Dynamics Modeling Method of Planetary Gear Train Considering Tooth Meshing Process and Structural Flexibility

Abstract

The present invention provides a dynamic modeling method for a planetary gear train that takes into account the tooth meshing process and structural flexibility, including: obtaining the free vibration equations of the condensed planet carrier and internal gear ring through substructure condensation; establishing a meshing unit model of the planetary gear train to obtain a meshing vector; equivalently decomposing the comprehensive meshing stiffness of the gear pair to each pair of meshing teeth according to the meshing vector according to its contact ratio; performing support unit modeling to obtain the coupling stiffness matrix between the pin condensation point and the corresponding planetary gear node; establishing the dynamic equation of the shaft segment beam element; performing exciting force unit modeling to obtain the error exciting force generated by the gear meshing error and the exciting force generated by the virtual vibration linear displacement of the internal gear ring; and establishing a dynamic model of the planetary gear train. The present invention can solve the technical problems in the prior art that it is impossible to consider the geometric characteristics of complex components, the calculation accuracy is low, the large-scale finite element calculation amount is large, the system-level modeling and analysis are difficult, and it is not applicable to the analysis of variable speed and variable load of the planetary gear train.

Description

Technical Field

[0001] The present invention relates to the technical field of wind power generation, and particularly relates to a dynamic modeling method for a planetary gear train that takes into account the tooth meshing process and structural flexibility. Background Art

[0002] For megawatt-class ultra-high-power wind turbines, a wind power gearbox with multi-planetary gear power splitting is widely used in the unit to transmit megawatt-class power and is an extremely important transmission device. In order to meet the transmission requirements of greater power, the sizes of components such as the internal gear ring and the planet carrier in the planetary gear train of the wind power gearbox will be designed larger, and the number of planet gears will also increase. In this case, it is easy to generate excessive system vibration noise and dynamic loads under the action of random aerodynamic torque, increasing the risk of fatigue failure. Therefore, carrying out research on the dynamic characteristics of the planetary gear train of the wind power gearbox has important guiding significance for the design of the wind power gearbox of megawatt-class ultra-high-power units.

[0003] Currently, the dynamic modeling methods for planetary gear trains can be roughly divided into lumped parameter models, finite element models, and hybrid models. For lumped parameter models, they focus on the preliminary analysis of the inherent characteristics of the system, excitation mechanisms, and dynamic load distribution, etc. When modeling, gears, shafts, and bearings are often simplified into one body, and the complex loading conditions of the elastic shaft are replaced by simple radial, bending, and torsional stiffnesses; because the elastic deformations of components such as the internal gear ring, planet carrier, and housing are not taken into account in the lumped parameter model, the overall calculation accuracy is not high.

[0004] For finite element models, the geometric characteristics of complex structures are considered during modeling, and the tooth contact state can be well simulated, comprehensively reflecting the loading conditions of each component of the planetary gear train; however, the modeling process of finite element models is complex, the calculation amount is huge, and system-level modeling and analysis are difficult, and it is generally not applicable to dynamic design occasions.

[0005] Hybrid models: including beam / shell element-lumped parameter hybrid models and finite element-lumped parameter hybrid models. Since such modeling methods take into account the elastic deformations of components such as the internal gear ring, planet carrier, and transmission shaft on the basis of the lumped parameter model, the overall calculation accuracy is improved. Compared with the beam / shell element-lumped parameter hybrid model, the finite element-lumped parameter hybrid model can consider the geometric characteristics of complex structures and has better applicability, but it is mostly used for vibration analysis at constant speed and is not applicable to the dynamic modeling of planetary gear trains under variable speed and variable load. Summary of the Invention

[0006] Aiming at the deficiencies of the existing technology, the present invention proposes a dynamic modeling method for a planetary gear train that takes into account the tooth meshing process and structural flexibility, so as to solve the technical problems existing in the prior art, such as the inability to consider the geometric characteristics of complex components, low calculation accuracy, large calculation amount of large-scale finite elements, difficulty in system-level modeling and analysis, and inapplicability to the variable speed and variable load analysis of planetary gear trains.

