Modeling method, system and equipment for gear rotor system dynamics and medium

Abstract

The invention discloses a modeling method, system, equipment and medium for gear rotor system dynamics, and the method comprises the steps: adding first kinetic energy, second kinetic energy and third kinetic energy corresponding to a small gear and a large gear to obtain total kinetic energy; the first strain energy, the second strain energy and the third strain energy corresponding to the small gear and the large gear, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy and the elastic potential energy formed by gear tooth meshing are added, and the total potential energy is obtained; the total kinetic energy and the total potential energy are substituted into a Lagrange equation for calculation, a control equation is obtained, and gear rotor system dynamics modeling is achieved. According to the method, by comprehensively considering the flexibility of the wheel body and the flexibility of the transmission shaft, the dynamic modeling of the gear rotor system can be better improved, so that the constructed dynamic model of the wheel rotating subsystem has stability and reliability.

Description

Technical Field

[0001] This application relates to the field of gear transmission technology, and in particular to a modeling method, system, device and medium for the dynamics of a gear rotor system. Background Technology

[0002] With the continuous upgrading of advanced mechanical design requirements, thin-walled gear transmission systems are constantly evolving in pursuit of higher power density, more precise transmission accuracy, better noise control, and more environmentally friendly adaptability, becoming a key technology in the field of high-performance mechanical transmission. Given the high flexibility and high sensitivity of thin-walled structures, research on thin-walled gear transmission systems needs to ensure their stability and reliability under extreme loads and high-speed conditions to adapt to complex and ever-changing operating environments.

[0003] During the operation of thin-walled gears, the transmission system is affected by internal and external excitation forces, leading to significant vibration of the rotor system, which poses a severe challenge to its safe and stable operation. Particularly in helical gear transmission systems, due to their lightweight design and thin-walled structure, inertial loads and assembly errors can cause significant dynamic responses. Simultaneously, the axial force balance requirements during gear operation further increase their sensitivity to dynamic loads. Furthermore, modern high-performance mechanical equipment places increasingly higher demands on gear systems, such as higher speeds, greater transmission torque, and longer service life. Therefore, further research is needed on the gyroscopic effect and high-frequency resonance phenomena under high-speed rotation of the system.

[0004] Currently, many modeling methods only consider the flexibility of the drive shaft and ignore the flexibility of the wheel itself, which leads to the loss of some resonant frequencies. Thin-walled gears are more susceptible to out-of-plane resonance, so dynamic modeling methods for wheel flexibility need to be improved. Summary of the Invention

[0005] This application aims to propose a modeling method, system, device, and medium for the dynamics of a gear rotor system. By comprehensively considering the flexibility of the wheel body and the flexibility of the transmission shaft, the dynamics modeling of the gear rotor system can be improved, and the constructed dynamics model of the gear rotor system can be made stable and reliable.

[0006] In a first aspect, embodiments of this application provide a method for modeling the dynamics of a gear rotor system, the method comprising:

[0007] When the gear rotor system moves, calculate the first displacement vector, second displacement vector, and third displacement vector of each of the shaft unit, rim unit, and spoke unit at any point in the absolute coordinate system;

[0008] Differentiating the first displacement vector, the second displacement vector, and the third displacement vector yields the first elastic deformation velocity vector of the shaft unit, the second elastic deformation velocity vector of the rim unit, and the third elastic deformation velocity vector of the spoke unit.

[0009] Calculate the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit;

[0010] Based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector, calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, respectively.

[0011] Based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress, calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, respectively.

[0012] Based on the bearing stiffness corresponding to the multiple degrees of freedom of the shaft unit, the bearing boundary condition potential energy is calculated, and based on the vector coordinates of the pinion and the gear in the absolute coordinate system, the elastic potential energy formed by gear meshing is calculated.

[0013] By analyzing the coupling constraint relationship between the shaft unit, the rim unit, and the spoke unit, the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft units are calculated.

[0014] The total kinetic energy is obtained by adding the first kinetic energy, the second kinetic energy, and the third kinetic energy corresponding to the pinion and the gear respectively. The total potential energy is obtained by adding the first strain energy, the second strain energy, and the third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy, and the elastic potential energy formed by the meshing of the gear teeth.

[0015] The total kinetic energy and the total potential energy are substituted into the Lagrange equations for calculation to obtain the control equations, thereby realizing the dynamic modeling of the gear rotor system.

[0016] Compared with the prior art, the first aspect of this application has the following beneficial effects:

[0017] This method obtains the total kinetic energy by adding the first, second, and third kinetic energies of the pinion and gear respectively, and the total potential energy by adding the first, second, and third strain energies of the pinion and gear, the potential energy of the bearing boundary conditions, the first, second, and third constraint potential energies, and the elastic potential energy generated by gear meshing. The total kinetic and potential energies are then substituted into the Lagrange equations to obtain the governing equations, thus achieving dynamic modeling of the gear rotor system. In this way, by comprehensively considering the kinetic and potential energies of the shaft element, the rim element, and the spoke element, the total kinetic and potential energies of the gear rotor system are calculated, thus comprehensively considering the flexibility of the wheel body and the transmission shaft, which can better improve the dynamic modeling of the gear rotor system. Finally, by substituting the total kinetic and potential energies into the Lagrange equations to obtain the governing equations, the dynamic modeling of the gear rotor system is realized, ensuring the stability and reliability of the constructed gear rotor system dynamic model.

[0018] Secondly, embodiments of this application also provide a modeling system for the dynamics of a gear rotor system, the system comprising:

[0019] The first calculation unit is used to calculate the first displacement vector, second displacement vector and third displacement vector of each of the shaft unit, rim unit and spoke unit at any point in the absolute coordinate system when the gear rotor system moves.

[0020] The data differentiation unit is used to differentiate the first displacement vector, the second displacement vector, and the third displacement vector to obtain the first elastic deformation velocity vector of the shaft unit, the second elastic deformation velocity vector of the rim unit, and the three elastic deformation velocity vectors of the spoke unit.

[0021] The second calculation unit is used to calculate the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit;

[0022] The third calculation unit is used to calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, respectively, based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector.

[0023] The fourth calculation unit is used to calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, respectively, based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress.

[0024] The fifth calculation unit is used to calculate the bearing boundary condition potential energy based on the bearing stiffness corresponding to the multiple degrees of freedom of the shaft unit, and to calculate the elastic potential energy formed by gear meshing based on the vector coordinates of the pinion and the gear in the absolute coordinate system.

[0025] The sixth calculation unit is used to calculate the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft unit by analyzing the coupling constraint relationship between the shaft unit, the rim unit and the spoke unit.

[0026] The data summation unit is used to add the first kinetic energy, the second kinetic energy, and the third kinetic energy corresponding to the pinion and the gear respectively to obtain the total kinetic energy, and to add the first strain energy, the second strain energy, and the third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy, and the elastic potential energy formed by the meshing of the gear teeth to obtain the total potential energy.

[0027] The modeling and determination unit is used to substitute the total kinetic energy and the total potential energy into the Lagrange equation for calculation to obtain the control equation, so as to realize the dynamic modeling of the gear rotor system.

[0028] Thirdly, embodiments of this application also provide an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, the instructions being executed by the at least one control processor to enable the at least one control processor to perform a gear rotor system dynamics modeling method as described above.

[0029] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for causing a computer to execute a modeling method for the dynamics of a gear-rotor system as described above.

[0030] It is understood that the beneficial effects of the second to fourth aspects compared with the related technologies are the same as the beneficial effects of the first aspect compared with the related technologies. Please refer to the relevant description in the first aspect above, which will not be repeated here. Attached Figure Description

[0031] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0032] Figure 1 This is a schematic flowchart of an embodiment of the gear rotor system dynamics modeling method provided in this application;

[0033] Figure 2 This is a schematic diagram of the relative positional relationship of the absolute coordinate system, rotating coordinate system, and body coordinate system from the same perspective in the best embodiment of the gear rotor system dynamics modeling method provided in this application, as well as the rim unit, spoke unit, shaft unit model, and discrete unit model.

[0034] Figure 3 This is a schematic diagram of the rim, spokes, and shaft units in the preferred embodiment of the gear rotor system dynamics modeling method provided in this application;

[0035] Figure 4 This is a schematic diagram illustrating the deformation and transmission error solution of a flexible gear system in the initial and meshing states in the best embodiment of the gear rotor system dynamics modeling method provided in this application.

