local coordinate systems of each beam element are in different directions, it is necessary to transform the stiffness matrix and mass matrix of the beam element from the local coordinate system to the gear ring coordinate system of the left and right gear rings, and finally to the global coordinate system of the entire planetary system. Figure 5 This is a schematic diagram of the discretization process of an internal gear ring provided in an embodiment of the present invention. The coordinate system is transformed from coordinate systems 1 and 2 under the local coordinate system to coordinate systems 3 and 4 under the internal gear ring coordinate system, and finally to coordinate system 5 under the global coordinate system. Taking one side of the gear ring as an example, the transformation matrix is ​​derived. The transformation relationship between the local coordinate system and the global coordinate system of the herringbone gear planetary transmission system is as follows:

[0083] ;

[0084] The other side is:

[0085] ;

[0086] In local coordinate system Axis and global coordinate system The included angle Let be the inner diameter of the internal gear ring. Let be the distance from the midpoint of the left gear to the midpoint of the right gear, and let be the local coordinate system. The coordinates of the global coordinate system are .

[0087] Furthermore, let ;

[0088] Then, the nodal displacements of the beam element in the local coordinate system can be expressed as the nodal displacements in the global coordinate system as follows:

[0089] ;

[0090] in , .

[0091] The transformation matrix between the local coordinate system of the other gear ring and the global coordinate system of the herringbone planetary system can be obtained similarly:

[0092] .

[0093] The nodal displacements of the beam element in the local coordinate system of the side gear ring, and their corresponding nodal displacements in the global coordinate system of the planetary system, can be expressed as:

[0094] ;

[0095] in , .

[0096] For the two internal gear rings, multiply the equation by... The stiffness matrix and mass matrix, transformed from the local coordinate system to the global coordinate system of the herringbone gear planetary transmission system, are thus obtained as follows:

[0097] .

[0098] The commonly used formula for calculating the damping matrix of a gear ring element in engineering is as follows: ,in, This is the mass proportion factor in Rayleigh damping. This represents the stiffness scaling factor in Rayleigh damping. After completing the coordinate transformation of the stiffness and mass matrices, the damping matrix can be obtained. Once the mass, stiffness, and damping matrices of the gear ring are obtained, the differential equations of motion for the gear ring can be derived:

[0099] ;

[0100] in, The mass matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The damping matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The stiffness matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. Let be the generalized coordinate vector of the internal gear ring. for The first partial derivative with respect to time, for Second-order partial derivative with respect to time.

[0101] Then, in steps S12 and S13, the dynamic differential equations of the entire system can be derived based on the transmission relationship between the components, and then the natural frequency and mode shape of the herringbone gear planetary transmission system can be obtained.

[0102] The inherent characteristic analysis method for herringbone gear planetary transmission systems that considers the flexibility of the gear ring provided in this invention addresses the problem of inaccurate analysis results in current technologies that neglect the flexible structural characteristics of the internal gear ring, leading to inaccurate results when analyzing the inherent characteristics of herringbone gear planetary transmission systems. This invention discretizes the internal gear ring into several uniformly curved micro-segments during modeling, constructs the motion differential equations of the internal gear ring through modeling, and fully considers the flexibility of the internal gear ring when assembling the motion differential equations of the herringbone gear planetary transmission system, providing a more accurate data foundation for subsequent inherent characteristic analysis. Furthermore, this invention also considers the structural characteristics of the herringbone gear, dividing it into left and right sides for modeling and calculation, improving the accuracy of the calculated data and achieving a more realistic and accurate analysis of the inherent characteristics of the herringbone gear planetary transmission system.

[0103] Based on the above embodiments, this embodiment provides a specific calculation method for the relative motion between components. First, the relative motion between components includes the relative motion between the sun gear and planet gears, the planet gears and the internal gear ring, and the planet gears and the planet carrier. The relative displacement between the sun gear and planet gears is obtained by projecting the displacements of the sun gear and planet gears towards the direction of the meshing line; the relative displacement between the internal gear ring and planet gears is obtained by projecting the displacements of the internal gear ring and planet gears towards the direction of the meshing line; and the relative displacement of the planet carrier relative to the planet gears is obtained based on the projection along the planet gear support direction.