[0007] The technical solution adopted by the present invention is as follows:

[0008] In a first aspect, a dynamic modeling method for a planetary gear train considering the tooth meshing process and structural flexibility is provided, including:

[0009] Performing substructure condensation on the finite element models of the planet carrier and the internal gear ring to obtain the free vibration equations of the condensed planet carrier and internal gear ring;

[0010] Establishing a meshing unit model of the planetary gear train to obtain a meshing vector;

[0011] According to the meshing vector, equivalently decomposing the comprehensive meshing stiffness of the gear pair according to its contact ratio onto each pair of meshing teeth to obtain the meshing stiffness equations between the sun gear and the planet gear after decomposition, and the meshing stiffness equations between the internal gear ring and the planet gear after decomposition;

[0012] Performing support unit modeling to obtain the coupling stiffness matrix between the pin condensation point and the corresponding planet gear node;

[0013] Establishing the dynamic equation of the shaft segment beam element;

[0014] Performing excitation force unit modeling to obtain the error excitation force generated by the gear meshing error and the excitation force generated by the virtual vibration linear displacement of the internal gear ring;

[0015] According to the free vibration equations of the condensed planet carrier and internal gear ring, the meshing stiffness equations between the sun gear and the planet gear after decomposition, the meshing stiffness equations between the internal gear ring and the planet gear after decomposition, the coupling stiffness matrix between the pin condensation point and the corresponding planet gear node, the dynamic equation of the shaft segment beam element, the error excitation force generated by the gear meshing error, and the excitation force generated by the virtual vibration linear displacement of the internal gear ring, establishing a dynamic model of the planetary gear train.

[0016] Further, performing substructure condensation on the finite element models of the planet carrier and the internal gear ring includes connecting the condensation point with the corresponding interface node through flexible multi-point constraints and adopting the fixed interface modal synthesis method to perform substructure condensation on the planet carrier and the internal gear ring;

[0017] The free vibration equations of the condensed planet carrier and internal gear ring are:

[0018]

[0019] In the above formula, M C , M r are respectively the mass matrix of the planet carrier and the mass matrix of the internal gear ring, C c , K r are respectively the damping matrix of the planet carrier and the damping matrix of the internal gear ring, K c , Kr They are the stiffness matrices of the planet carrier and the internal gear ring respectively, and {q} is the generalized displacement vector of the condensed points.

[0020] Furthermore, establishing the meshing element model of the planetary gear train includes: introducing the virtual vibration linear displacement of the internal gear ring into the relative displacement at the meshing plane of the teeth of the internal gear ring - planetary gear to generate a time - varying parameter excitation;

[0021] The meshing vectors include:

[0022]

[0023]

[0024] In the above formula, V spi is the meshing vector between the sun gear and the planetary gear, and V rpi is the meshing vector between the internal gear ring and the planetary gear; V s and V pi are the generalized displacement vectors of the sun gear and the planetary gear respectively, and V r is the generalized displacement vector of the internal gear ring.

[0025] Furthermore, the decomposed meshing stiffness equations between the sun gear and the planetary gear, and the decomposed meshing stiffness equations between the internal gear ring and the planetary gear are as follows:

[0026]

[0027]

[0028] In the above formula, K sp is the meshing stiffness between the decomposed sun gear and the planetary gear, K rp is the meshing stiffness between the decomposed internal gear ring and the planetary gear, N p is the number of planetary gears, N r is the number of teeth of the internal gear ring, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planetary gear, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planetary gear, K spi is the comprehensive meshing stiffness between the sun gear and the planetary gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planetary gear, V spi is the meshing vector between the sun gear and the planetary gear, V rpi is the meshing vector between the internal gear ring and the planetary gear, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planetary gear, ξ rpi is the contact ratio between the internal gear ring and the planetary gear.

[0029] Further, the support unit modeling includes coupling the pin condensation point of the planet carrier pin with the planet gear through a bearing support unit, and using a rotation matrix to transform the coordinate system of the pin condensation point;

[0030] The coupling stiffness matrix between the pin condensation point and the corresponding planet gear node is

[0031]

[0032] In the above formula, K b is the K cp submatrix, are diagonal matrices respectively.