[0036] Figure 5 This is a schematic diagram of an embodiment of the gear rotor system dynamics modeling system provided in this application. Detailed Implementation

[0037] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0038] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0039] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0040] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0041] Currently, many modeling methods only consider the flexibility of the drive shaft and ignore the flexibility of the wheel itself, which leads to the loss of some resonant frequencies. Thin-walled gears are more susceptible to out-of-plane resonance, so dynamic modeling methods for wheel flexibility need to be improved.

[0042] To address the shortcomings of existing technologies in modeling the dynamics of wheel flexibility, this application proposes a modeling method, system, device, and medium for the dynamics of a gear rotor system.

[0043] Reference Figure 1 This application provides a schematic flowchart of a method for modeling the dynamics of a gear-rotor system. This method is applied to electronic devices, such as servers or mobile terminals. Figure 1 As shown, the modeling method for the dynamics of this gear-rotor system may include the following steps:

[0044] Step S100: When the gear rotor system moves, calculate the first displacement vector, second displacement vector, and third displacement vector of each of the shaft unit, rim unit, and spoke unit at any point in the absolute coordinate system.

[0045] Step S200: Differentiate the first displacement vector, the second displacement vector, and the third displacement vector to obtain the first elastic deformation velocity vector of the shaft element, the second elastic deformation velocity vector of the rim element, and the third elastic deformation velocity vector of the spoke element.

[0046] Step S300: Calculate the first strain and first stress of the shaft element, the second strain and second stress of the rim element, and the third strain and third stress of the spoke element;

[0047] Step S400: Based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector, calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, respectively.

[0048] Step S500: Based on the first strain and first stress, the second strain and second stress, and the third strain and third stress, calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, respectively.

[0049] Step S600: Calculate the bearing boundary condition potential energy based on the bearing stiffness corresponding to the multiple degrees of freedom of the shaft element, and calculate the elastic potential energy formed by gear meshing based on the vector coordinates of the pinion and gear in the absolute coordinate system.

[0050] Step S700: By analyzing the coupling constraint relationship between the shaft unit, the rim unit, and the spoke unit, calculate the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft unit.

[0051] Step S800: Add the first kinetic energy, second kinetic energy and third kinetic energy corresponding to the pinion and the gear respectively to obtain the total kinetic energy; and add the first strain energy, second strain energy and third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy and the elastic potential energy formed by gear meshing to obtain the total potential energy.

[0052] Step S900: Substitute the total kinetic energy and total potential energy into the Lagrange equations for calculation to obtain the control equations, thereby realizing the dynamic modeling of the gear rotor system.

[0053] In this embodiment, the total kinetic energy is obtained by adding the first, second, and third kinetic energies corresponding to the pinion and gear respectively. The total potential energy is obtained by adding the first, second, and third strain energies corresponding to the pinion and gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy, and the elastic potential energy formed by gear meshing. The total kinetic energy and total potential energy are then substituted into the Lagrange equations for calculation to obtain the governing equations, thereby achieving dynamic modeling of the gear rotor system. Thus, by comprehensively considering the kinetic and potential energies corresponding to the shaft element, rim element, and spoke element, the total kinetic and potential energy of the gear rotor system are calculated, comprehensively considering the wheel body flexibility and the transmission shaft flexibility, which better improves the dynamic modeling of the gear rotor system. Then, by substituting the total kinetic and potential energy into the Lagrange equations for calculation to obtain the governing equations, the dynamic modeling of the gear rotor system is realized, ensuring the stability and reliability of the constructed gear rotor system dynamic model.

[0054] The aforementioned gear rotor system includes a large gear and a small gear.

[0055] In some embodiments, calculating the first strain and first stress of the shaft element, the second strain and second stress of the rim element, and the third strain and third stress of the spoke element includes:

[0056] Using the Timoshenko straight beam model, the first strain and first stress of the shaft element are calculated.

[0057] Using Timoshenko's bending beam principle, the second strain and second stress of the rim element are calculated.

[0058] The third strain and third stress of the spoke element are calculated using the Mindlin plate element model.

[0059] In this embodiment, by comprehensively considering the strain and stress of the shaft unit, rim unit, and spoke unit, a good data foundation is laid for the subsequent calculation of the potential energy corresponding to the shaft unit, rim unit, and spoke unit, so as to better improve the dynamic modeling of the gear rotor system.

[0060] In some implementations, based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector, the first kinetic energy of the shaft unit corresponding to the pinion and the gear, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit are calculated, including:

[0061] Based on the first elastic deformation velocity vector, calculate the first kinetic energy of the shaft elements corresponding to the pinion and gear:

[0062]

[0063] Based on the second elastic deformation velocity vector, calculate the second kinetic energy of the corresponding rim elements of the pinion and gear:

[0064]

[0065] Based on the third elastic deformation velocity vector, calculate the third kinetic energy of the corresponding spoke elements of the pinion and gear:

[0066]

[0067] Among them, K S,i,k Let S represent the first kinetic energy of the i-th discrete unit, S represent the shaft element, k = p represent the small gear, k = g represent the large gear, ρ represent the density, and R represent the density. S L represents the radius of the shaft element. s,i L represents the length of the i-th axis segment. s,i-1 This represents the length of the (i-1)th axis segment. Let r denote the derivative of the first elastic deformation velocity vector, T denote the transpose, and r S,k The x-axis represents the polar radius of any point within the axis element in the body coordinate system. S,k θ represents the macroscopic length coordinates of the section containing the shaft element before deformation relative to the origin of the body coordinate system. S,k The angle of any point within the axis element in the body coordinate system is represented by K. R,i,k Let θ represent the second kinetic energy of the i-th rim element mesh, R represent the rim element, and θ represent the second kinetic energy of the rim element mesh. R,i,k H represents the angle between any point on the i-th rim element and the origin before rim deformation. R B represents the width of the rim. R Indicates the thickness of the rim. R represents the derivative of the second elastic deformation velocity vector. R,kThe radius r represents the central axis radius of the rim element. R,k The polar radius x represents the radius of any point on the rim element before rim deformation relative to the origin. R,k θ represents the macroscopic x-axis distance between any point on the rim element before rim deformation and the origin of the coordinate system. R,k K represents the angle between any point on the rim element and the origin before rim deformation. W,i,j,k Let θ represent the third kinetic energy of the j-th grid cell in the i-th spoke cell, W represent the spoke cell, and θ represent the third kinetic energy of the j-th grid cell in the i-th spoke cell. W,j,k R represents the angle between any point on the j-th spoke mesh element and the origin before the rim deformation. W,i,k Let represent the radius of the i-th ring of spokes. The derivative of the third elastic deformation velocity vector, r W,k The polar radius x represents the radius of any point on the spoke element relative to the origin before the spoke deformation. W,k θ represents the macroscopic x-axis distance between any point on the spoke element and the origin of the coordinate system before the spoke deformation. W,k This represents the angle between any point on the spoke unit and the origin of the coordinate system before the spoke deforms.

[0068] In some embodiments, based on the first strain and first stress, the second strain and second stress, and the third strain and third stress, the first strain energy of the shaft element corresponding to the pinion and the gear, the second strain energy of the rim element, and the third strain energy of the spoke element are calculated, including:

[0069] Based on the first strain and the first stress, calculate the first strain energy of the shaft elements corresponding to the pinion and gear respectively:

[0070]

[0071] Based on the second strain and the second stress, calculate the second strain energy of the corresponding rim elements of the pinion and gear:

[0072]

[0073] Based on the first strain and the first stress, calculate the third strain energy of the corresponding spoke elements of the pinion and gear:

[0074]

[0075] Among them, P S,i,k R represents the first strain energy of the shaft element. s,k σ represents the radius of the shaft element. S,x,k ε represents the first normal stress of the shaft element. S,x,k τ represents the first normal strain of the shaft element. S,xy,k and τ S,xz,kγ represents the first shear stress of the shaft element along the xy and xz directions, respectively. S,xy,k and γ S,xz,k P represents the first shear strain of the shaft element along the xy and xz directions, respectively. R,i,k ε represents the second strain energy of the rim element. R,i and ε R,o χ represents the second normal strain in-plane and out-of-plane of the rim element, respectively. R,i and χ R,o γ represents the in-plane and out-of-plane normal strain along the x-axis of the rim element, respectively. R,i and γ R,o σ represents the second shear strain in and out of the plane of the rim element, respectively. R,i and σ R,o V represents the second normal stress in and out of the plane of the rim element, respectively. R,i and v R,o Let τ represent the in-plane and out-of-plane normal stresses along the x-axis of the rim element, respectively. R,i and τ R,o P represents the second shear stress in and out of the plane of the rim element, respectively. W,i,j,k ε represents the third strain energy of the spoke unit. W,rr,k ,ε W,θθ,k γ represents the third normal strain in the radial and tangential directions of the spoke element, respectively. W,rθ,k ,γ W,θx,k ,γ W,rx,k σ represents the third shear strain of the spoke element in the rθ, θx, and rx planes, respectively. W,rr,k ,σ W,θθ,k τ represents the third normal stress in the radial and tangential directions of the spoke unit, respectively. W,rθ,k ,τ W,θx,k ,τ W,rx,k These represent the third shear stress of the spoke element in the rθ, θx, and rx planes, respectively.

