Dynamic Modeling Methods for Rigid-Flexible Coupled Planetary Gear and Rotor Systems

Abstract

This invention provides a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system, comprising: constructing a gear ring element model using a shell element model; establishing a finite element model of the input shaft and planet carrier; establishing a meshing model of the sun gear and planet gears; establishing a meshing model of the planet gears and gear ring; coupling the gear ring element model, the finite element model of the input shaft and planet carrier, the meshing model of the sun gear and planet gears, and the meshing model of the planet gears and gear ring to obtain a dynamic model of the planetary gear system, which considers both the flexibility of the input shaft, planet carrier, and gear ring, and the influence of gear meshing and planet gear revolution.

Description

Technical Field

[0001] This invention relates to the field of dynamic modeling technology, and more particularly to a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system. Background Technology

[0002] Planetary gears, as a common transmission mechanism, are widely used in various mechanical systems. Their dynamic modeling is the foundation for understanding their working principle and design optimization.

[0003] Compared to the lumped mass model method, the rigid-flexible coupling dynamic model can take into account the influence of flexible components in the planetary gear system, which typically include flexible gear rings and flexible planetary carriers, thus more accurately describing the dynamic response of actual engineering systems.

[0004] In view of this, the present invention provides a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system. Summary of the Invention

[0005] To address the shortcomings of existing dynamic modeling techniques, this invention provides a rigid-flexible coupled dynamic modeling method for planetary gear and rotor systems. The invention primarily involves establishing a gear ring element model, finite element models of the input shaft and planet carrier, a meshing model of the sun gear and planet gears, and a meshing model of the planet gears and gear ring. Finally, these models are coupled to obtain a dynamic model of the planetary gear system, which considers both the flexibility of the input shaft, planet carrier, and gear ring, as well as the effects of gear meshing and planetary gear revolution.

[0006] The technical means employed in this invention are as follows:

[0007] This invention provides a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system, comprising:

[0008] A gear ring element model is constructed using a shell element model, the gear ring element model including the mass matrix and the stiffness matrix of the gear ring element model;

[0009] Establish finite element models of the input shaft and planetary carrier, wherein the finite element models of the input shaft and planetary carrier include the mass matrix and the stiffness matrix of the finite element models of the input shaft and planetary carrier;

[0010] A meshing model of the sun gear and planet gears is established, which includes the mass matrix and stiffness matrix of the meshing model of the sun gear and planet gears.

[0011] Establish a planetary gear and ring gear meshing model, which includes the mass matrix and stiffness matrix of the planetary gear and ring gear meshing model;

[0012] The mass matrix of the gear ring element model, the stiffness matrix of the gear ring element model, the mass matrix of the finite element model of the input shaft and planet carrier, the stiffness matrix of the finite element model of the input shaft and planet carrier, the mass matrix of the meshing model of the sun gear and planet gears, the stiffness matrix of the meshing model of the sun gear and planet gears, the mass matrix of the meshing model of the planet gear and gear ring, the stiffness matrix of the meshing model of the planet gear and gear ring, and the total damping matrix are coupled to obtain the dynamic model of the planetary gear system.

[0013] The dynamic equations are solved using the Newmark method. In each substep, the meshing matrix is ​​transformed according to the angle rotated by the planetary carrier and the modal contribution coefficient, and the dynamic response of the system is finally obtained.

[0014] Furthermore, before coupling, the mass matrix and the stiffness matrix are subjected to dimension reduction processing and calculated in the following manner:

[0015]

[0016]

[0017] in, Let M be the mass matrix after dimensional reduction. Let K be the stiffness matrix after dimensional reduction, and S be the transformation matrix.

[0018] Furthermore, the total damping matrix is ​​calculated as follows:

[0019]

[0020]

[0021]

[0022] Where C is the total damping matrix, C α C is the mass-related Ruili damping coefficient. β C is the Ruili damping coefficient related to stiffness. spi Let c be the damping matrix of the meshing model of the sun gear and planet gears. spi C is the damping coefficient of the meshing model of the sun gear and planet gears. pri Let c be the damping matrix of the planetary gear and ring gear meshing model. pri v is the damping coefficient of the planetary gear and ring gear meshing model. spiand v pri Let M' be the projection vector, M' be the set of combinations of the mass matrices, and K' be the set of combinations of the stiffness matrices.

