Dynamic modeling method and system for double-internal-gearing planetary gear transmission system
By establishing a pure torsional dynamics model for a dual internal meshing planetary gear transmission system, the problem that existing modeling methods cannot describe dynamic characteristics is solved, resonance avoidance and force optimization of the system are realized, and dynamic analysis and vibration control of the transmission device are supported.
Patent Information
- Application Number
- CN202511131692.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-13
- Publication Date
- 2025-11-14
Smart Images
Figure CN120951487A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of planetary gear technology, and in particular to a dynamic modeling method and system for a dual internal meshing planetary gear transmission system. Background Technology
[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.
[0003] Planetary gear transmission systems are a crucial component of transmission systems, suitable for speed reduction in machinery used in metallurgy, mining, hoisting, and transportation. They offer advantages such as compact structure, small size, light weight, high load capacity, wide transmission power and range, low operating noise, high efficiency, and long service life. Typically, traditional NGW-type planetary gear transmission systems contain multiple planetary gears meshing with a central sun gear and an external ring gear, with each planetary gear's shaft fixed. In contrast, the double internal meshing planetary gear transmission system contains only one planetary gear, which is ring-shaped. The inner gear of the ring meshes with the central sun gear, while the outer gear meshes with the external ring gear, and its shaft is not fixed. Compared to traditional planetary gear transmission systems, the double internal meshing planetary gear transmission system has a more compact structure, higher stability, higher overlap ratio, and stronger load capacity.
[0004] However, existing dynamic modeling methods are mostly proposed for traditional planetary gear transmission systems, without considering the special characteristics of double internal meshing structures, such as the synergistic effect of double meshing pairs and more complex component motion relationships. This makes it impossible to accurately describe the dynamic characteristics of double internal meshing planetary gear transmission systems and to meet their needs for structural frequency tuning, resonance avoidance and stress optimization. Summary of the Invention
[0005] To address the shortcomings of the existing technology, this invention provides a dynamic modeling method and system for a double internal meshing planetary gear transmission system. It studies the nonlinear dynamics of the double internal meshing planetary gear transmission system, employs the lumped mass parameter method, and establishes a dynamic model and equations for the pure torsion of the system. This provides a basis for structural frequency tuning of the transmission device and avoidance of system resonance, facilitating the improvement of the stress conditions of various components in the system.
[0006] In a first aspect, the present invention provides a dynamic modeling method for a dual internal meshing planetary gear transmission system.
[0007] A dynamic modeling method for a dual internal meshing planetary gear transmission system includes: The components and transmission form of the transmission system are clearly defined. Only the vibration in the torsional direction of each component is considered. A coordinate system is constructed with the center of each component as the origin. The system generalized coordinates based on 4 degrees of freedom are defined in the coordinate system. The components include the sun gear, planet gears, planet carrier, and external gear ring. Based on the system's generalized coordinates, the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears are derived, and deformation formulas are established. Based on the deformation formula, a set of dynamic differential equations for a double internal meshing planetary gear transmission system is constructed. The dynamic excitation of the system is calculated by finite element analysis. The excitation is input into the system of equations, and the nonlinear response characteristics of the system are solved.
[0008] A further technical solution is that the system's generalized coordinates include the minute angular displacements of each component in the circumferential direction. Represented as: ; in, It is a tiny angular displacement of the sun gear in the circumferential direction. This represents the minute linear displacement of the sun gear along the line of meshing. It is a tiny angular displacement in the circumferential direction of the external gear ring. This indicates the minute displacement of the external gear ring of the planetary transmission along the line of meshing. It is a small angular displacement in the circumferential direction of the planetary carrier. This indicates a minute circumferential displacement of the planet carrier in a planetary transmission. It is a tiny angular displacement of the planetary gear in the circumferential direction. This represents the minute linear displacement of the inner ring of planetary gear p along the line of meshing. This represents the minute linear displacement of the outer ring of planetary gear p along the line of meshing. Indicates the base circle radius of each component. , These represent the sun gear, external gear ring, planet carrier, and planet gears, respectively. This indicates the internal gear ring of the planetary gear. This refers to the external gear ring of a planetary gear.