[0076] In some implementations, the bearing boundary condition potential energy is calculated based on the bearing stiffness corresponding to multiple degrees of freedom of the shaft element, including:

[0077]

[0078] Among them, P bearing k represents the potential energy of the bearing boundary conditions. Bw ,k Bu ,k Bv ,k By ,k Bz These represent the bearing stiffness in different degrees of freedom, u S ,v S ,w SThese represent the microscopic instantaneous deformation disturbances of any point on the shaft element in the radial direction u, tangential direction v, and axial direction w, respectively. Let x represent the micro-rotation angles about the y-axis and about the z-axis, respectively. S L represents the macroscopic length coordinate of the section containing the shaft element before deformation relative to the origin of the body coordinate system. S This indicates the length of each shaft segment. Indicates in x S The micro-displacement of the shaft element at the position of length 0 along the w direction. Indicates in x S The micro-displacement of the shaft element at the position of length 0 along the u direction. This represents the minute displacement of the shaft element along the v direction at the position where the v length is 0. Indicates in x S The micro-rotational displacement of the shaft element at the position of length 0 along the y-axis. Indicates in x S The micro-rotational angular displacement of the shaft element at the position with length 0 along the z-axis. Indicates in x S Length L S The micro-displacement of the shaft element along the w direction at the given position. Indicates in x S Length L S The micro-displacement of the shaft element along the u-direction at position. This indicates that when v is of length L S The minute displacement of the shaft element along the v direction at the given position. Indicates in x S Length L S The micro-rotational displacement of the shaft element along the y-axis at the position. Indicates in x S Length L S The micro-rotation angular displacement of the shaft element along the z-axis at the location.

[0079] In some implementations, the elastic potential energy generated by tooth meshing is calculated based on the vector coordinates of the pinion and gear in the absolute coordinate system, including:

[0080] Calculate the first vector coordinate of the small gear in the absolute coordinate system at the initial moment, and calculate the second vector coordinate of the large gear in the absolute coordinate system at the initial moment;

[0081] Calculate the dynamic propagation error at the initial moment based on the first vector coordinates and the second vector coordinates;

[0082] Calculate the third vector coordinate of the pinion in the absolute coordinate system at the next moment, and calculate the fourth vector coordinate of the gear in the absolute coordinate system at the next moment;

[0083] Calculate the dynamic transmission error at the next moment based on the third and fourth vector coordinates;

[0084] The difference in transmission error is obtained by subtracting the dynamic transmission error at the initial moment from the dynamic transmission error at the next moment.

[0085] The elastic potential energy generated by gear meshing is calculated based on the difference in transmission error.

[0086] In this embodiment, the elastic potential energy formed by the meshing of the gear teeth is calculated based on the vector coordinates of the pinion and gear in the absolute coordinate system. The flexible deformation of the gear body is taken into account, which lays a good data foundation for the subsequent calculation of the total potential energy of the gear rotor system, so as to better improve the dynamic modeling of the gear rotor system.

[0087] In some implementations, calculating the first constraint potential energy between the shaft element and the spoke element, the second constraint potential energy between the rim element and the spoke element, and the third constraint potential energy between the shaft elements includes:

[0088] Calculate the first constraint potential energy between the shaft element and the spoke element:

[0089]

[0090] Calculate the second constraint potential energy between the rim element and the spoke element:

[0091]

[0092] Calculate the third constraint potential energy between axis elements:

[0093]

[0094] Among them, P SW Let P represent the first constraint potential energy. WR Let P represent the second constraint potential energy. SS Let C represent the third constraint potential energy, and C represent a large number. This indicates that each degree of freedom of the spoke element is within a radius of R. S The micro-lateral displacement with an angle of 0 to 2π, r W R represents the polar coordinate radius of any point on the spoke element before the spoke deformation relative to the origin. S θ represents the radius of the axis element. W This represents the angle between any point on the spoke element and the origin of the coordinate system before the spoke deforms. This indicates that each degree of freedom of the spoke element is within a radius of R. S The micro-rotation angle is between 0 and 2π. This indicates that each transverse degree of freedom of the spoke element is within a radius of R. W The angle is θR The slight lateral movement of the position, This represents the micro-lateral displacement of the rim element at the coordinate angle corresponding to the spoke element. This indicates that each rotational degree of freedom of the spoke element is within a radius of R. W The angle is θ R The slight rotation of the position, R represents the micro-rotation angle of the rim element in the coordinate angle corresponding to the spoke element. W θ represents the radius of the spoke unit. R t represents the angle of the rim element. S The x represents the micro-lateral displacement of each degree of freedom of the axis element. S L represents the macroscopic length coordinate of the section containing axis element S before deformation relative to the origin of the body coordinate system. S x represents the length of each axis segment. S+1 This represents the macroscopic length coordinates of the section containing shaft element S+1 before deformation relative to the origin of the body coordinate system, rot. S This represents the micro-rotation angle of each degree of freedom of the axis element.

[0095] To facilitate understanding by those skilled in the art, a set of preferred embodiments is provided below:

[0096] With the continuous upgrading of advanced mechanical design requirements, thin-walled gear transmission systems are constantly evolving in pursuit of higher power density, more precise transmission accuracy, better noise control, and more environmentally friendly adaptability, becoming a key technology in the field of high-performance mechanical transmission. Given the high flexibility and high sensitivity of thin-walled structures, research on thin-walled gear transmission systems needs to ensure their stability and reliability under extreme loads and high-speed conditions to adapt to complex and ever-changing operating environments.

[0097] Thin-walled gear transmission systems offer significant advantages in terms of lightweight design and high-efficiency transmission. For example, in the field of aerospace mechanical transmissions, thin-walled herringbone gears have become indispensable key components. Due to their light weight and low inertia, thin-walled gears can effectively reduce the overall weight of aircraft, thereby significantly improving fuel efficiency and maneuverability, making them particularly suitable for fighter jets and high-speed aircraft with stringent requirements for portability and high performance. However, the lightweight design of thin-walled structures also makes them more susceptible to dynamic coupling effects and external load disturbances under complex operating conditions, potentially leading to vibration, noise, and reliability issues. Therefore, accurate dynamic modeling is crucial in the development of thin-walled gear transmission systems. Dynamic modeling allows for in-depth study of the dynamic behavior and performance boundaries of thin-walled gears, providing a reliable theoretical basis for optimized design and improved system stability.

[0098] During the operation of thin-walled gears, the transmission system is affected by internal and external excitation forces, leading to significant vibration of the rotor system, which poses a severe challenge to its safe and stable operation. Particularly in helical gear transmission systems, due to their lightweight design and thin-walled structure, inertial loads and assembly errors can cause significant dynamic responses. Simultaneously, the axial force balance requirements during gear operation further increase their sensitivity to dynamic loads. Furthermore, modern high-performance mechanical equipment places increasingly higher demands on gear systems, such as higher speeds, greater transmission torque, and longer service life. Therefore, further research is needed on the gyroscopic effect and high-frequency resonance phenomena under high-speed rotation of the system.

[0099] However, many current modeling methods only consider the flexibility of the drive shaft and ignore the flexibility of the wheel itself, which leads to the loss of some resonant frequencies. Thin-walled gears are more susceptible to out-of-plane resonance, so dynamic modeling methods for wheel flexibility need to be improved.