[0023] Furthermore, the mass matrix of the shell element model is calculated as follows:

[0024]

[0025] in, Let ρ be the mass matrix of the shell element model, ρ be the density of the gear ring, N be the element shape function, J be the Jacobian matrix, and ξ, η, and ζ be the parametric coordinates of the shell element model.

[0026] Furthermore, the stiffness matrix of the shell element model is calculated as follows:

[0027]

[0028] in, Let B be the stiffness matrix of the shell element model, D be the strain matrix, J be the constitutive matrix, and ξ, η, and ζ be the parametric coordinates of the shell element model.

[0029] Furthermore, the establishment of the finite element model of the input shaft and planetary carrier includes:

[0030] Obtain the geometric drawings of the input shaft and planetary carrier, input the geometric drawings into the finite element analysis software, and the finite element analysis software outputs the mass matrix and stiffness matrix of the finite element model of the input shaft and planetary carrier.

[0031] Furthermore, the stiffness matrix of the sun gear and planet gear meshing model is calculated as follows:

[0032]

[0033] Among them, K spi Let k be the stiffness matrix of the meshing model of the sun gear and planet gears. spi v represents the meshing stiffness of the sun gear and planet gears. spi Let be the projection vector of the gear pair of the i-th sun gear and planet gear along the meshing line.

[0034] Furthermore, the stiffness matrix of the planetary gear and ring gear meshing model is calculated as follows:

[0035]

[0036] Among them, K pri Let k be the stiffness matrix of the planetary gear and ring gear meshing model. priv represents the meshing stiffness of the planetary gear and the ring gear. pri Let be the projection vector of the gear pair of the i-th planetary gear and the ring gear along the meshing line.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] The rigid-flexible coupled planetary gear and rotor system dynamics modeling method provided by this invention constructs a gear ring element model using shell elements, establishes finite element models of the input shaft and planet carrier, establishes meshing models of the sun gear and planet gears, and establishes meshing models of the planet gears and gear ring. Finally, these models are coupled to obtain a dynamic model of the planetary gear system. This method considers the flexibility of the input shaft, planet carrier, and gear ring, as well as the influence of gear meshing and planet gear revolution. The entire method has high computational efficiency and fills the gap in the current dynamics modeling of planetary gear and rotor systems that considers the rigid-flexible coupling of the flexible gear ring and planet gear revolution. It can provide a theoretical basis for the optimized design and vibration control of transmission systems. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a flowchart illustrating a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system provided by the present invention.

[0041] Figure 2 This is a schematic diagram of a gear ring.

[0042] Figure 3 This is a schematic diagram of the input shaft and planetary carrier.

[0043] Figure 4 This is a schematic diagram of the sun wheel and planetary wheels.

[0044] Figure 5 This is a schematic diagram of a planetary gear and a ring gear.

[0045] Figure 6 This is a schematic diagram of a planetary gear and rotor system.

[0046] Figure 7 This is a schematic diagram of the principal mode shape of the gear ring.

[0047] Figure 8 This is a schematic diagram of the tooth root circular vibration mode of the main mode of the gear ring.

[0048] Figure 9This is a schematic diagram of a gear-ring constrained mode shape.

[0049] Figure 10 A graph showing the contribution coefficients of the first 10 principal modes.

[0050] Figure 11 A graph showing the contribution coefficients of the first 10 constrained modes.

[0051] Figure 12 This is a schematic diagram of the first 10 modes of planetary gear vibration.

[0052] Figure 13 This is a graph showing the time-varying meshing stiffness of the sun gear and planet gears.

[0053] Figure 14 This is a graph showing the time-varying meshing stiffness of the planetary gear and the ring gear.

[0054] Figure 15 Simulation and experimental comparison figures are used to extract the time-domain and frequency-domain curves of the radial acceleration response of the gear ring at an input speed of 600 r / min.