[0009] A further technical solution is provided, wherein the derivation process of the elastic deformation is as follows: Projecting the vibration displacements of the sun gear and planet gears onto the meshing line, calculating the relative displacement of the two components in that direction, and combining this with the meshing error, yields the elastic deformation, expressed as: ; Projecting the vibration displacements of the external gear ring and planetary gears onto the meshing line, calculating the relative displacement of the two components in that direction, and combining this with the meshing error, yields the elastic deformation, expressed as: ; in, This refers to the meshing error when the sun gear and planet gears mesh. This represents the meshing error when the planetary gear meshes with the external gear ring.
[0010] A further technical solution involves deriving the tangential and radial deformations of the planetary gear as follows: The planetary gears exhibit no relative radial deformation. The tangential relative deformation of the planetary gear is as follows: ;in, It is a small angular displacement in the circumferential direction of the planetary carrier. This indicates the base circle radius of the planetary carrier.
[0011] A further technical solution is that the dynamic differential equations of the dual internal meshing planetary gear transmission system include: The vibration equation of the sun gear is: ; The vibration equation of the external gear ring is: ; The vibration equation of the planetary carrier is: ; The vibration equation of the planetary gear is: ; in, Let be the moment of inertia of each component; The torsional vibration displacement of each component; The torsional vibration velocity of each component; The torsional vibration acceleration of each component; To support damping; To support stiffness; T represents the meshing stiffness; T represents the external load torque. For meshing damping, , m For the mass of the gear, Indicates the mass of the sun gear. Indicates the mass of the planetary gear. ξ The damping ratio; This indicates the base circle radius of each component.
[0012] A further technical solution is that the dynamic excitation includes gear time-varying meshing stiffness excitation and gear meshing error excitation; The analysis and calculation process for the time-varying meshing stiffness excitation of gears is as follows: The transmission error between two meshing gears is obtained through finite element analysis; the two meshing gears are the sun gear and the planet gear, and the planet gear and the external gear ring. Based on the transmission error, the meshing stiffness of the two meshing gears is calculated, and the meshing stiffness is expressed as a square wave form related to the speed to obtain the time-varying meshing stiffness excitation of the gears. The analysis and calculation process for gear meshing error excitation is as follows: Finite element analysis was used to obtain the tooth pitch error and tooth profile error. Based on gear error and tooth profile error, the amplitude of the meshing error of the two meshing gears is calculated, and a simple harmonic function representing the error excitation is formed to obtain the gear meshing error excitation.
[0013] Secondly, the present invention provides a dynamic modeling system for a dual internal meshing planetary gear transmission system.
[0014] A dynamic modeling system for a dual internal meshing planetary gear transmission system includes: The coordinate system construction module is used to define the components and transmission form of the transmission system. It only considers the vibration in the torsional direction of each component and constructs a coordinate system with the center of each component as the origin. The system generalized coordinates based on 4 degrees of freedom are defined in the coordinate system. The components include the sun gear, planet gears, planet carrier, and external gear ring. The system generalized coordinates include the small circumferential angular displacements of each component. The deformation derivation module is used to derive the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears based on the system's generalized coordinates, and to establish deformation formulas. The dynamic modeling module is used to construct a set of dynamic differential equations for a double internal meshing planetary gear transmission system based on deformation formulas. The excitation analysis and response solution module is used to calculate the dynamic excitation of the system through finite element analysis, input the excitation into the equation system, and solve for the nonlinear response characteristics of the system.
[0015] Thirdly, the present invention also provides an electronic device, comprising: a memory for storing executable instructions; and a processor for implementing the above-described dynamic modeling method for a dual internal meshing planetary gear transmission system when executing the executable instructions stored in the memory.
[0016] Fourthly, the present invention also provides a computer-readable storage medium storing executable instructions for causing a processor to execute the executable instructions to implement the above-described dynamic modeling method for a dual internal meshing planetary gear transmission system.