[0033] Further, establishing the dynamic equation of the shaft segment beam element includes combining the structural characteristics of the sun gear shaft and using a modified Euler-Bernoulli beam element considering the influence of shear deformation;

[0034] The dynamic equation of the shaft segment beam element is as follows:

[0035]

[0036] In the above formula, M s is the shaft segment mass matrix, K s is the shaft segment stiffness matrix, C s is the shaft segment damping matrix, X s is the generalized displacement vector of the shaft segment defined in its own reference coordinate system.

[0037] Further, when modeling the exciting force unit, considering the meshing error of the gear pair caused by the single-tooth tangential deviation, the periodic displacement excitation and the exciting force generated by the virtual vibration linear displacement of the internal gear ring during the gear meshing process are considered;

[0038] The meshing error of the gear pair is as follows:

[0039]

[0040] In the above formula, is the gear meshing error between the sun gear and the planet gear, is the gear meshing error between the internal gear ring and the planet gear, f′ i_s is the single-tooth tangential deviation of the sun gear, f′ i_r is the single-tooth tangential deviation of the internal gear ring, f′ i_pi is the single-tooth tangential deviation of the planet gear, w m_spi is the meshing frequency between the sun gear and the planet gear, w m_rpi is the meshing frequency between the internal gear ring and the planet gear, is the initial phase between the sun gear and the planet gear, is the initial phase between the internal gear ring and the planet gear, and t is the time.

[0041] Furthermore, the error exciting force generated by the gear pair meshing error is:

[0042]

[0043]

[0044] In the above formula, F sp is the error exciting force generated by the gear meshing error between the sun gear and the planet gear, F rp is the error exciting force generated by the gear meshing error between the internal gear ring and the planet gear, is the gear meshing error between the sun gear and the planet gear, is the gear meshing error between the internal gear ring and the planet gear, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planet gear, ξ rpi is the contact ratio between the internal gear ring and the planet gear, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planet gear, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K spi is the comprehensive meshing stiffness between the sun gear and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V spi is the meshing vector between the sun gear and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear;

[0045] The exciting force generated by the virtual vibration linear displacement of the internal gear ring is:

[0046]

[0047] In the above formula, is the virtual vibration linear displacement of the internal gear ring, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding up towards positive infinity, ξ rpi is the contact ratio between the internal gear ring and the planet gear, Λ is the positioning matrix, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear.

[0048] Further, establishing a planetary gear train dynamics model includes assembling various mass matrices, stiffness matrices, and damping matrices of the sun gear, internal gear ring, planet carrier, and planet gear nodes according to their degrees of freedom and coupling relationships; the planetary gear train dynamics model is as follows:

[0049]

[0050] In the above formula, M C 、M r 、M s are the mass matrices of the planet carrier, internal gear ring, and shaft section respectively, C c 、C r 、C s are the damping matrices of the planet carrier, internal gear ring, and shaft section respectively, K c 、K r 、K s are the stiffness matrices of the planet carrier, internal gear ring, and shaft section respectively, K sp is the meshing stiffness between the decomposed sun gear and planet gear, K rp is the meshing stiffness between the decomposed internal gear ring and planet gear, K cp is the coupling stiffness matrix between the pin shaft condensation point and the corresponding planet gear node, is the virtual vibration linear displacement excitation of the internal gear ring, F sp is the error excitation force generated by the gear meshing error between the sun gear and planet gear, F rp is the error excitation force generated by the gear error meshing between the internal gear ring and planet gear, T in is the input torque, T out is the load, X sys is the generalized displacement vector of the coupling system in the global coordinate system.

[0051] In the second aspect, a gearbox of a wind turbine generator is provided, and the planet carrier, internal gear ring, sun gear, planet gear, and shaft section in the gearbox are designed by using any of the modeling methods in the first aspect.