[0055] Figure 16 Simulation and experimental comparison figures are used to extract the time-domain and frequency-domain curves of the radial acceleration response of the gear ring at an input speed of 1382 r / min. Detailed Implementation

[0056] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0057] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0058] Combination Figures 1 to 6 , Figure 1 This is a flowchart illustrating a dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system provided by the present invention. Figure 2 This is a schematic diagram of a gear ring. Figure 3 This is a schematic diagram of the input shaft and planetary carrier. Figure 4 This is a schematic diagram of the sun gear and planetary gears. Figure 5 This is a schematic diagram of a planetary gear and a ring gear. Figure 6 This is a schematic diagram of a planetary gear and rotor system, illustrating a specific embodiment of the rigid-flexible coupling planetary gear and rotor system dynamics modeling method provided by the present invention, including:

[0059] S1: The gear ring element model is constructed by using the shell element model. The gear ring element model includes the mass matrix and stiffness matrix of the gear ring element model.

[0060] S2: Establish the finite element model of the input shaft and planet carrier. The finite element model of the input shaft and planet carrier includes the mass matrix and stiffness matrix of the finite element model of the input shaft and planet carrier.

[0061] S3: Establish the meshing model of the sun gear and planet gears, which includes the mass matrix and stiffness matrix of the meshing model of the sun gear and planet gears;

[0062] S4: Establish the meshing model of the planetary gear and the ring gear, which includes the mass matrix and stiffness matrix of the planetary gear and the ring gear meshing model.

[0063] S5: The mass matrix of the gear ring element model, the stiffness matrix of the gear ring element model, the mass matrix of the input shaft and planet carrier finite element model, the stiffness matrix of the input shaft and planet carrier finite element model, the mass matrix of the sun gear and planet gear meshing model, the stiffness matrix of the sun gear and planet gear meshing model, the mass matrix of the planet gear and gear ring meshing model, the stiffness matrix of the planet gear and gear ring meshing model, and the total damping matrix are coupled to obtain the dynamic model of the planetary gear system;

[0064] S6: Solve the dynamic equations using the Newmark method. In each substep, perform coordinate transformation on the meshing matrix based on the angle rotated by the planetary carrier and the modal contribution coefficients to finally obtain the dynamic response of the system.

[0065] Understandably, by establishing a gear ring element model, a finite element model of the input shaft and planetary carrier, a meshing model of the sun gear and planetary gears, and a meshing model of the planetary gears and gear ring, and finally coupling these models to obtain a dynamic model of the planetary gear system, the method considers both the flexibility of the input shaft, planetary carrier, and gear ring, as well as the influence of gear meshing and planetary gear revolution. The entire method has high computational efficiency and fills the gap in the current dynamic modeling of planetary gear and rotor systems that considers the rigid-flexible coupling of the flexible gear ring and planetary gear revolution. It can provide a theoretical basis for the optimized design and vibration control of transmission systems.

[0066] In some optional embodiments, prior to coupling, the mass matrix and the stiffness matrix are reduced in dimension and calculated as follows:

[0067]

[0068]

[0069] in, Let M be the mass matrix after dimensional reduction. Let K be the stiffness matrix after dimensional reduction, and S be the transformation matrix.

[0070] Understandably, dimensionality reduction processing needs to be based on modal synthesis. The effectiveness and performance of modal synthesis largely depend on the construction of S. By reasonably selecting the basis, constructing S can reduce dimensionality while preserving the main features of the data as much as possible, thereby improving the efficiency and accuracy of data processing.

[0071] Taking the flexible gear ring as an example, since the gear ring is fixed to the box by bolts, it provides sufficient constraints. When selecting the base, the fixed interface modal synthesis method is adopted. When selecting the main node, only the bolt hole node is selected and the gear ring meshing point is ignored, thereby avoiding the interference of local deformation of the node on the calculation results.

[0072] When constructing S using the fixed-interface modal synthesis method, the modal coordinates of the principal and constraint modal sets are primarily based on the modal coordinates, which can be expressed as:

[0073] S=[φ f φ b ]

[0074]

[0075] Where, φ f The eigenvector of the dominant mode, φ b These are the eigenvectors of the constrained modes. is the eigenvector of the nth principal mode.