[0017] Fifthly, the present invention also provides a computer program product comprising executable instructions stored in a computer-readable storage medium; wherein, when the processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the above-mentioned dynamic modeling method for a dual internal meshing planetary gear transmission system is implemented.
[0018] The above one or more technical solutions have the following beneficial effects: 1. This invention proposes a dynamic modeling method and system for a double internal meshing planetary gear transmission system. The lumped mass method is used to establish a dynamic model of this new structure of double internal meshing planetary gears. This dynamic model is a pure torsional model. Based on the dynamic model, corresponding dynamic equations are established, which can provide a basis for the dynamic characteristic analysis of the double internal meshing planetary gear transmission system and the analysis of the natural frequency under different working conditions. This facilitates the structural frequency adjustment of the transmission device, avoids resonance in the system, and improves the stress condition of each component of the system.
[0019] 2. In the dynamic modeling method proposed in this invention, time-varying stiffness excitation and comprehensive error excitation are considered in the modeling process. One of the internal and external excitations is selected respectively to determine the basic conditions for the dynamic analysis of the new structure of double internal meshing planetary gear transmission, providing an effective basis and basis for gear vibration control, noise and defect detection.
[0020] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.
[0022] Figure 1 This is an overall flowchart of the dynamic modeling method for a dual internal meshing planetary gear transmission system proposed in this embodiment of the invention; Figure 2 This is a schematic diagram of the structure of the double internal meshing star wheel gear transmission system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the dynamic model of the double internal meshing star gear transmission system according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the coordinate system of the dual internal meshing planetary gear transmission system according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the transmission error curves between the sun gear and planet gears in a double internal meshing planetary gear transmission system according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the transmission error curve between the external gear ring and the planetary gears in the dual internal meshing planetary gear transmission system of this invention. Figure 7 This is a schematic diagram of the combined meshing error curve of the sun gear and planet gears in the double internal meshing planetary gear transmission system of this invention. Figure 8 This is a schematic diagram of the comprehensive meshing error curve between the external gear ring and the planetary gears in the dual internal meshing planetary gear transmission system of this invention. Detailed Implementation
[0023] It should be noted that the following detailed descriptions are exemplary and are intended only to describe specific embodiments and to provide further explanation of the invention, and are not intended to limit the scope of exemplary embodiments of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0024] Example 1 This embodiment proposes a dynamic modeling method for a dual internal meshing planetary gear transmission system. Using the lumped mass parameter method, a pure torsional dynamic model and dynamic equations are established for the dual internal meshing planetary gear transmission system, such as... Figure 1 As shown, the method specifically includes the following steps: Step S1: Establish a pure torsional dynamic model. That is, clarify the components and transmission form of the transmission system, consider only the vibration of each component in the torsional direction, construct a coordinate system with the center of each component as the origin, and define the system generalized coordinates based on 4 degrees of freedom in the coordinate system.
[0025] Specifically, such as Figure 2 As shown, the components of the double internal meshing planetary gear transmission system include a sun gear, planet gears, a planet carrier, and an external gear ring (also known as an internal gear ring). Its transmission form is as follows: the sun gear inputs power, the sun gear meshes with the planet gears, the planet gears mesh with the external gear ring, the external gear ring is fixed, and the planet carrier outputs power.
[0026] Based on a clear understanding of the components and transmission configuration, and ignoring the influence of nonlinear factors such as tooth backlash and tooth surface friction, this model only considers the effects of gear meshing stiffness, transmission error, meshing damping, and bearing support stiffness. Spring symbols are introduced at the system supports and meshing pairs. Using the lumped mass parameter method, the gears and planetary carrier are treated as rigid bodies. It is assumed that all components do not vibrate in the translational direction but do vibrate in the torsional direction; that is, only the torsional vibration of each component is considered, ignoring axial and radial vibrations and displacements. Based on this, a dynamic model of the double internal meshing planetary gear system is established. Figure 3 As shown.