[0100] To address the aforementioned issues, this embodiment proposes a dynamic modeling method for flexible thin-walled gear rotor systems that considers the coupling of multiple flexible bodies theory, referring to... Figure 2 , Figure 2 Image (a) shows a schematic diagram of three types of coordinate systems and a gear rotor system. Figure 2 (b) is a schematic diagram of discrete spokes and discrete rims. Figure 2 (c) is a schematic diagram of a discrete rotating axis. The method in this embodiment specifically includes the following:

[0101] First, the elastic component energy method is used to derive the elastic deformation velocity vectors, stresses, and strains of the shaft, rim, and spokes in the rotating gear rotor system. Considering the flexible deformation of the flexible gear transmission system, it is necessary to establish different coordinate systems for study. The basic idea for dynamic modeling of the fully flexible gear rotor system is as follows: the flexible deformation of the gear rotor system is regarded as the motion of countless random particles. To study the flexible deformation of the components, it is necessary to derive their position vectors relative to the stationary ground, so an absolute coordinate system R0 is established. Considering the rotational characteristics of the gear shaft, a rotating coordinate system R1 located at the shaft end face is also needed. At the same time, to further simplify the motion description, a body coordinate system R2 is established to eliminate the influence of shaft segment flexible deformation and rotation effects. Subsequently, the coordinates are transformed to the absolute coordinate system. The relative positional relationships of each coordinate system are as follows: Figure 2 As shown in (a).

[0102] The following is an introduction to the three coordinate system types:

[0103] (1) R0(x0,y0,z0): Absolute coordinate system, an inertial reference system fixed on the ground. At this time, the coordinate system does not move at all relative to the ground. The coordinate plane x0O0y0 is parallel to the ground, and the coordinate axis O0z0 is perpendicular to the ground. The origin O1 of the rotating coordinate system R1(x1,y1,z1) is located in the absolute coordinate system at the position vector R0.

[0104] (2) R1(x1,y1,z1): The rotating coordinate system is a coordinate system located on the end face of the rotation axis, with the x1 axis parallel to the undeformed rotation axis. The other two coordinate axes, y1 and z1, rotate around the x1 axis at a speed of Ω. At the initial moment, the origin O2 of the body coordinate system R2(x2,y2,z2) is located at the position vector R1 in the absolute coordinate system. At any subsequent moment, the position vector changes with the deformation of the nodes at the origin of the body coordinate system and the rotation of the rotating coordinate system.

[0105] (3)R2(x2,y2,z2): The body coordinate system is located at the coupling point between the rotor and the spokes. This coordinate system is always fixed at the circular cross section of the shaft and moves with the micro-displacement and micro-rotation of the shaft at that point.

[0106] When the gear rotor system is running, at any point P on the shaft section in the absolute coordinate system... S (0,r s ,θ s The displacement of the shaft component can be constructed using the Timoshenko beam element theory, as shown in the schematic diagram below. Figure 3 As shown in (c), Figure 3 (c) is a schematic diagram of the cross-section of the shaft element. The displacement of any point inside the established rotating shaft is first analyzed in the body coordinate system R2(x2,y2,z2). After establishing the displacement vector in the body coordinate system, it is extended to the absolute coordinate system R0(x0,y0,z0), which can be expressed as:

[0107]

[0108] Where R0 is the position vector of the origin O1 of the rotated coordinate system in the absolute coordinate system. (r s ,θ s ) represent any point P within the axis element. S The polar radius and angle at the point in the body coordinate system, x S The macroscopic length coordinates of the cross section containing the shaft element before deformation relative to the origin of the body coordinate system, u S ,v S ,w S This represents the instantaneous microscopic deformation disturbance at any point, corresponding to displacements in the radial, tangential, and axial directions, respectively. Figure 3 As shown in (a), Figure 3(a) is a schematic diagram of the degrees of freedom of deformation at any point on the axis element. T2 represents the micro-rotation angle in the body coordinate system. The directions of rotation are about the x-axis, about the y-axis, and about the z-axis, respectively. Figure 3 As shown in (b), Figure 3 Figure (b) shows a schematic diagram of the axis element model. The global coordinate transformation matrix generated relative to the absolute coordinate system is expressed as follows:

[0109]

[0110] The displacement of any point on the spokes in the absolute coordinate system can be modeled using Mindlin plate theory, as illustrated in the diagram below. Figure 3 As shown in (e), Figure 3 (e) is the front view of a spoke element, where point P is located on any spoke element. W (x W ,r W ,θ W After deformation, it is first calculated in the body coordinate system R2(x2,y2,z2) and can be represented as U. 2,W Then, extending further to the absolute coordinate system R0(x0,y0,z0), it can be expressed as:

[0111] U 0,W =R0+(R 1,SW +U 2,W T2)T1

[0112] Among them, U 2,W Represents any point P W In the body coordinate system, T1 represents the angular micro-motion in the rotating coordinate system. The resulting global coordinate transformation matrix to the absolute coordinate system is expressed as follows:

[0113]

[0114] Similarly u W ,v W ,w W , These represent the microscopic instantaneous deformation disturbance at any point, with the subscript W indicating that the displacement is the displacement of the spoke element, such as... Figure 3 As shown in (d), Figure 3 (d) is a three-dimensional view of the spoke unit. Where, u W ,v W ,w W This represents the minute transverse displacement at any point, corresponding to displacements in the radial, tangential, and axial directions, respectively. This represents the micro-rotation angle at any point, with the rotation directions being around the y-axis and around the z-axis, respectively. (Refer to...) Figure 3 The coordinate system of the spoke element in (f), Figure 3 (f) is a cross-sectional view of the spoke unit. θ W Represent any point P W The angle r between the spokes and the origin before deformation is given by the following formula: W Represent any point P W The polar radius x relative to the origin before the spoke deformation W Represent any point P W The macroscopic x-axis distance between the spokes and the origin of the coordinate system before the spokes deform. 1,SW This represents the coordinates of the origin of the body coordinate system within the rotating coordinate system. Due to elastic deformation, these coordinates will undergo slight changes. Therefore, R 1,SW It can be represented as:

[0115] R 1,SW =[w SW +x SW u SW v SW ]

[0116] The subscript SW indicates that the corresponding point is the point where the axis and the spoke are coupled, representing the influence of the change of the axis node on the spoke unit.

[0117] For the rim unit, its schematic diagram is as follows: Figure 3 As shown in (h), Figure 3 The middle (h) is the front view of the rim element. The position vector of the origin of the body coordinate system under the rotating coordinate system can be obtained in the same way:

[0118] R 1,SR =[w SR +x SR u SR v SR ]

[0119] It can be observed that the coupling points of the same component should be completely consistent, i.e., R 1,SW =R 1,SR Similarly, we can obtain any rim point P. R (x R ,r R ,θ R The position vector U in the body coordinate system R2(x2,y2,z2) after deformation 2,R Then, extending the coordinates of any point to the absolute coordinate system R0(x0,y0,z0) can be represented as the following position vector:

[0120] U 0,R =R0+(R 1,SR +U2,R T2)T1

[0121] Among them, U 2,R P represents any point on the rim element. R The coordinate position in the body coordinate system is expressed as follows:

[0122]

[0123] Among them, u R ,v R ,w R , These represent the microscopic instantaneous deformation disturbance at any point, with the subscript R indicating that the displacement is the displacement of the spoke element. Figure 3 As shown in (g), Figure 3 (g) is a three-dimensional view of the rim element. Where u R ,v R ,w R This represents the minute lateral displacement of any point on the rim, corresponding to displacements in the radial, tangential, and axial directions, respectively. This represents the micro-rotation angle at any point, with the rotation directions being about the x-axis, y-axis, and z-axis, respectively. R Represent any point P R The macroscopic x-axis distance between the rim and the origin before rim deformation, θ R Represent any point P R The angle r between the rim and the origin before rim deformation. R Represent any point P R The polar radius R between the rim and the origin before rim deformation. R Indicates the radius of the center axis of the rim, such as Figure 3 As shown in (i), Figure 3 (i) is a cross-sectional view of the rim element.