[0076] The displacement vector of a node in the gear ring element model can be expressed as:

[0077]

[0078] Where I is the identity matrix of the master node degrees of freedom, V is the slave node displacement vector, and F is the external force vector.

[0079] eigenvectors φ of constrained modes b Calculated as follows:

[0080]

[0081] Specifically, a flexible gear ring model is established based on the 3D CAD model. Then, the principal modal matrix and constraint modal matrix of the flexible gear ring are calculated and assembled into a coordinate transformation matrix. Finally, node i on the inner ring of the flexible gear ring is connected to the origin, and the angle between this connection and the x-axis is denoted as θ. i Let V(θ) be the projection of the unit vectors of the i-th degree of freedom of node into modal coordinates. i ), can be represented as:

[0082] V(θ i ) = I i S

[0083] Extract V(θ) corresponding to different nodes i i This yields a set of discretized V(θ) calculation results. In this embodiment, V(θ) is referred to as the modal coordinate contribution coefficient, and its internal structure can be expressed as:

[0084]

[0085] Wherein, any element within the matrix This represents the contribution of mode j to the unit force or torque in the direction a.

[0086] Before coupling, a transformation matrix is ​​constructed using the principal mode and constraint mode to reduce the matrix dimension and thus improve computational efficiency.

[0087] In some optional embodiments, the mass matrix set formed by coupling the mass matrix of the gear ring element model, the mass matrix of the finite element model of the input shaft and planet carrier, the mass matrix of the sun gear and planet gear meshing model, and the mass matrix of the planet gear and gear ring meshing model can be represented as:

[0088]

[0089] Among them, S in M is the transformation matrix for the input axis. in M is the mass matrix of the input axis. s Let S be the mass matrix of the sun gear.ring M is the transformation matrix of the gear ring. ring Let M be the mass matrix of the gear ring. p Let S be the mass matrix of the planetary gears. c M is the transformation matrix of the planetary carrier. c This is the mass matrix of the planet carrier.

[0090] The stiffness matrix set formed by coupling the stiffness matrix of the gear ring element model, the stiffness matrix of the input shaft and planet carrier finite element model, the stiffness matrix of the sun gear and planet gear meshing model, and the stiffness matrix of the planet gear and gear ring meshing model can be represented as:

[0091]

[0092] Among them, K in K is the stiffness matrix of the input shaft. s Let K be the stiffness matrix of the sun gear. ring Let K be the stiffness matrix of the gear ring. p K is the stiffness matrix of the planetary gear. c Here is the stiffness matrix of the planetary carrier. Here is the stiffness matrix of the meshing pair of the sun gear and planet gears. Here is the stiffness matrix of the meshing pair of the planetary gear and the ring gear. Let be the stiffness matrix of the planetary gears and planet carrier.

[0093] Considering that the inner ring node of the flexible gear ring may not coincide with the theoretical connection node when the planetary gear rotates to any angle θ, a modal contribution coefficient matrix V(θ) is introduced, and the meshing stiffness matrix of the planetary gear and the flexible gear ring is rewritten as follows:

[0094]

[0095]

[0096] In some optional embodiments, the total damping matrix is ​​calculated as follows:

[0097]

[0098]

[0099]

[0100] Where C is the total damping matrix, C α C is the mass-related Ruili damping coefficient. β C is the Ruili damping coefficient related to stiffness. spi Let c be the damping matrix of the sun gear and planet gear meshing model. spi C is the damping coefficient of the sun gear and planet gear meshing model.pri Let c be the damping matrix of the planetary gear and ring gear meshing model. pri v is the damping coefficient of the planetary gear and ring gear meshing model. spi and v pri Let M' be the projection vector, M' be the set of combinations of mass matrices, and K' be the set of combinations of stiffness matrices.

[0101] In some alternative embodiments, considering the structural characteristics and flexibility of the gear ring, shell element theory (Mindlin-Reissner) is adopted, which, based on shell element theory (Kirchhoff), takes into account the influence of shear deformation. This allows for an accurate description of the complex response of the shell structure under external forces, including:

[0102] The mass matrix of the shell element model is calculated as follows:

[0103]

[0104] in, Let ρ be the mass matrix of the shell element model, ρ be the density of the gear ring, N be the element shape function, J be the Jacobian matrix, and ξ, η, and ζ be the parametric coordinates of the shell element model.