[0052] It can be seen from the above technical solutions that the beneficial technical effects of the present invention are as follows:

[0053] Considering the complex structural geometric features of the transmission components and the multi-tooth meshing state, the conventional equivalent single-point meshing of the planetary gear train meshing pair is refined to multi-pair tooth meshing. By introducing the variable representing the transmission speed of the meshing pair and the virtual vibration linear displacement of the internal gear ring, the mapping relationship between the driving wheel rotation angle and the multi-tooth meshing state of the planetary gear train is constructed, avoiding the insufficient accuracy caused by the simplified treatment. Considering the flexibility of the internal gear ring and the planet carrier, a variable-speed dynamics model of the planetary gear train of the wind power gearbox is established, which can reflect the geometric features of complex components, the dynamic loads of the teeth, and is applicable to variable-speed operation, improving the prediction accuracy of the dynamic performance of the planetary gear train of the wind power gearbox under variable-speed and variable-load conditions, and providing a theoretical basis for the dynamic design of the planetary gear train of the wind power gearbox. Description of the Drawings

[0054] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0055] Figure 1(a) is a schematic diagram of the finite element condensation model of the internal gear ring according to an embodiment of the present invention;

[0056] Figure 1(b) is a schematic diagram of the finite element condensation model of the planet carrier according to an embodiment of the present invention;

[0057] Figure 2 is a schematic diagram of the coupling model of the planetary gear train according to an embodiment of the present invention;

[0058] Figure 3 is a comparative graph of the curve of the change in the rotational speed of the planet carrier according to an embodiment of the present invention;

[0059] Figure 4 is a comparative graph of the curves of the loads of the meshing pair between the internal gear ring and the planet gear 1 under the steady-state condition according to an embodiment of the present invention;

[0060] Figure 5 is a comparative graph of the curves of the loads of the meshing pair between the internal gear ring and the planet gear 1 under the variable-speed and variable-load condition according to an embodiment of the present invention;

[0061] Figure 6 is a flow chart of the variable-speed dynamics modeling method for the planetary gear train of the wind power gearbox according to an embodiment of the present invention. Detailed Embodiments

[0062] The following will describe in detail the embodiments of the technical solutions of the present invention in conjunction with the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and therefore are only examples and cannot be used to limit the protection scope of the present invention.

[0063] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in this application shall have the ordinary meanings understood by those skilled in the art to which the present invention pertains.

[0064] Embodiment

[0065] This embodiment provides a dynamic modeling method for a planetary gear train considering the tooth meshing process and structural flexibility, including the following steps:

[0066] Step 1: Condense the substructures of the finite element models of the planet carrier and the internal gear ring to obtain the free vibration equations of the condensed planet carrier and internal gear ring

[0067] In this step, the methods for establishing the finite element models of the planet carrier and the internal gear ring are not limited, and any available implementation method in the prior art can be selected. Figures 1(a) and 1(b) are schematic diagrams of the finite element condensation points of the internal gear ring and the planet carrier of the planetary gear train in a wind power gearbox, and the numbers in the figures represent the respective condensation points; the condensation points are connected to the corresponding interface nodes through flexible multi-point constraints (MPC), and the fixed interface modal synthesis method is used to condense the substructures of the planet carrier and the internal gear ring, and the free vibration equations of the condensed planet carrier and internal gear ring can be obtained as:

[0068]

[0069] In the above formula (1), M C , M r are the mass matrices of the planet carrier and the internal gear ring respectively, C c , C r are the damping matrices of the planet carrier and the internal gear ring respectively, K c , K r are the stiffness matrices of the planet carrier and the internal gear ring respectively, {q} is the generalized displacement vector of the condensation points, are the second and first derivatives of the generalized displacement vector of the condensation points with respect to time respectively.

[0070] The parameters M C , M r , C c , C r can be introduced through formula (1) in this step for subsequent modeling.

[0071] Step 2: Establish a meshing unit model of the planetary gear train to obtain the meshing vector

[0072] In order to enable the torsional vibration displacement of the tooth nodes of the internal gear ring to be feedback to the meshing line between the internal gear ring and the planet gear, in this step, when establishing the meshing unit model of the planetary gear train, a virtual vibration linear displacement c of the internal gear ring is introduced into the relative displacement at the meshing plane M Generate time-varying parameter excitation, and the meshing vectors are as follows:

[0073]

[0074]

[0075] In the above equations (2) and (3), V spi is the meshing vector between the sun gear and the planet gear, and V rpi is the meshing vector between the ring gear and the planet gear; V s and V pi are the generalized displacement vectors of the sun gear and the planet gear respectively, and V r is the generalized displacement vector of the ring gear.