[0104] Figure 6 This is a schematic diagram illustrating the relative positional relationship between the sun gear and planet gears in a meshing state, provided in an embodiment of the present invention. The displacement caused by the compression deformation of the spring that provides the equivalent meshing stiffness of the sun gear and planet gears is taken as the positive direction. Projecting the displacements of the sun gear and planet gears onto the meshing line (the tangent to the base circles of the two gears, hereinafter the same) yields the relative displacement between the sun gear and planet gears. Taking the external meshing of the left gear as an example, the lateral linear displacement of the sun gear's center of mass... , and The projections toward the meshing plane are respectively , and The projection of its torsional linear displacement onto the meshing plane is The lateral linear displacement of the planetary gear's center of mass , and The projections toward the meshing plane are respectively , and Its torsional linear displacement projected onto the meshing direction is .

[0105] Because the external meshing relationship between the sun gear and the planetary gears of a herringbone gear involves helical gear meshing on one side, the angle between the direction of the left helical gear meshing line and the tangent direction within the meshing plane is defined as follows: Then, the angle between the direction of the meshing line of the right helical gear and the tangent direction in the meshing plane is... Therefore, the projections of the relative displacements of the left and right sides of the sun gear and planet gear along their respective meshing lines are:

[0106] .

[0107] Figure 7 This is a schematic diagram illustrating the relative positional relationship between the internal gear ring and the planetary gears in a meshing state, provided in an embodiment of the present invention. The displacement of the spring that causes the equivalent meshing stiffness of the internal gear ring and the planetary gears to compress is taken as the positive direction. Projecting the displacements of the internal gear ring and the planetary gears towards the direction of the meshing line yields the relative displacement between them.

[0108] Taking the left gear as an example, the lateral linear displacement of the center of mass of the internal gear ring... , and The projections toward the meshing plane are respectively , and The projection of its torsional linear displacement onto the meshing plane is , and Its torsional linear displacement projected onto the meshing direction is ;

[0109] Because the internal meshing of the system occurs through the herringbone planetary gears meshing with two independent internal gear rings, the internal meshing on one side can be considered as helical gear meshing. The angle between the direction of the left helical gear's meshing line and the tangent direction within the meshing plane is defined as follows: Then, the angle between the direction of the meshing line of the right helical gear and the tangent direction in the meshing plane is... Therefore, the projection of the relative displacement of the planetary gears along their respective meshing lines when they mesh with the two internal gear rings is:

[0110] .

[0111] Figure 8 This is a schematic diagram illustrating the relative positional relationship between the planet carrier and planet gears in an engaged state, as provided in an embodiment of the present invention. The displacement of the spring causing compressive deformation of the equivalent planet gear support stiffness is taken as the positive direction. The relative displacement of the planet carrier relative to the planet gears needs to be projected onto two support directions, respectively using... and The relative displacement between the two support directions in the local moving coordinate system of the planetary gear can be expressed by the following two formulas:

[0112] ;

[0113] in, ; ,in The end face pressure angle of the gear teeth; For the first The installation position angles of each planetary gear. For a planetary transmission system with evenly distributed planetary gears, , , This represents the number of planetary gears. In a herringbone planetary gear system, the herringbone gears are divided into left and right helical gears, which respectively realize the meshing relationship on the left and right sides of the system. Therefore, when establishing the dynamic differential equation of the herringbone planetary gear system, the dynamic equations are divided into left and right side equations, where... Represents the left side. Representing the right side. In the main components of the herringbone planetary transmission system, both the sun gear and planet gears have herringbone tooth structures. Therefore, when modeling the dynamics of the herringbone planetary transmission system, considering the complexity and special characteristics of the herringbone tooth structure, the lumped mass method is applied to model the left and right gears of the sun gear and planet gear respectively. To account for the interaction between the left and right teeth of the herringbone gear, Timoshenko beam elements are used to connect the left and right parts of the herringbone gear, considering four degrees of freedom at each lumped mass point, i.e. degrees of freedom of movement and rotation Torsional degree of freedom of the shaft. Figure 9 This is a simplified schematic diagram of the sun gear and planet gears in the dynamic model provided in an embodiment of the present invention. The left and right sun gears and the left and right planet gears are connected by beam elements.

[0114] When performing dynamic modeling of the herringbone gear planetary transmission system using the lumped mass method, two sets of moving coordinate systems are used. One set is the global coordinate system used by the sun gear and the internal gear ring, with the center of the sun gear as the origin. The other set of coordinate systems is the follower coordinate system used by the planet gears, which rotates with the planet carrier and has its rotation center as the origin.