[0027] Furthermore, to simplify the dynamic analysis process of the dual internal meshing transmission system, such as... Figure 4 As shown, the coordinate system of this system is defined as follows: a coordinate system is constructed with the centers of the sun gear, the external gear ring, and the planet carrier as the origin; at the same time, a planet gear coordinate system is constructed with the tangential and radial axes of the planet gears as the axes and the center of the planet gears as the origin; the above coordinate systems rotate with the revolution of the planet gears.
[0028] Based on the coordinate system defined above, it can be determined that the double internal meshing transmission system has a total of 4 degrees of freedom. Therefore, a generalized coordinate system based on these 4 degrees of freedom is defined. Including the minute angular displacements of each component in the circumferential direction, it can be expressed as: ; in, It is a tiny angular displacement of the sun gear in the circumferential direction. This represents the minute linear displacement of the sun gear along the line of meshing. It is a tiny angular displacement in the circumferential direction of the external gear ring. This indicates the minute displacement of the external gear ring of the planetary transmission along the line of meshing. It is a small angular displacement in the circumferential direction of the planetary carrier. This indicates a minute circumferential displacement of the planet carrier in a planetary transmission. It is a tiny angular displacement of the planetary gear in the circumferential direction. This represents the minute linear displacement of the inner ring of planetary gear p along the line of meshing. This represents the minute linear displacement of the outer ring of planetary gear p along the line of meshing. Indicates the base circle radius of each component. , These represent the sun gear, external gear ring, planet carrier, and planet gears, respectively. This refers to the internal gear ring of the planetary gear (which can be simply called the inner ring). This refers to the outer ring gear of the planetary gear (which can be simply called the outer ring).
[0029] Step S2: Elastic Deformation Coordination Conditions of the Gear System. That is, based on the system's generalized coordinates, derive the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears, and establish deformation formulas.
[0030] Considering that establishing the deformation relationship between the sun gear and planet gears, and the external gear ring and planet gears during meshing is a prerequisite for establishing a dynamic model of the new transmission system, this embodiment first establishes the elastic deformation coordination relationship between the two pairs of meshing teeth, and derives the relationship expressions of the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears in the system.
[0031] The derivation process of elastic deformation is as follows: Project the vibration displacement of the center of mass of each component onto the direction of the meshing action line, calculate the relative displacement of the two components in this direction, and then obtain the elastic deformation when the sun gear and planet gears mesh, and the external gear ring and planet gears mesh in the gear transmission system. Specifically, this includes: Step S2.1: Derive the elastic deformation between the sun gear and the planet gears.
[0032] 1) Project the torque vibration displacement of the sun gear and planet gears onto the direction of the meshing line. This projection is expressed as follows: and ; 2) Calculate the relative displacement of the two components in this direction. ; 3) Combining the meshing error between the two meshing gears, the elastic deformation is calculated and can be expressed as: .in, This represents the meshing error when the sun gear and planet gears mesh.
[0033] Step S2.2: Derive the elastic deformation between the external gear ring and the planetary gears.
[0034] 1) Project the torque vibration displacement of the external gear ring and planetary gears onto the meshing line direction. This projection is expressed as follows: and ; 2) Calculate the relative displacement of the two components in this direction. ; 3) Combining the meshing error between the two meshing gears, the elastic deformation is calculated and can be expressed as: .in, This represents the meshing error when the planetary gear meshes with the external gear ring.
[0035] Further, in step S2.3, the tangential and radial deformations of the planetary gears are derived.
[0036] Since only the deformation caused by vibration in the torsional direction is considered, the planetary gear and planet carrier have no relative deformation along the radial direction of the planetary gear. The relative deformation of the two components along the tangential direction of the planetary gear is as follows: ;in, It is a small angular displacement in the circumferential direction of the planetary carrier. This indicates the base circle radius of the planetary carrier.
[0037] Step S3: Based on the deformation formula, construct the dynamic differential equations of the double internal meshing planetary gear transmission system.