[0076] Through equations (2) and (3) in this step, the parameters V spi and V rpi can be introduced for subsequent modeling use.

[0077] Step 3: According to the meshing vectors obtained in Step 2, decompose the comprehensive meshing stiffness of the gear pair equivalently according to its contact ratio to each pair of meshing teeth, and obtain the meshing stiffness equations between the decomposed sun gear and the planet gear, and the meshing stiffness equations between the decomposed ring gear and the planet gear

[0078] Based on the meshing vectors obtained in Step 2, establish the meshing stiffness equations of the meshing pairs between the sun gear and the planet gear, and between the ring gear and the planet gear respectively, as follows:

[0079]

[0080]

[0081] In the above equations (4) and (5), N p is the number of planet gears, Λ is the positioning matrix, K spi , K rpi are the meshing stiffness between the sun gear and the planet gear, and the comprehensive meshing stiffness between the ring gear and the planet gear respectively, and V spi , V rpi are the meshing vectors between the sun gear and the planet gear, and between the ring gear and the planet gear respectively.

[0082] In the prior art, the lumped parameter model and the hybrid model often simplify the multi-tooth meshing of the gear pair into equivalent single-point meshing, and replace the complex multi-tooth meshing process with a simple comprehensive meshing stiffness, which is different from the actual tooth meshing process, resulting in low accuracy in solving the dynamic load of the tooth. To improve the accuracy of solving the dynamic load of the tooth, in this step, the comprehensive meshing stiffness of the gear pair is equivalently decomposed into each pair of meshing teeth according to its contact ratio, and the meshing stiffness equations between the decomposed sun gear and the planet gear and between the decomposed internal gear ring and the planet gear are obtained as follows:

[0083]

[0084]

[0085] In the above equations (6) and (7), K sp is the meshing stiffness between the decomposed sun gear and the planet gear, K rp is the meshing stiffness between the decomposed internal gear ring and the planet gear, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planet gear, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K spi is the comprehensive meshing stiffness between the sun gear and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V spi is the meshing vector between the sun gear and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planet gear, ξ rpi is the contact ratio between the internal gear ring and the planet gear. K spi , K rpi , Θ spi and Θ rpi can also be called the variable representing the speed change of the meshing pair.

[0086] Step 4: Model the support unit to obtain the coupling stiffness matrix between the pin condensation point and the corresponding planet gear node

[0087] Couple the pin condensation point of the planet carrier with the planet gear through the bearing support unit, and use the rotation matrix to transform the coordinate system of the pin condensation point to obtain the coupling stiffness matrix K cp as

[0088]

[0089] In the above equation (8), K b is Kcp Sub - matrix are diagonal matrices respectively.

[0090] Step 5: Establish the dynamic equation of the shaft - segment beam element

[0091] Combined with the structural characteristics of the sun - gear shaft, a modified Euler - Bernoulli beam element considering the influence of shear deformation is adopted to establish the dynamic equation of the shaft - segment beam element as follows:

[0092]

[0093] In the above formula (9), M s is the mass matrix of the shaft segment, K s is the stiffness matrix of the shaft segment, C s is the damping matrix of the shaft segment, X s is the generalized displacement vector of the shaft segment defined in its own reference coordinate system, are the first - order and second - order derivatives of the generalized displacement vector with respect to time respectively.

[0094] Through formula (9) of this step, the parameters M s , K s , C s can be introduced for subsequent modeling use.