[0124] The position vector U of any point in the absolute coordinate system based on three unit types: shaft, spoke, and rim. 0,S U 0,W U 0,R The elastic deformation velocity vector at any point can be calculated using the following method:

[0125]

[0126] Where the subscripts C = S, W, R represent the structure of the shaft, spokes, and rim, and for the position vector R 1,C Corresponding to R respectively 1,S R 1,SW R 1,SR For ease of explanation, the subsequent time derivative calculations with respect to any physical quantity A will all use the […]. Method description.

[0127] For strain and stress, based on the Timoshenko straight beam model, the normal strain and shear strain of the shaft element can be obtained as follows:

[0128]

[0129] Therefore, the corresponding stress can be expressed as:

[0130] σ S,x =Eε S,x

[0131]

[0132] Where, σ S,x It is the normal stress (i.e., the first normal stress), τ S,xy ,τ S,xz For shear stress (i.e., the first shear stress), ε S,x For normal strain (i.e., the first normal strain), γ S,xy ,γ S,xz Let κ1 be the shear strain (i.e., the first shear strain), then κ1 = 6(1 + μ). 2 / (7+12μ+4μ 2 ) is the shear coefficient of the shaft element.

[0133] Based on the Mindlin plate element model, the normal strain and shear strain of the spoke element can be derived as follows:

[0134]

[0135] The meanings of each parameter are as follows:

[0136]

[0137] The corresponding stresses are as follows:

[0138]

[0139] Where, ε W,rr ,ε W,θθ For radial and tangential normal strains (i.e., the third normal strain), γ W,rθ ,γ W,θx ,γ W,rx For shear strain (i.e., the third shear strain), σ W,rr ,σ W,θθ The radial and tangential normal stresses (i.e., the third normal stress), τ W,rθ ,τ W,θx ,τ W,rx This is the shear stress (i.e., the third shear stress).

[0140] Based on Timoshenko's bending beam principle, the strain ε of the rim element is obtained. R,i ,χ R,i ,γ R,i ,ε R,o ,χ R,o ,γ R,o The expression is:

[0141]

[0142] and the stress σ of the rim element R,i ,v R,i ,τ R,i ,σ R,o ,v R,o ,τ R,o for:

[0143] σ R,i =Eε R,i ,v R,i =Eχ R,i ,τ R,i =κ1Gγ R,i

[0144] σ R,o =Eε R,o ,v R,o =Eχ R,o ,τ R,o =T R Gγ R,o

[0145] The subscripts i and o represent the in-plane and out-of-plane stress and strain of the rim element, respectively, and ε R,i and ε R,o χ represents the in-plane and out-of-plane normal strain (i.e., the second normal strain). R,i and χ R,o γ represents the in-plane and out-of-plane normal strain along the x-axis. R,i and γ R,o σ represents the in-plane and out-of-plane shear strain (i.e., the second shear strain). R,i and σ R,o Represents the in-plane and out-of-plane normal stresses (i.e., the second normal stress), v R,i and v R,o τ represents the in-plane and out-of-plane normal stress along the x-axis. R,i and τ R,o This represents the in-plane and out-of-plane shear stresses (i.e., the second shear stress).

[0146] Furthermore, based on the elastic deformation velocity vector, stress, and strain of each component, the kinetic and potential energy of each component's discrete element is derived using a discrete node element modeling method.

[0147] For gear shaft components, the shaft unit can be divided into N segments. S There are several small shaft segments, each with a length of L. S =L / N S Where L is the total length of the gear shaft. For the spoke unit, it can be divided into M segments radially using equal radii and equal angles. W The area is divided equally, therefore the radius of each spoke unit is R. W =(R W,o -R W,i ) / M W , where R W,o and R W,i These are the inner and outer diameters of the spokes, respectively, divided into N angles. W The area is divided equally, therefore the angle of each spoke unit is divided into θ. W =2π / M W Therefore, the spoke components can be divided into M W ×N W N elements. For the rim element, the rim is divided into N sections using an equal-angle method. R There are 10 units, therefore the angle of each rim unit is divided into θ. R =2π / N R A schematic diagram of each grid cell division and grid size is shown below. Figure 2 As shown.

[0148] Therefore, based on the velocities (i.e., elastic deformation velocity vectors) of any point on the shaft, spokes, and rim obtained above, applying the velocity integral to different discrete elements yields the general kinetic energy expression for the shaft element:

[0149]

[0150] In the formula, the subscripts S, i, and p on the left side represent: S: axis element, i: the i-th discrete element, and p: the object of study is a pinion, respectively. Let ρ represent the velocity of the pinion shaft element. The kinetic energy expression of the discrete shaft element is obtained by integrating the square of the velocity over the entire volume domain of the element. ρ represents the density.

[0151] Similarly, the kinetic energy expressions for the spoke element and the rim element are as follows:

[0152]

[0153] Similar to coaxial elements, the subscripts W, i, j, p on the left side of the spokes represent W: spoke element, i: the i-th spoke element mesh, j: the j-th mesh element in one ring, and p: the object of study is a small gear, respectively. This represents the velocity of the pinion spoke unit, H. W This indicates the width of the spokes.

[0154] The subscripts R, i, p on the left side of the formula for the corresponding rim element represent R: rim element, i: the i-th rim element mesh, and p: the object of study is a small gear, respectively; This represents the velocity of the pinion rim unit, H. R B represents the width of the rim. R This indicates the thickness of the rim.

[0155] After solving for the kinetic energy, the expressions for normal stress and shear stress on the shaft, spokes, and rim are then solved based on the stress and strain expressions.

[0156] The expression for the strain energy of a shaft element is:

[0157]

[0158] The parameters in the formula are calculated in the strain formula of the shaft element.

[0159] Similarly, the strain energy expression for the elements of the spokes and rims is:

[0160]

[0161] Based on the above methods for solving the kinetic and strain energies of individual units, the overall kinetic and potential energies of the shaft, spokes, and rim are obtained by summing them up. The overall kinetic and strain energies of the shaft, spokes, and rim are shown in Table 1.

[0162] Table 1. Overall kinetic and strain energies of the shaft, spokes, and rim.

[0163]

[0164] To avoid loss of generality, the subscript p in the table is replaced with (k = p, g) to represent the two gears, large and small, in the gear pair.

[0165] The contribution of boundary condition constraints to potential energy is analyzed, the potential energy contributed by constraints such as bearings and element coupling to the system is established, and the coupling relationships between elements and between elements and the outside are proposed.

[0166] Considering that the strain energy of currently established flexible component systems is expressed under unconstrained conditions, practical applications involve at least bearing constraints, gear shaft and spoke constraints, and spoke and rim constraints. Therefore, it is necessary to consider the impact of these constraints on the system energy. Starting with bearing constraints, which restrict the degrees of freedom of the corresponding nodes, all degrees of freedom except for the x-axis (which allows rotation) are restricted. Therefore, the bearing stiffness k can be used. Bw ,kBu ,k Bv ,k By ,k Bz The motion of the corresponding nodes is constrained in the form of [formula missing]. The bearing stiffness can be found in a manual or calculated using existing technology; this embodiment does not describe it in detail. The bearings are defined as being installed at both ends of the gear shaft, with the bearing position being x. S =0,x S =L S At this point, the potential energy of the bearing boundary condition is defined using the potential energy method as follows:

[0167]

[0168] Regarding the coupling relationship between the gear shaft and the spokes, since the elastic displacements of each degree of freedom of the spokes are defined in the body coordinate system, the rigid connection between the shaft and the spokes can be defined as the elastic displacement of the inner ring of the spokes being 0, i.e.: t W =u W ,v W ,w W , Among them, R S The radius of the representative shaft unit is also the size of the inner ring of the spoke. The micro-rotation angle at any point is represented by the rotation direction around the x-axis. To constrain the displacement and rotation of the inner spoke element to zero, the multiplication method can be used, which involves multiplying the displacement of the degree of freedom by a large number C. The value of C is several orders of magnitude larger than the conventional stiffness, C∈

[10] . 13 10 20 The symbol ] indicates that the stiffness is extremely high at this point, achieving the effect of rigid constraint. The constraint here can be expressed in terms of potential energy (i.e., the first constraint potential energy):

[0169]

[0170] Similarly, a similar approach can be used to constrain the spoke and rim elements. However, in this case, the elastic displacement of the outer ring of the spoke in the body coordinate system is not zero, but rather the relative displacement with respect to the rim node is zero, i.e.: t R =u R ,v R ,w R , Using the same multiplication method, this constraint can be expressed in terms of potential energy (i.e., the second constraint potential energy) as follows:

[0171]

[0172] Finally, the constraint potential energy between shaft elements needs to be defined. Since the shaft element is divided into independent small shaft ends, a rigid connection between the shaft ends needs to be defined, resulting in the six-degree-of-freedom elastic displacements at the end point of the previous shaft end and the beginning point of the next shaft segment being completely consistent. t S =u S ,v S ,w S , The potential energy (i.e., the third constraint potential energy) of the rigid constraint between the shaft ends is obtained by defining the large number method:

[0173]

[0174] At this point, all boundary conditions and constraints have been defined. The potential energy method is used to record all constraints in the form of energy, preparing for the subsequent determination of the governing equations using the Lagrange equations.