[0105] The element shape function N is calculated as follows:

[0106] N = [N1 N2 ... N8]

[0107]

[0108]

[0109] Among them, l i m i and n i It is the direction cosine of the angle between the nodal coordinate system and the global coordinate system, t i It is the thickness at node i.

[0110] The Jacobian matrix J is calculated as follows:

[0111]

[0112] The stiffness matrix of the shell element model is calculated as follows:

[0113]

[0114] in, Let ξ be the stiffness matrix of the shell element model, B be the strain matrix, D be the constitutive matrix, J be the Jacobian matrix, and ξ, η, and ζ be the parametric coordinates of the shell element model.

[0115] Specifically, strain matrix B is calculated as follows:

[0116]

[0117]

[0118] Where I3 is a 3×3 identity matrix.

[0119]

[0120]

[0121]

[0122]

[0123] The constitutive matrix D is calculated as follows:

[0124]

[0125]

[0126] Where K is the correction factor for shear stress, E is the elastic modulus, and μ is Poisson's ratio. In this embodiment, K is taken as 1.2, but it is not limited to this and can be adjusted according to actual needs. (l1, m1, n1), (l2, m2, n2) and (l3, m3, n3) are the direction cosines between the unit vector in the nodal coordinate system and the global coordinate system.

[0127] In some optional embodiments, finite element models of the input shaft and planetary carrier are established, including:

[0128] Obtain the geometric drawings of the input shaft and planetary carrier, input the geometric drawings into the finite element analysis software, and the finite element analysis software outputs the mass matrix and stiffness matrix of the finite element model of the input shaft and planetary carrier.

[0129] Understandably, in this embodiment, the finite element analysis software used is ANSYS. The meshing of the finite element models of the input shaft and planetary carrier, the construction of the mass matrices of the input shaft and planetary carrier finite element models, and the construction of the stiffness matrices of the input shaft and planetary carrier finite element models are all completed within ANSYS. During this process, the required data is stored in the computer as sparse matrices via HBMAT files, and then retrieved by the MATLAB program.

[0130] In some alternative embodiments, the finite element model of gear meshing is simplified to a spring and damping system, and meshing models of the sun gear and planet gears, and planet gears and ring gears are established respectively.

[0131] Continue to refer to Figure 4 Gear meshing can be viewed as a spring-damped system connecting the two nodes of a gear.

[0132] The displacement vector of gear pair i in the meshing model of the sun gear and planet gears can be denoted as:

[0133] q spi =[x s y s , z s θ xs θ ys θ zs x pi y pi , z pi θ xpi θ ypi θ zpi ] T

[0134] Where, x s y s Indicates the lateral degree of freedom of the sun gear; z s θ represents the axial degree of freedom of the sun gear; xs θ ys θ represents the degree of freedom of the sun gear's oscillation; zs Indicates the torsional degree of freedom of the sun gear; x pi y pi z represents the lateral degree of freedom of the i-th planetary gear; pi θ represents the axial degree of freedom of the i-th planetary gear; xpi θ ypi θ represents the degree of freedom of the i-th planetary gear's oscillation; zpi This represents the torsional degree of freedom of the i-th planetary gear;

[0135] The stiffness matrix of the sun gear and planet gear meshing model is calculated as follows:

[0136]

[0137] Among them, K spi Let k be the stiffness matrix of the sun gear and planet gear meshing model. spi v represents the meshing stiffness of the sun gear and planet gears. spi Let be the projection vector of the gear pair of the i-th sun gear and planet gear along the meshing line.

[0138] v spi Calculate as follows:

[0139]

[0140]

[0141]

[0142] Where β is the helix angle, Let be the angle between the line of meshing of the i-th sun gear and planet gear pair and the y-axis. Let r be the phase angle of planetary gear i. s and r p Let be the base circle radius of the sun gear and planet gears.

[0143] Continue to refer to Figure 5 Since the nodes of the flexible gear ring are not located at the origin of the coordinate system, the meshing model containing the flexible gear ring is significantly different from that of the rigid gear ring.