[0095] Step 6: Conduct the modeling of the exciting - force element to obtain the error exciting force generated by the gear - meshing error and the exciting force generated by the virtual vibration linear displacement of the internal gear ring

[0096] Considering the periodic displacement excitation caused by the tooth - profile error during the gear - meshing process and the exciting force generated by the virtual vibration linear displacement of the internal gear ring, the modeling of the exciting - force element is completed. In this step, the single - tooth tangential deviation is considered, and the gear - pair meshing - error expression is:

[0097]

[0098] In the above formula (10), is the gear - meshing error between the sun gear and the planet gear, is the gear - meshing error between the internal gear ring and the planet gear, f′ i_s is the single - tooth tangential deviation of the sun gear, f′ i_r is the single - tooth tangential deviation of the internal gear ring, f′ i_pi is the single - tooth tangential deviation of the planet gear, w m_spi is the meshing frequency between the sun gear and the planet gear, w m_rpi is the meshing frequency between the internal gear ring and the planet gear, is the initial phase between the sun gear and the planet gear, is the initial phase between the internal gear ring and the planet gear, and t is time.

[0099] Combined with Equation (10), the error excitation force generated by the gear pair meshing error is divided into:

[0100]

[0101]

[0102] In the above Equations (11) and (12), F sp is the error excitation force generated by the gear meshing error between the sun gear and the planet gear, and F rp is the error excitation force generated by the gear meshing error between the internal gear ring and the planet gear. is the gear meshing error between the sun gear and the planet gear, is the gear meshing error between the internal gear ring and the planet gear, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planet gear, ξ rpi is the contact ratio between the internal gear ring and the planet gear, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planet gear, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K spi is the comprehensive meshing stiffness between the sun gear and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V spi is the meshing vector between the sun gear and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear.

[0103] Combined with Equations (6) and (7), the excitation force generated by the virtual vibration linear displacement of the internal gear ring is:

[0104]

[0105] In the above Equation (13), is the virtual vibration linear displacement of the internal gear ring, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding up towards positive infinity, ξ rpi is the contact ratio between the internal gear ring and the planet gear, Λ is the positioning matrix, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear.

[0106] Step 7: Establish the dynamic model of the planetary gear train based on the free vibration equation of the planet carrier and the inner gear ring after condensation, the meshing stiffness equation between the decomposed sun gear and the planet gear, the meshing stiffness equation between the decomposed inner gear ring and the planet gear, the coupling stiffness matrix between the pin condensation point and the corresponding planet gear node, the dynamic equation of the shaft segment beam unit, the error excitation force generated by the gear meshing error and the excitation force generated by the virtual vibration line displacement of the inner gear ring.

[0107] like Figure 2 As shown in FIG, according to the degrees of freedom of the nodes of the sun gear, inner gear ring, planet carrier and planet gear and their coupling relationship, the various mass matrices, stiffness matrices and damping matrices of the sun gear, inner gear ring, planet carrier and planet gear are assembled, and the planetary gear train dynamic model is established by combining equations (1), (6), (7), (8), (9), (11), (12) and (13) as follows:

[0108]

[0109] In the above formula (14), M C 、M r 、M s are the mass matrices of the planet carrier, inner gear ring, and shaft segment, respectively, c , C r , C s are the damping matrices of the planet carrier, inner gear ring, and shaft segment, respectively, K c , K r , K s are the stiffness matrices of the planet carrier, inner gear ring, and shaft segment, respectively, K sp K is the meshing stiffness between the sun gear and the planet gear after decomposition. rp K is the meshing stiffness between the internal gear ring and the planetary gear after decomposition. cp is the coupling stiffness matrix between the pin condensation point and the corresponding planetary gear node, is the virtual vibration linear displacement excitation of the inner gear ring, F sp is the error exciting force caused by the gear meshing error between the sun gear and the planetary gear, F rp is the error exciting force caused by the gear meshing error between the inner gear ring and the planetary gear, T in is the input torque, T out is the load, X sys is the generalized displacement vector of the coupled system in the global coordinate system, are the second-order and first-order derivatives of the generalized displacement vector of the coupled system with respect to time, respectively.

[0110] In the above formula (14), the input torque T in and load T outis the design input quantity according to actual requirements and is a known parameter. Through Equation (14), the output information of the system parameters of the entire planetary gear train of the gearbox can be obtained, including the parameters of the planet carrier, internal gear ring, sun gear, planet gear, and shaft section. The output information of the entire system parameters can be used for dynamic characteristic analysis, such as analyzing objects that need to be focused on during the design process, such as rotational speed and gear dynamic load. The following is an example:

[0111] As shown in Figure 1, Figure 2 a total of 138 nodes and 120 internal node retained modes, as well as 948 degrees of freedom are shown.