[0115] ( These represent the sun wheel and the three planetary wheels, respectively. (representing the left and right gears of the herringbone gear respectively) This indicates that due to system vibration, the center of mass of gear-like components moves along... direction, direction and The linear displacement in the direction is measured in the system coordinate system for the central gear and in the local moving coordinate system for the planetary gears. This represents the angular displacement of all components due to system vibration. Since all herringbone gears are divided into left and right helical gears, each herringbone gear has 8 degrees of freedom. Components with these degrees of freedom include the sun gear and three planetary gears, totaling 8 concentrated masses. Each concentrated mass has three translational degrees of freedom and one rotational degree of freedom. Therefore, all herringbone gears in the system have a total of 32 degrees of freedom. Based on the transmission relationships between each component in the system and Newton's second law, the differential equations of motion for each component in the herringbone planetary transmission system are written, ultimately forming the system of dynamic differential equations for the entire system.

[0116] The differential equation of motion for the sun gear is:

[0117] ;

[0118] The differential equation of motion for the planetary gears is:

[0119] ;

[0120] The kinematic differential equation of the internal gear ring is:

[0121] ;

[0122] The differential equation of motion for the planetary carrier is:

[0123] ;

[0124] In the formula, ( Let be the mass of the single-sided herringbone toothed sun gear, the single-sided herringbone toothed planet gears, the internal gear ring, and the planet carrier in the herringbone toothed planetary system. ( In a herringbone-tooth planetary system, the single-sided herringbone-tooth sun gear, the single-sided herringbone-tooth planet gear, the internal gear ring, and the planet carrier each revolve around... Moment of inertia of the shaft; For the sun wheel and the first The first planetary wheel, the first The normal combined meshing stiffness of the planetary gear and the internal gear ring pair, the time-varying meshing stiffness can be replaced by the average meshing stiffness within one meshing cycle; The Sun Wheel and the First The first planetary wheel, the first Each planetary gear meshes with the internal gear ring for damping.

[0125] Finally, a system of differential equations for system dynamics is constructed based on the relative displacement relationships and the motion differential equations of each component. The natural frequencies and mode shapes of the herringbone gear planetary transmission system are then obtained from this system of differential equations. Specifically, this invention transforms the problem of solving the inherent characteristics of the system into a problem of solving eigenvalues. Obtaining the natural frequencies and mode shapes of the herringbone gear planetary transmission system from the system of differential equations for system dynamics includes: determining the stiffness matrix and mass matrix from the system of differential equations for system dynamics to determine the characteristic equations required to solve the inherent characteristics of the herringbone gear planetary transmission system; and solving the characteristic equations to obtain the natural frequencies and mode shapes from the inherent characteristics.

[0126] The system dynamics differential equations can be expressed as:

[0127] ;

[0128] in, The mass matrix of a herringbone gear planetary transmission system The stiffness matrix of a herringbone gear planetary transmission system The first of the herringbone gear planetary transmission system First natural frequency, The first of the herringbone gear planetary transmission system The mode shape corresponding to the first natural frequency.

[0129] The foregoing has provided a detailed description of the method for analyzing the inherent characteristics of herringbone gear planetary gear trains considering the flexibility of the gear ring, as provided by this invention. The various embodiments in the specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring, characterized in that, include: Based on the structural characteristics of the internal gear ring, the internal gear ring is discretized into several uniformly curved gear ring micro-segment units and the dynamics of the internal gear ring are modeled. The dynamics of other components in the herringbone gear planetary transmission system are also modeled. Based on dynamic modeling, the stiffness matrix, mass matrix, and damping matrix of each component are determined, and the corresponding differential equations of motion are constructed. Based on the relative motion relationships between each component, the relative displacement relationships between each pair of components are constructed. Based on the relative displacement relationship and the motion differential equations of each component, a system dynamic differential equation set is constructed, and the natural frequency and mode shape of the herringbone gear planetary transmission system are obtained from the system dynamic differential equation set.

2. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 1, characterized in that, Other components in the herringbone gear planetary transmission system include: a planet carrier, a sun gear, and planet gears; both the sun gear and planet gears are herringbone gears. Based on the structural characteristics of the internal gear ring, the internal gear ring is discretized into several uniformly curved micro-segment units, and the dynamics modeling of the internal gear ring is performed. Dynamics modeling of other components in the herringbone gear planetary transmission system includes: Based on the meshing relationship between each herringbone gear and the internal gear ring, the two gears in each herringbone gear are divided into a left gear and a right gear, with opposite helix angles. The left gear and the right gear are connected by beam elements, and the lumped mass method is applied to the left gear and the right gear for dynamic modeling. The lumped mass method was used to perform dynamic modeling of the planetary carrier. The internal gear ring is discretized into a ring composed of several uniformly curved Timoshenko beam elements for dynamic modeling. Each Timoshenko beam element constituting the internal gear ring contains two nodes, and each node contains three translational degrees of freedom and one rotational degree of freedom.

3. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 2, is characterized in that... The equations of motion for the internal gear ring are as follows: Determine the nodal coordinates of each Timoshenko beam element of the internal gear ring in the local coordinate system; The stiffness matrix and mass matrix are determined based on the horizontal and torsional displacements of the nodes in the local coordinate system. The stiffness matrix and mass matrix in the local coordinate system are transformed into matrices in the coordinate system of the internal gear ring, and then into stiffness matrix and mass matrix in the overall coordinate system of the herringbone gear planetary transmission system. The damping matrix is ​​determined based on the stiffness matrix and the mass matrix; The kinematic differential equations of the internal gear ring are constructed based on the stiffness matrix, mass matrix, and damping matrix.

4. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 3, is characterized in that, The process of constructing relative displacement relationships between any two components based on the relative motion relationships between each component includes: By projecting the displacements of the sun gear and planet gears toward the direction of the meshing line, the relative displacements between the sun gear and planet gears can be obtained. Projecting the displacements of the internal gear ring and planetary gears towards the direction of the meshing line yields the relative displacement between the internal gear ring and the planetary gears. The relative displacement of the planet carrier with respect to the planet gears is obtained by projecting the planet gears onto the planet gear support direction.

5. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in any one of claims 1 to 4, characterized in that, The natural frequencies and mode shapes of the herringbone gear planetary transmission system obtained from the system dynamics differential equations include: The stiffness matrix and mass matrix are determined based on the system dynamics differential equations, which are then used to determine the characteristic equations required to solve the inherent characteristics of the herringbone gear planetary transmission system. Solve the characteristic equation to obtain the natural frequencies and mode shapes in the inherent properties.

6. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 3, is characterized in that, The stiffness matrix of the internal gear ring in the local coordinate system is: ； The mass matrix of the internal gear ring in the local coordinate system is: ； The elastic modulus of the material. For the material shear elasticity model, Let be the cross-sectional area of ​​the element. The length of the unit, In order to be in Moment of inertia of the cross section in the coordinate plane As a correction factor, For material density, It is the polar moment of inertia. Here is the stiffness matrix of the internal gear ring in the local coordinate system. This is the mass matrix of the internal gear ring in the local coordinate system.

7. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 6, characterized in that, The kinematic differential equation of the internal gear ring is: ； The mass matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The damping matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. The stiffness matrix of the internal gear ring in the global coordinate system of the herringbone gear planetary transmission system. Let be the generalized coordinate vector of the internal gear ring. for The first partial derivative with respect to time, for Second-order partial derivative with respect to time.

8. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 7, characterized in that, The relationship between the local coordinate system and the global coordinate system of the herringbone gear planetary transmission system is as follows: or ; In local coordinate system Global coordinate system of shaft and herringbone gear planetary transmission system The included angle, Let be the inner diameter of the internal gear ring. Let be the distance from the midpoint of the left gear to the midpoint of the right gear, and let be the local coordinate system. The global coordinate system of the herringbone gear planetary transmission system is .

9. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 8, characterized in that, The stiffness matrix and mass matrix after transformation from the local coordinate system to the global coordinate system of the herringbone gear planetary transmission system are: ； in, , , or .

10. The method for analyzing the inherent characteristics of a herringbone gear planetary gear train considering the flexibility of the gear ring as described in claim 5, characterized in that, The system dynamics differential equations include: ； in, The mass matrix of a herringbone gear planetary transmission system The stiffness matrix of a herringbone gear planetary transmission system The first of the herringbone gear planetary transmission system First natural frequency, The first of the herringbone gear planetary transmission system The mode shape corresponding to the first natural frequency.

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