[0144] The coordinates of the planetary gear and ring gear pair i can be denoted as:

[0145] q pri =[x pi ,y pi ,z pi ,θ xpi ,θ ypi ,θ zpi ,x ri ,y ri ,z ri ,θ xri ,θ yri ,θ zri ] T

[0146] The stiffness matrix of the planetary gear and ring gear meshing model is calculated as follows:

[0147]

[0148] Among them, K pri Let k be the stiffness matrix of the planetary gear and ring gear meshing model. pri v represents the meshing stiffness of the planetary gear and the ring gear. pri Let be the projection vector of the gear pair of the i-th planetary gear and the ring gear along the meshing line.

[0149] v pri Calculate as follows:

[0150]

[0151] Where d is the distance from the gear ring node to the meshing surface, φpri is the angle between the meshing line of the i-th planetary gear and the flexible gear ring pair and the y-axis, and β is the pressure angle.

[0152] In some alternative embodiments, refer to Figure 7 , Figure 8 and Figure 9 , Figure 7 This is a schematic diagram of one of the principal mode shapes of the gear ring. Figure 8 This is a schematic diagram of the root circular vibration mode of the main mode of the gear ring. Figure 9 This is a schematic diagram of a gear-ring constrained mode shape. Figure 7 The first 10 main mode shapes of the flexible gear ring are shown, with corresponding frequencies of 7351Hz, 7703Hz, 8665Hz, 10044Hz, 11654Hz, 11914Hz, 12009Hz, 12432Hz, 12702Hz and 12962Hz. Figure 8 The mode shapes of the inner ring of the first 10 principal modes of the flexible gear ring are shown, along with their corresponding frequency values. Figure 7 same; Figure 9 This is the mode shape diagram of the flexible gear ring constrained mode.

[0153] In some alternative embodiments, refer to Figure 10 and Figure 11 , Figure 10 A graph showing the contribution coefficients of the first 10 principal modes. Figure 11 A graph showing the contribution coefficients of the first 10 constrained modes. Figure 10 and Figure 11 It can be seen that the modal contribution coefficients exhibit a periodic variation within one rotation cycle of the planetary carrier. For the principal modes, the variation period is also affected by the pitch diameter and the number of bolt holes. Among them, the modal contribution coefficients of the radial and tangential directions, as well as the modal contribution coefficients of the axial rotation angle, are dominated by higher-order frequencies; while the modal contribution coefficients of the axial direction, as well as the modal contribution coefficients of the radial and tangential rotation angles, are mainly dominated by lower-order modes. This means that radial, tangential, and torsional excitations on the inner ring of the flexible gear ring are more likely to excite the higher-order principal modes of the gear ring, while axial, radial, and tangential rotation angle excitations are more likely to excite the lower-order principal modes of the gear ring.

[0154] In some alternative embodiments, refer to Figures 12 to 16 , Figure 12 This is a schematic diagram of the first 10 modes of planetary gear vibration. Figure 13 A graph showing the time-varying meshing stiffness of the sun gear and planet gears. Figure 14 This is a graph showing the time-varying meshing stiffness of the planetary gear and the ring gear. Figure 15 To extract the time-domain and frequency-domain curves of the radial acceleration response of the gear ring at an input speed of 600 r / min, simulation and experimental comparison graphs were used. Figure 16 Simulation and experimental comparison figures are used to extract the time-domain and frequency-domain curves of the radial acceleration response of the gear ring at an input speed of 1382 r / min.

[0155] Understandably, the time-varying meshing stiffness is substituted into the dynamic model, and the New-Mark method is used to solve the dynamic response of the system. Rayleigh damping is employed in the solution, with a damping ratio of 0.025 at both rotational speeds. The radial acceleration vibration signal of the gear ring is extracted from the simulation results and compared with the experimental signal, such as... Figure 15 and Figure 16 As shown, the experimental data and simulation results agree well. In both the experimental and simulated time-domain signals, a "pass-through effect" occurs, meaning that as the planetary gears approach and move away from the measuring point, periodic response peaks appear in the test signal. For the experimental data and simulation results at 600 r / min, the frequency components in the spectrum are mainly concentrated around the 7th harmonic frequency (1802 Hz). For the experimental data and simulation results at 1382 r / min, the frequency components in the spectrum are mainly concentrated around the 3rd harmonic frequency (1802 Hz). This is because these two frequencies are located between the system's natural frequencies f8 (1761 Hz) and f9 (1823 Hz), which causes the gear meshing to excite the system's superharmonic resonance.