[0112] Due to the large number of degrees of freedom in the model, in a specific implementation manner, the precise integration method (PIM) can be used for solution, and the step size is taken as 1×10 -5 . Under the constant input torque (T in = 4×10 6 N·m) and the torque mutation working condition (T in = 4->2->4×10 6 N·m, T in = 4->0.2->4×10 6 N·m), the change in the rotational speed of the planet carrier is shown in Figure 3. When the input torque is constant, the rotational speed of the planet carrier gradually increases in the initial stage, and then reaches the rated speed (input rotational speed 11.27 r / min) and tends to fluctuate stably; when the input torque suddenly decreases, the rotational speed of the planet carrier decreases accordingly, and when the torque recovers, it gradually increases to the rated speed. At the same time, it can also be observed that the greater the torque drop amplitude, the greater the rotational speed fluctuation of the planet carrier.

[0113] Figure 4 For the steady-state working condition of constant input torque (T in = 4×10 6 N·m), the influence of different modeling methods on the load of the meshing pair between the internal gear ring and planet gear 1. After considering the flexibility of components, the peak value of the tooth dynamic load of the meshing pair between the internal gear ring and planet gear will shift to the left (i.e., beside the starting point of meshing-in). Considering the structural flexibility of the internal gear ring helps to obtain a more accurate gear dynamic load distribution of the internal gear ring - planet gear.

[0114] Figure 5 For the influence of different modeling methods on the load of the meshing pair between the sun gear and planet gear 1 under the variable speed and variable load working condition; the working conditions include when t ≤ 1 s, T in = 4×10 6 N·m; when 1 s < t ≤ 1.2 s, T in = 4×10 5 N·m; when 1.2 s < t, T in = 4×10 6N·m; In the fully flexible model, the input torque drop will reduce the dynamic load of the gear teeth. Due to the flexibility of the internal gear ring structure, it will absorb part of the gear tooth node vibration caused by the impact load, resulting in the transient load of some gear teeth in the internal gear ring - planet gear meshing pair calculated by the rigid model being slightly greater than the calculation result of the fully flexible model.

[0115] The method for modeling the dynamics model of the planetary gear train of a wind power gearbox provided in this embodiment takes into account the complex structural geometric characteristics of the transmission components and the multi - tooth meshing state. It refines the conventional equivalent single - point meshing of the meshing pairs of the planetary gear train to multi - tooth meshing. By introducing the variable representing the speed change of the meshing pair and the virtual vibration linear displacement of the internal gear ring, it constructs the mapping relationship between the driving wheel rotation angle and the multi - tooth meshing state of the planetary gear train, avoiding the lack of accuracy caused by simplified processing. Considering the flexibility of the internal gear ring and the planet carrier, it establishes a variable - speed dynamics model of the planetary gear train of a wind power gearbox that can reflect the geometric characteristics of complex components, the dynamic load of gear teeth and is applicable to variable - speed operation, improving the prediction accuracy of the dynamic performance of the planetary gear train of a wind power gearbox under variable - speed and variable - load conditions, and providing a theoretical basis for the dynamic design of the planetary gear train of a wind power gearbox.

[0116] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered by the scope of the claims and the specification of the present invention.