[0038] Specifically, based on the derived formulas and combined with Newtonian mechanics principles, a set of dynamic differential equations for a double internal meshing planetary gear transmission system is established, including: The vibration equation of the sun gear is: ; The vibration equation of the external gear ring is: ; The vibration equation of the planetary carrier is: ; The vibration equation of the planetary gear is: ; in, Let be the moment of inertia of each component; The torsional vibration displacement of each component; The torsional vibration velocity of each component; The torsional vibration acceleration of each component; T represents the meshing stiffness; T represents the external load torque. To support damping; To support stiffness; For meshing damping, it is represented as: , m For the mass of the gear, Indicates the mass of the sun gear. Let ξ represent the mass of the planetary gear and ξ be the damping ratio. This indicates the base circle radius of each component.
[0039] Step S4: Calculate the dynamic excitation of the system through finite element analysis, input the excitation into the equation system, and solve for the nonlinear response characteristics of the system.
[0040] Step S4.1: Dynamic excitation factor analysis of the dual internal meshing transmission system. Specifically, determining the dynamic excitation of the system is a fundamental condition for dynamic analysis. In this embodiment, only the time-varying stiffness excitation between meshing teeth and the comprehensive gear meshing error excitation caused by manufacturing and processing are considered.
[0041] (1) The time-varying stiffness excitation is related to the gear tooth meshing stiffness and the normal force between the gear meshing points, and can be expressed as: ;in, The normal force at the point of engagement; This represents the linear deformation of the gear along the line of meshing. Considering that the meshing point changes continuously during gear meshing, the transmission error between two meshing gears can be extracted using finite element analysis software. The formula between the angular deformation and the normal deformation at the meshing point (i.e., the linear deformation of the gear along the line of meshing) is as follows: ;in, This refers to the angle error (or angle deformation, transmission error); Let be the radius of the base circle. Based on this, and Substituting into the above equation, we obtain the meshing stiffness formula as follows: Here, T represents torque. Preferably, for ease of calculation, the average meshing stiffness in the single-tooth meshing zone and the multiple single-tooth meshing zone is taken as the calculation quantity of stiffness excitation.
[0042] In this embodiment, the analysis and calculation process of the time-varying meshing stiffness excitation of the gear is as follows: First, the transmission error between the two meshing gears is obtained through finite element analysis, such as... Figure 5 , Figure 6 The figures shown are the transmission error curves between the sun gear and planet gears, and between the planet gears and the external gear ring, respectively.
[0043] Secondly, based on transmission error, through formula Calculate the meshing stiffness of two meshing gears and express the meshing stiffness as a velocity-dependent square wave, such as using a square wave function. Let A, B, Ω, and P represent the mean, amplitude, meshing frequency, and duty cycle, respectively, to obtain the time-varying stiffness excitation between meshing teeth.
[0044] For example, the meshing stiffness of two meshing gears can be expressed as a square wave form related to the rotational speed: The time-varying stiffness excitation equations for the sun gear and planet gears are as follows: ; The time-varying stiffness excitation equation for the planetary gear and the external gear ring is: .
[0045] (2) When analyzing the comprehensive meshing error excitation, it is decomposed into pitch error and tooth profile error for calculation. Typically, a simple harmonic function is used to represent the gear meshing error excitation. The simple harmonic function of the meshing error excitation can be expressed as: ; in, , For the mean and amplitude, It is the frequency during meshing. It is the initial phase. Typically, we take... , .
[0046] Furthermore, through finite element analysis, the tooth pitch error and tooth profile error are obtained, such as... Figure 7 , Figure 8 The error curve shown is then used to determine the tooth pitch error. and tooth profile error Calculate the amplitude of the meshing error between the two meshing gears. ,for: .
[0047] The gear meshing error excitation can be analyzed and calculated using the above method.
[0048] Step S4.2: After determining the dynamic excitation of the system, input the excitation into the system of equations and solve for the nonlinear response characteristics of the system.