[0156] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0157] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system, characterized in that, include: A gear ring element model is constructed using a shell element model, the gear ring element model including the mass matrix and the stiffness matrix of the gear ring element model; Before coupling, the mass matrix and the stiffness matrix are reduced in dimension and calculated as follows: in, The mass matrix is ​​the reduced-dimensional version. For the mass matrix, The stiffness matrix is ​​the reduced dimension. Let be the stiffness matrix. This is the transformation matrix; Establish finite element models of the input shaft and planetary carrier, wherein the finite element models of the input shaft and planetary carrier include the mass matrix and the stiffness matrix of the finite element models of the input shaft and planetary carrier; A meshing model of the sun gear and planet gears is established, which includes the mass matrix and stiffness matrix of the meshing model of the sun gear and planet gears. Establish a planetary gear and ring gear meshing model, which includes the mass matrix and stiffness matrix of the planetary gear and ring gear meshing model; The mass matrix of the gear ring element model, the stiffness matrix of the gear ring element model, the mass matrix of the finite element model of the input shaft and planet carrier, the stiffness matrix of the finite element model of the input shaft and planet carrier, the mass matrix of the meshing model of the sun gear and planet gears, the stiffness matrix of the meshing model of the sun gear and planet gears, the mass matrix of the meshing model of the planet gear and gear ring, the stiffness matrix of the meshing model of the planet gear and gear ring, and the total damping matrix are coupled to obtain the dynamic model of the planetary gear system. The dynamic equations are solved using the Newmark method. In each substep, the meshing matrix is ​​transformed according to the angle rotated by the planetary carrier and the modal contribution coefficient, and the dynamic response of the system is finally obtained.

2. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The total damping matrix is ​​calculated as follows: in, Let be the total damping matrix. The Ruili damping coefficient is related to mass. The Ruili damping coefficient is related to stiffness. Let be the damping matrix of the meshing model of the sun gear and planet gears. The damping coefficient of the sun gear and planet gear meshing model is given. Let be the damping matrix of the planetary gear and ring gear meshing model. The damping coefficient of the planetary gear and ring gear meshing model is given. and For projection vectors, The set of combinations of the quality matrices. is the set of combinations of the stiffness matrices.

3. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The mass matrix of the shell element model is calculated as follows: in, The mass matrix of the shell element model is... The density of the gear ring, For unit shape functions, It is a Jacobian matrix. , , These are the parameter coordinates of the shell element model.

4. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The stiffness matrix of the shell element model is calculated as follows: in, Let be the stiffness matrix of the shell element model. The strain matrix, The constitutive matrix is It is a Jacobian matrix. , , These are the parameter coordinates of the shell element model.

5. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The establishment of the finite element model of the input shaft and planet carrier includes: Obtain the geometric drawings of the input shaft and planetary carrier, input the geometric drawings into the finite element analysis software, and the finite element analysis software outputs the mass matrix and stiffness matrix of the finite element model of the input shaft and planetary carrier.

6. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The stiffness matrix of the sun gear and planet gear meshing model is calculated as follows: in, Here is the stiffness matrix of the sun gear and planet gear meshing model. For the meshing stiffness of the sun gear and planet gears, For the first i The projection vectors of the gear pairs of the sun gear and planet gears along the meshing line.

7. The dynamic modeling method for a rigid-flexible coupled planetary gear and rotor system according to claim 1, characterized in that, The stiffness matrix of the planetary gear and ring gear meshing model is calculated as follows: in, Let be the stiffness matrix of the planetary gear and ring gear meshing model. For the meshing stiffness of the planetary gear and the ring gear, For the first i The projection vector of the gear pair of planetary gears and ring gear along the meshing line.

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