[0175] Taking the initial and rotating working conditions as examples, the meshing points of the large and small gears in the initial state and the deformation state after meshing are derived. The vector coordinates of the transmission error in the initial position and the deformation state after meshing are also derived. The strain of the transmission error and the potential energy generated by meshing are further calculated.

[0176] In traditional rigid wheel models, the wheel is treated as a single unit, while this model considers the flexible deformation of the gear. (Refer to...) Figure 4 , Figure 4 (a) is a schematic diagram illustrating the solution for deformation and transmission error of the gear in its initial state. Figure 4 (a) shows a schematic diagram of the deformation and transmission error calculation under gear meshing conditions. A method based on meshing potential energy is used to incorporate the energy of the meshing effect into the overall system, calculating the meshing potential energy by the change in position of the meshing point before and after deformation. First, the meshing potential energy at the initial position is calculated. The vector coordinates of the meshing point of the driving gear in the absolute coordinate system are:

[0177] U 0,m,p =R 0,p +(R 1,SR,p +U 2,R,p T 2,p )T 1,p

[0178] The vector coordinates of the meshing point in the body coordinate system are Figure 4 (a) can be expressed as U 2,R,p Specifically, it can be expressed as:

[0179]

[0180] The corresponding micro-motion coordinate transformation matrix T in the body coordinate system 1,p T2,p for:

[0181] T 2,p =T R,x,p T R,y,p T R,z,p

[0182]

[0183] The rotational speed of the pinion is Ω. p The corresponding rotational speed of the large gear is Ω. p =z p Ω p / z g , z p and z g R represents the number of teeth on the pinion and gear, respectively. 0,p R is the vector from the origin of the fixed coordinate system to the origin of the rotating coordinate system. 1,SR,p U is the vector from the origin of the rotating coordinate system to the origin of the body coordinate system. 2,R,p This is the vector from the origin of the body coordinate system to the meshing point. The coordinate transformation matrix T 2,p Let T be the matrix formed by the micro-rotations of the nodes containing the origin of the body coordinate system, and let T be the coordinate transformation matrix. 1,p The matrix is ​​formed by the micro-rotations of the nodes containing the origin of the rotating coordinate system. Since the angular displacement is relatively small, the parameters in the matrix can be linearized. Based on the above method, the vector coordinates of the large gear in the absolute coordinate system can be calculated as follows: U 0,m,g =R 0,g +(R 1,SR,g +U 2,R,g T 2,g )T 1,g Simply change the subscript p to g to complete the calculation using the same formula. After obtaining the vector coordinates of the two meshing points, the vector coordinates of the transmission error can be calculated: δ0 = U 0,m,p -U 0,m,g δ0 represents the dynamic propagation error at the initial moment.

[0184] At the next moment Δt, the component deformation, the coordinate transformation of the previous moment, and the change of the meshing point are as follows: Figure 4 As shown in (b), the position vector of the meshing point at the new moment is U. 2,R,p,1 and U 2,R,g,1 Each component undergoes deformation. Simultaneously, the large gear and small gear rotate by a certain angle, Ω respectively. p Δt and Ω g Δt. Therefore, the transmission error at this moment can be denoted as δ1 = U. 0,m,p,1 -U 0,m,g,1The difference Δδ between the transmission error at the previous moment and at this moment is calculated as follows:

[0185] Δδ=δ1-δ0=[x m y m z m ]

[0186] The data are as follows:

[0187] x m =r m1 q m ,y m =r m2 q m ,z m =r m3 q m

[0188] r m1 =[r p,m1 r g,m1 ],r m2 =[r p,m2 r g,m2 ]

[0189] r m3 =[r p,m3 r g,m3 ],q m =[q p,m q g,m ] T

[0190]

[0191] r p,m1,out =[0 0 0 1 0-H p / 2] T ,r g,m1,out =[0 0 0 -1 0H g / 2] T

[0192]

[0193] r p,m1,in =r g,m1,in =r p,m2,out =r g,m2,out =r p,m3,out =r g,m3,out =[0 0 0 0 0 0] T

[0194] Among them, R g,b ,R p,bThe base circle radii of the driven wheel and driving wheel are respectively represented by g, p, and b, which represent the driven wheel, driving wheel, and base circle, respectively. p H g These represent the width dimensions of the rim, Ω. p ,Ω g ,t represent the rotational speed and time of the driving wheel and driven wheel, respectively, θ p ,θ g These represent the angular coordinates of the meshing point of the driving wheel and the driven wheel, respectively.

[0195] Matrix q p,in q p,out q g,in q g,out Let q represent the in-plane and out-of-plane vibration micro-displacement matrices of the driving gear and the driven gear, respectively. p,m q g,m Let represent the coupled displacement and micro-displacement matrices of the driving wheel and driven wheel, respectively, and q m For matrix q p,m and q g,m The sum represents all displacement information at the meshing point of the driving and driven wheels. Matrix r m1 r m2 r m3 The submatrices of the r series are directional projection matrices, which project the micro-displacement at the meshing node onto the direction of the meshing line.

[0196] Therefore, the elastic potential energy P generated by the meshing of gear teeth m (t) can be represented as:

[0197]

[0198] Where, k m (t) represents the meshing stiffness at time t.

[0199] Introducing the above kinetic and potential energies into the dynamic system, a gear rotor dynamic model considering the wheel's flexibility is formed. The overall kinetic energy (i.e., total kinetic energy) K and the overall potential energy (i.e., total potential energy) P can be expressed as:

[0200] K = K S,p +K W,p +K R,p +K S,g +K W,g +K R,g

[0201] P = P S,p +P W,p +P R,p +P S,g +P W,g +P R,g +Pbearing +P SS +P SW +P WR +P m (t)

[0202] The above description is not a simple addition of kinetic energy, but rather matrix assembly.

[0203] Substituting the total kinetic energy and total potential energy into the Lagrange equation:

[0204]

[0205] Where L = KP is the Lagrange operator, q is the degree of freedom of each displacement, including u, v, w, x, y and z, and Q is the generalized force of each type.

[0206] The governing equations can be obtained through calculation:

[0207]

[0208] Where M is the mass matrix, C g and C d These are the Coriolis acceleration matrix and the Rayleigh damping matrix, respectively. K(t) is the overall stiffness matrix, which includes the structural stiffness of each component and the meshing stiffness between gears. Q internal and Q external These represent the internal centrifugal force load and the external input load, respectively.

[0209] Compared with the prior art, the technical solution of this embodiment has the following advantages:

[0210] 1. The technical solution in this embodiment calculates the elastic deformation velocity vector, stress, and strain of the shaft unit, rim unit, and spoke unit, and then calculates the corresponding kinetic and potential energy of the shaft unit, rim unit, and spoke unit, thereby calculating the overall kinetic and potential energy of the gear rotor system. This comprehensively considers the flexibility of the wheel body and the transmission shaft, which can better improve the dynamic modeling of the gear rotor system, making the constructed gear rotor system dynamic model stable and reliable.

[0211] 2. The technical solution of this embodiment takes into account that the kinetic energy and strain energy of the flexible component system currently established are energy expressions under unconstrained conditions. In actual work, there are at least bearing constraints, gear shaft-spoke constraints, and spoke-rim constraints, etc. Therefore, the influence of these constraints on the system energy is considered, which makes the constructed gear rotor system dynamic model more in line with the actual situation and improves the accuracy.