[0049] Example 2 This embodiment provides a dynamic modeling system for a dual internal meshing planetary gear transmission system, including: The coordinate system construction module is used to define the components and transmission form of the transmission system. It only considers the vibration in the torsional direction of each component and constructs a coordinate system with the center of each component as the origin. The system generalized coordinates based on 4 degrees of freedom are defined in the coordinate system. The components include the sun gear, planet gears, planet carrier, and external gear ring. The system generalized coordinates include the small circumferential angular displacements of each component. The deformation derivation module is used to derive the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears based on the system's generalized coordinates, and to establish deformation formulas. The dynamic modeling module is used to construct a set of dynamic differential equations for a double internal meshing planetary gear transmission system based on deformation formulas. The excitation analysis and response solution module is used to calculate the dynamic excitation of the system through finite element analysis, input the excitation into the equation system, and solve for the nonlinear response characteristics of the system.
[0050] Example 3 This embodiment provides an electronic device, including: a memory for storing executable instructions; and a processor for executing the executable instructions stored in the memory to implement the method provided in this embodiment.
[0051] Example 4 This embodiment also provides a computer-readable storage medium storing executable instructions, which, when executed by a processor, will cause the processor to execute the method described above in this embodiment.
[0052] Example 5 This embodiment provides a computer program product including executable instructions, which are computer instructions; the executable instructions are stored in a computer-readable storage medium. When the processor of an electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, the electronic device performs the method described in this embodiment.
[0053] The steps and methods involved in Embodiments 2 to 5 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.
[0054] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.
[0055] The above description is only a preferred embodiment of the present invention. Although the specific implementation of the present invention has been described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the present invention.
Claims
1. A dynamic modeling method for a dual internal meshing planetary gear transmission system, characterized in that, include: The components and transmission form of the transmission system are clearly defined. Only the vibration in the torsional direction of each component is considered. A coordinate system is constructed with the center of each component as the origin. The system generalized coordinates based on 4 degrees of freedom are defined in the coordinate system. The components include the sun gear, planet gears, planet carrier, and external gear ring. Based on the system's generalized coordinates, the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears are derived, and deformation formulas are established. Based on the deformation formula, a set of dynamic differential equations for a double internal meshing planetary gear transmission system is constructed. The dynamic excitation of the system is calculated by finite element analysis. The excitation is input into the system of equations, and the nonlinear response characteristics of the system are solved.
2. The dynamic modeling method for a dual internal meshing planetary gear transmission system as described in claim 1, characterized in that, The system's generalized coordinates include the minute angular displacements of each component in the circumferential direction. Represented as: ； in, It is a tiny angular displacement of the sun gear in the circumferential direction. This represents the minute linear displacement of the sun gear along the line of meshing. It is a tiny angular displacement in the circumferential direction of the external gear ring. This indicates the minute displacement of the external gear ring of the planetary transmission along the line of meshing. It is a tiny angular displacement in the circumferential direction of the planetary carrier. This indicates a minute circumferential displacement of the planet carrier in a planetary transmission. It is a tiny angular displacement of the planetary gear in the circumferential direction. This represents the minute linear displacement of the inner ring of planetary gear p along the line of meshing. This represents the minute linear displacement of the outer ring of planetary gear p along the line of meshing. Indicates the base circle radius of each component. , These represent the sun gear, external gear ring, planet carrier, and planet gears, respectively. This indicates the internal gear ring of the planetary gear. This refers to the external gear ring of a planetary gear.
3. The dynamic modeling method for a dual internal meshing planetary gear transmission system as described in claim 2, characterized in that, The derivation process of the elastic deformation is as follows: Projecting the vibration displacements of the sun gear and planet gears onto the meshing line, calculating the relative displacement of the two components in that direction, and combining this with the meshing error, yields the elastic deformation, expressed as: ； Projecting the vibration displacements of the external gear ring and planetary gears onto the meshing line, calculating the relative displacement of the two components in that direction, and combining this with the meshing error, yields the elastic deformation, expressed as: ； in, This refers to the meshing error when the sun gear and planet gears mesh. This represents the meshing error when the planetary gear meshes with the external gear ring.