[0212] Reference Figure 5This application also provides a modeling system for the dynamics of a gear rotor system. The system includes a first calculation unit 100, a data differentiation unit 200, a second calculation unit 300, a third calculation unit 400, a fourth calculation unit 500, a fifth calculation unit 600, a sixth calculation unit 700, a data summation unit 800, and a modeling determination unit 900, wherein:

[0213] The first calculation unit 100 is used to calculate the first displacement vector, the second displacement vector, and the third displacement vector of each of the shaft unit, the rim unit, and the spoke unit at any point in the absolute coordinate system when the gear rotor system is moving.

[0214] The data differentiation unit 200 is used to differentiate the first displacement vector, the second displacement vector, and the third displacement vector to obtain the first elastic deformation velocity vector of the shaft element, the second elastic deformation velocity vector of the rim element, and the three elastic deformation velocity vectors of the spoke element.

[0215] The second calculation unit 300 is used to calculate the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit.

[0216] The third calculation unit 400 is used to calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector.

[0217] The fourth calculation unit 500 is used to calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress.

[0218] The fifth calculation unit 600 is used to calculate the bearing boundary condition potential energy based on the bearing stiffness corresponding to multiple degrees of freedom of the shaft unit, and to calculate the elastic potential energy formed by gear meshing based on the vector coordinates of the pinion and gear in the absolute coordinate system.

[0219] The sixth calculation unit 700 is used to calculate the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft unit, the spoke unit and the spoke unit by analyzing the coupling constraint relationship between the shaft unit, the rim unit and the spoke unit.

[0220] The data summation unit 800 is used to add the first kinetic energy, the second kinetic energy and the third kinetic energy corresponding to the pinion and the gear respectively to obtain the total kinetic energy, and to add the first strain energy, the second strain energy and the third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy and the elastic potential energy formed by gear meshing to obtain the total potential energy.

[0221] The modeling and determination unit 900 is used to substitute the total kinetic energy and total potential energy into the Lagrange equations for calculation to obtain the control equations, thereby realizing the dynamic modeling of the gear rotor system.

[0222] It should be noted that since the modeling system for gear rotor system dynamics in this embodiment is based on the same inventive concept as the modeling method for gear rotor system dynamics described above, the corresponding content in the method embodiment is also applicable to this system embodiment, and will not be described in detail here.

[0223] This application also provides an electronic device, including: at least one control processor and a memory for communicatively connecting to at least one control processor.

[0224] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0225] The non-transient software program and instructions required to implement the gear rotor system dynamics modeling method of the above embodiments are stored in memory. When executed by the processor, the gear rotor system dynamics modeling method of the above embodiments is executed, for example, the method described above is executed. Figure 1 The method steps S100 to S900.

[0226] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0227] This application also provides a computer-readable storage medium storing computer-executable instructions. These instructions, when executed by one or more control processors, cause the processors to perform a gear-rotor system dynamics modeling method described in the above-described method embodiments. For example, they can execute the above-described... Figure 1 The functions of steps S100 to S900 in the method.

[0228] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0229] The above is a detailed description of the preferred embodiments of this application. However, the embodiments of this application are not limited to the above-described implementation methods. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the embodiments of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of the embodiments of this application.

Claims

1. A method for modeling the dynamics of a gear-rotor system, characterized in that, The method includes: When the gear rotor system moves, calculate the first displacement vector, second displacement vector, and third displacement vector of each of the shaft unit, rim unit, and spoke unit at any point in the absolute coordinate system; Differentiating the first displacement vector, the second displacement vector, and the third displacement vector yields the first elastic deformation velocity vector of the shaft unit, the second elastic deformation velocity vector of the rim unit, and the third elastic deformation velocity vector of the spoke unit. Calculate the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit; Based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector, calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, respectively. Based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress, calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, respectively. Based on the bearing stiffness corresponding to the multiple degrees of freedom of the shaft unit, the bearing boundary condition potential energy is calculated, and based on the vector coordinates of the pinion and the gear in the absolute coordinate system, the elastic potential energy formed by gear meshing is calculated. By analyzing the coupling constraint relationship between the shaft unit, the rim unit, and the spoke unit, the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft units are calculated. The total kinetic energy is obtained by adding the first kinetic energy, the second kinetic energy, and the third kinetic energy corresponding to the pinion and the gear respectively. The total potential energy is obtained by adding the first strain energy, the second strain energy, and the third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy, and the elastic potential energy formed by the meshing of the gear teeth. The total kinetic energy and the total potential energy are substituted into the Lagrange equations for calculation to obtain the control equations, thereby realizing the dynamic modeling of the gear rotor system.

2. The modeling method for the dynamics of a gear-rotor system according to claim 1, characterized in that, The calculation of the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit includes: Using the Timoshenko straight beam model, the first strain and first stress of the shaft element are calculated. The second strain and second stress of the rim element are calculated using the Timoshenko bending beam principle. The third strain and third stress of the spoke element are calculated using the Mindlin plate element model.

3. The modeling method for the dynamics of a gear-rotor system according to claim 1, characterized in that, The calculation of the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to each of the pinion and the gear, based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector, includes: Based on the first elastic deformation velocity vector, calculate the first kinetic energy of the shaft unit corresponding to each of the small gear and the large gear: Based on the second elastic deformation velocity vector, calculate the second kinetic energy of the rim unit corresponding to each of the pinion and the gear: Based on the third elastic deformation velocity vector, calculate the third kinetic energy of the spoke unit corresponding to each of the pinion and the gear: Among them, K S,i,k Let S represent the first kinetic energy of the i-th discrete unit, S represent the shaft element, k = p represent the small gear, k = g represent the large gear, ρ represent the density, and R represent the density. S L represents the radius of the shaft element. s,i L represents the length of the i-th axis segment. s,i-1 This represents the length of the (i-1)th axis segment. Let r denote the derivative of the first elastic deformation velocity vector, T denote the transpose, and r S,k The x-axis represents the polar radius of any point within the axis element in the body coordinate system. S,k θ represents the macroscopic length coordinates of the section containing the shaft element before deformation relative to the origin of the body coordinate system. S,k The angle of any point within the axis element in the body coordinate system is represented by K. R,i,k Let θ represent the second kinetic energy of the i-th rim element mesh, R represent the rim element, and θ represent the second kinetic energy of the rim element mesh. R,i,k H represents the angle between any point on the i-th rim element and the origin before rim deformation. R B represents the width of the rim. R Indicates the thickness of the rim. R represents the derivative of the second elastic deformation velocity vector. R,k The radius r represents the central axis radius of the rim element. R,k The polar radius x represents the radius of any point on the rim element before rim deformation relative to the origin. R,k θ represents the macroscopic x-axis distance between any point on the rim element before rim deformation and the origin of the coordinate system. R,k K represents the angle between any point on the rim element and the origin before rim deformation. W,i,j,k Let θ represent the third kinetic energy of the j-th grid cell in the i-th spoke cell, W represent the spoke cell, and θ represent the third kinetic energy of the j-th grid cell in the i-th spoke cell. W,j,k R represents the angle between any point on the j-th spoke mesh element and the origin before the rim deformation. W,i,k Let represent the radius of the i-th ring of spokes. The derivative of the third elastic deformation velocity vector, r W,k The polar radius x represents the radius of any point on the spoke element relative to the origin before the spoke deformation. W,k θ represents the macroscopic x-axis distance between any point on the spoke element and the origin of the coordinate system before the spoke deformation. W,k This represents the angle between any point on the spoke unit and the origin of the coordinate system before the spoke deforms.

4. The modeling method for the dynamics of a gear-rotor system according to claim 3, characterized in that, The calculation of the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to each of the pinion and the gear, based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress, includes: Based on the first strain and the first stress, calculate the first strain energy of the shaft unit corresponding to each of the pinion and the gear: Based on the second strain and the second stress, calculate the second strain energy of the rim unit corresponding to each of the pinion and the gear: Based on the first strain and the first stress, calculate the third strain energy of the spoke unit corresponding to each of the pinion and the gear: Among them, P S,i,k R represents the first strain energy of the shaft element. s,k σ represents the radius of the shaft element. S,x,k ε represents the first normal stress of the shaft element. S,x,k τ represents the first normal strain of the shaft element. S,xy,k and τ S,xz,k γ represents the first shear stress of the shaft element along the xy and xz directions, respectively. S,xy,k and γ S,xz,k P represents the first shear strain of the shaft element along the xy and xz directions, respectively. R,i,k ε represents the second strain energy of the rim element. R,i and ε R,o χ represents the second normal strain in-plane and out-of-plane of the rim element, respectively. R,i and χ R,o γ represents the in-plane and out-of-plane normal strain along the x-axis of the rim element, respectively. R,i and γ R,o σ represents the second shear strain in and out of the plane of the rim element, respectively. R,i and σ R,o V represents the second normal stress in and out of the plane of the rim element, respectively. R,i and v R,o Let τ represent the in-plane and out-of-plane normal stresses along the x-axis of the rim element, respectively. R,i and τ R,o P represents the second shear stress in and out of the plane of the rim element, respectively. W,i,j,k ε represents the third strain energy of the spoke unit. W,rr,k ,ε W,θθ,k γ represents the third normal strain in the radial and tangential directions of the spoke element, respectively. W,rθ,k ,γ W,θx,k ,γ W,rx,k σ represents the third shear strain of the spoke element in the rθ, θx, and rx planes, respectively. W,rr,k ,σ W,θθ,k τ represents the third normal stress in the radial and tangential directions of the spoke unit, respectively. W,rθ,k ,τ W,θx,k ,τ W,rx,k These represent the third shear stress of the spoke element in the rθ, θx, and rx planes, respectively.

5. The modeling method for the dynamics of a gear-rotor system according to claim 1, characterized in that, The step of calculating the bearing boundary condition potential energy based on the bearing stiffness corresponding to multiple degrees of freedom of the shaft element includes: Among them, P bearing k represents the potential energy of the bearing boundary conditions. Bw ,k Bu ,k Bv ,k By ,k Bz These represent the bearing stiffness in different degrees of freedom, u S ,v S ,w S These represent the microscopic instantaneous deformation disturbances of any point on the shaft element in the radial direction u, tangential direction v, and axial direction w, respectively. Let x represent the micro-rotation angles about the y-axis and about the z-axis, respectively. S L represents the macroscopic length coordinate of the section containing the shaft element before deformation relative to the origin of the body coordinate system. S This indicates the length of each shaft segment. Indicates in x S The micro-displacement of the shaft element at the position of length 0 along the w direction. Indicates in x S The micro-displacement of the shaft element at the position of length 0 along the u direction. This represents the minute displacement of the shaft element along the v direction at the position where the v length is 0. Indicates in x S The micro-rotational displacement of the shaft element at the position of length 0 along the y-axis. Indicates in x S The micro-rotational angular displacement of the shaft element at the position with length 0 along the z-axis. Indicates in x S Length L S The micro-displacement of the shaft element along the w direction at the given position. Indicates in x S Length L S The micro-displacement of the shaft element along the u-direction at position. This indicates that when v is of length L S The minute displacement of the shaft element along the v direction at the given position. Indicates in x S Length L S The micro-rotational displacement of the shaft element along the y-axis at the position. Indicates in x S Length L S The micro-rotation angular displacement of the shaft element along the z-axis at the location.

6. The method for modeling the dynamics of a gear-rotor system according to claim 1, characterized in that, The step of calculating the elastic potential energy generated by tooth meshing based on the vector coordinates of the pinion and the gear in the absolute coordinate system includes: Calculate the first vector coordinate of the small gear in the absolute coordinate system at the initial moment, and calculate the second vector coordinate of the large gear in the absolute coordinate system at the initial moment; Calculate the dynamic propagation error at the initial moment based on the first vector coordinates and the second vector coordinates; Calculate the third vector coordinate of the small gear in the absolute coordinate system at the next moment, and calculate the fourth vector coordinate of the large gear in the absolute coordinate system at the next moment; Calculate the dynamic transmission error at the next moment based on the third vector coordinate and the fourth vector coordinate; The difference in transmission error is obtained by subtracting the dynamic transmission error at the initial moment from the dynamic transmission error at the next moment. Based on the difference in transmission error, the elastic potential energy generated by gear meshing is calculated.

7. The method for modeling the dynamics of a gear-rotor system according to claim 1, characterized in that, The calculation of the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft units includes: Calculate the first constraint potential energy between the shaft unit and the spoke unit: Calculate the second constraint potential energy between the rim unit and the spoke unit: Calculate the third constraint potential energy between the shaft elements: Among them, P SW Let P represent the first constraint potential energy. WR Let P represent the second constraint potential energy. SS Let C represent the third constraint potential energy, and C represent a large number. This indicates that each degree of freedom of the spoke element is within a radius of R. S The micro-lateral displacement with an angle of 0 to 2π, r W R represents the polar coordinate radius of any point on the spoke element before the spoke deformation relative to the origin. S θ represents the radius of the axis element. W This represents the angle between any point on the spoke element and the origin of the coordinate system before the spoke deforms. This indicates that each degree of freedom of the spoke element is within a radius of R. S The micro-rotation angle is between 0 and 2π. This indicates that each transverse degree of freedom of the spoke element is within a radius of R. W The angle is θ R The slight lateral movement of the position, This represents the micro-lateral displacement of the rim element at the coordinate angle corresponding to the spoke element. This indicates that each rotational degree of freedom of the spoke element is within a radius of R. W The angle is θ R The slight rotation of the position, R represents the micro-rotation angle of the rim element in the coordinate angle corresponding to the spoke element. W θ represents the radius of the spoke unit. R t represents the angle of the rim element. S The x represents the micro-lateral displacement of each degree of freedom of the axis element. S L represents the macroscopic length coordinate of the section containing axis element S before deformation relative to the origin of the body coordinate system. S x represents the length of each axis segment. S+1 This represents the macroscopic length coordinates of the section containing shaft element S+1 before deformation relative to the origin of the body coordinate system, rot. S This represents the micro-rotation angle of each degree of freedom of the axis element.

8. A modeling system for the dynamics of a gear-rotor system, characterized in that, The system includes: The first calculation unit is used to calculate the first displacement vector, second displacement vector and third displacement vector of each of the shaft unit, rim unit and spoke unit at any point in the absolute coordinate system when the gear rotor system moves. The data differentiation unit is used to differentiate the first displacement vector, the second displacement vector, and the third displacement vector to obtain the first elastic deformation velocity vector of the shaft unit, the second elastic deformation velocity vector of the rim unit, and the three elastic deformation velocity vectors of the spoke unit. The second calculation unit is used to calculate the first strain and first stress of the shaft unit, the second strain and second stress of the rim unit, and the third strain and third stress of the spoke unit; The third calculation unit is used to calculate the first kinetic energy of the shaft unit, the second kinetic energy of the rim unit, and the third kinetic energy of the spoke unit corresponding to the pinion and the gear, respectively, based on the first elastic deformation velocity vector, the second elastic deformation velocity vector, and the third elastic deformation velocity vector. The fourth calculation unit is used to calculate the first strain energy of the shaft unit, the second strain energy of the rim unit, and the third strain energy of the spoke unit corresponding to the pinion and the gear, respectively, based on the first strain and the first stress, the second strain and the second stress, and the third strain and the third stress. The fifth calculation unit is used to calculate the bearing boundary condition potential energy based on the bearing stiffness corresponding to the multiple degrees of freedom of the shaft unit, and to calculate the elastic potential energy formed by gear meshing based on the vector coordinates of the pinion and the gear in the absolute coordinate system. The sixth calculation unit is used to calculate the first constraint potential energy between the shaft unit and the spoke unit, the second constraint potential energy between the rim unit and the spoke unit, and the third constraint potential energy between the shaft unit by analyzing the coupling constraint relationship between the shaft unit, the rim unit and the spoke unit. The data summation unit is used to add the first kinetic energy, the second kinetic energy, and the third kinetic energy corresponding to the pinion and the gear respectively to obtain the total kinetic energy, and to add the first strain energy, the second strain energy, and the third strain energy corresponding to the pinion and the gear respectively, the bearing boundary condition potential energy, the first constraint potential energy, the second constraint potential energy, the third constraint potential energy, and the elastic potential energy formed by the meshing of the gear teeth to obtain the total potential energy. The modeling and determination unit is used to substitute the total kinetic energy and the total potential energy into the Lagrange equation for calculation to obtain the control equation, so as to realize the dynamic modeling of the gear rotor system.

9. An electronic device, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform the modeling method for the dynamics of the gear rotor system as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the modeling method for the dynamics of a gear-rotor system as described in any one of claims 1 to 7.

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