4. The dynamic modeling method for a dual internal meshing planetary gear transmission system as described in claim 2, characterized in that, The derivation process of the tangential and radial deformation of the planetary gear is as follows: The planetary gears exhibit no relative radial deformation. The relative tangential deformation of the planetary gear is as follows: ;in, It is a tiny angular displacement in the circumferential direction of the planetary carrier. This indicates the base circle radius of the planetary carrier.
5. The dynamic modeling method for a dual internal meshing planetary gear transmission system as described in claim 1, characterized in that, The dynamic differential equations of the dual internal meshing planetary gear transmission system include: The vibration equation of the sun gear is: ； The vibration equation for the external gear ring is: ； The vibration equation of the planetary carrier is: ； The vibration equation of the planetary gear is: ； in, Let be the moment of inertia of each component; The torsional vibration displacement of each component; The torsional vibration velocity of each component; The torsional vibration acceleration of each component; To support damping; To support stiffness; T represents the meshing stiffness; T represents the external load torque. For meshing damping, , m For the mass of the gear, Indicates the mass of the sun gear. Let ξ represent the mass of the planetary gear and ξ be the damping ratio. This indicates the base circle radius of each component.
6. The dynamic modeling method for a dual internal meshing planetary gear transmission system as described in claim 1, characterized in that, The dynamic excitation includes time-varying gear meshing stiffness excitation and gear meshing error excitation; The analysis and calculation process of the time-varying meshing stiffness excitation of the gear is as follows: The transmission error between two meshing gears is obtained through finite element analysis; the two meshing gears are the sun gear and the planet gear, and the planet gear and the external gear ring. Based on the transmission error, the meshing stiffness of the two meshing gears is calculated, and the meshing stiffness is expressed as a square wave form related to the speed to obtain the time-varying meshing stiffness excitation of the gears. The analysis and calculation process of the gear meshing error excitation is as follows: Finite element analysis was used to obtain the tooth pitch error and tooth profile error. Based on gear error and tooth profile error, the amplitude of the meshing error of the two meshing gears is calculated, and a simple harmonic function representing the error excitation is formed to obtain the gear meshing error excitation.
7. A dynamic modeling system for a dual internal meshing planetary gear transmission system, characterized in that, include: The coordinate system construction module is used to define the components and transmission form of the transmission system. It only considers the vibration in the torsional direction of each component and constructs a coordinate system with the center of each component as the origin. The system generalized coordinates based on 4 degrees of freedom are defined in the coordinate system. The components include the sun gear, planet gears, planet carrier, and external gear ring. The system generalized coordinates include the small circumferential angular displacements of each component. The deformation derivation module is used to derive the elastic deformation of the meshing pairs of the sun gear and planet gears, the meshing pairs of the external gear ring and planet gears, and the tangential and radial deformation of the planet gears based on the system's generalized coordinates, and to establish deformation formulas. The dynamic modeling module is used to construct a set of dynamic differential equations for a double internal meshing planetary gear transmission system based on deformation formulas. The excitation analysis and response solution module is used to calculate the dynamic excitation of the system through finite element analysis, input the excitation into the equation system, and solve for the nonlinear response characteristics of the system.
8. An electronic device, characterized in that, include: Memory, used to store executable instructions; The processor, when executing executable instructions stored in the memory, implements the dynamic modeling method for a dual internal meshing planetary gear transmission system as described in any one of claims 1-6.
9. A computer-readable storage medium, characterized in that, The system stores executable instructions that, when executed by a processor, implement the dynamic modeling method for a dual internal meshing planetary gear transmission system as described in any one of claims 1-6.
10. A computer program product, characterized in that, The computer program product includes executable instructions stored in a computer-readable storage medium; When the processor of the electronic device reads the executable instructions from the computer-readable storage medium and executes the executable instructions, it implements the dynamic modeling method for a dual internal meshing planetary gear transmission system as described in any one of claims 1-6.