Claims

1. A dynamic modeling method for a planetary gear train considering the tooth meshing process and structural flexibility, characterized in that, Including: Performing substructure condensation on the finite element model of the planet carrier and the finite element model of the internal gear ring to obtain the free vibration equations of the condensed planet carrier and internal gear ring; Establishing a meshing unit model of the planetary gear train to obtain a meshing vector; According to the meshing vector, equivalently decomposing the comprehensive meshing stiffness of the gear pair onto each pair of meshing teeth according to its contact ratio to obtain the meshing stiffness equations between the sun gear and the planetary gear after decomposition, and the meshing stiffness equations between the internal gear ring and the planetary gear after decomposition, specifically as follows: In the above formula, K sp is the meshing stiffness between the sun gear and the planet gear after decomposition, K rp is the meshing stiffness between the ring gear and the planet gear after decomposition, N p is the number of planet gears, N r is the number of teeth of the ring gear, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planet gear, Θ rpi is the tooth meshing judgment coefficient between the ring gear and the planet gear, K spi is the comprehensive meshing stiffness between the sun gear and the planet gear, K rpi is the comprehensive meshing stiffness between the ring gear and the planet gear, V spi is the meshing vector between the sun gear and the planet gear, V rpi is the meshing vector between the ring gear and the planet gear, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planet gear, ξ rpi is the contact ratio between the ring gear and the planet gear; Performing support unit modeling to obtain the coupling stiffness matrix between the pin condensation point and the corresponding planetary gear node; Establishing the dynamic equation of the shaft segment beam element; Performing excitation force unit modeling to obtain the error excitation force generated by the gear meshing error and the excitation force generated by the virtual vibration linear displacement of the internal gear ring; According to the free vibration equations of the condensed planet carrier and internal gear ring, the meshing stiffness equations between the sun gear and the planetary gear after decomposition, the meshing stiffness equations between the internal gear ring and the planetary gear after decomposition, the coupling stiffness matrix between the pin condensation point and the corresponding planetary gear node, the dynamic equation of the shaft segment beam element, the error excitation force generated by the gear meshing error, and the excitation force generated by the virtual vibration linear displacement of the internal gear ring, establishing the dynamic model of the planetary gear train.

2. The modeling method according to claim 1, characterized in that Performing substructure condensation on the finite element model of the planet carrier and the finite element model of the internal gear ring, including connecting the condensation point with the corresponding interface node through flexible multi-point constraints, and using the fixed interface modal synthesis method to perform substructure condensation on the planet carrier and the internal gear ring; The free vibration equations of the condensed planet carrier and internal gear ring are: In the above formula, M c and M r are the mass matrices of the planet carrier and the internal gear ring respectively, C c and C r are the damping matrices of the planet carrier and the internal gear ring respectively, K c and K r are the stiffness matrices of the planet carrier and the internal gear ring respectively, and {q} is the generalized displacement vector of the condensed point.

3. The modeling method according to claim 1, wherein Establishing a meshing unit model of the planetary gear train includes: introducing the virtual vibration linear displacement of the internal gear ring into the relative displacement at the meshing plane of the internal gear ring teeth - planetary gear to generate a time-varying parameter excitation; The meshing vector includes: In the above formula, V spi is the meshing vector between the sun gear and the planet gear, and V rpi is the meshing vector between the internal gear ring and the planet gear; V s and V pi are the generalized displacement vectors of the sun gear and the planet gear respectively, and V r is the generalized displacement vector of the internal gear ring.

4. The modeling method according to claim 1, characterized in that, Support unit modeling includes coupling the pin condensation point of the planet carrier with the planetary gear through a bearing support unit and using a rotation matrix to transform the coordinate system of the pin condensation point; The coupling stiffness matrix between the pin condensation point and the corresponding planetary gear node is In the above formula, K b is the K cp submatrix, which are diagonal matrices respectively.

5. The modeling method according to claim 1, characterized in that Establishing the dynamic equation of the shaft segment beam element includes combining the structural characteristics of the sun gear shaft and using a modified Euler - Bernoulli beam element considering the influence of shear deformation; The dynamic equation of the shaft segment beam element is as follows: In the above formula, M s is the mass matrix of the shaft segment, K s is the stiffness matrix of the shaft segment, C s is the damping matrix of the shaft segment, and X s is the generalized displacement vector of the shaft segment defined in its own reference coordinate system.

6. The modeling method according to claim 1, characterized in that When performing excitation force unit modeling, considering the meshing error of the gear pair caused by the tangential deviation of a single tooth, which causes periodic displacement excitation during the gear meshing process and the excitation force generated by the virtual vibration linear displacement of the internal gear ring; The meshing error of the gear pair is as follows: In the above formula, is the gear meshing error between the sun gear and the planet gear, is the gear meshing error between the ring gear and the planet gear, f′ i_s is the single-tooth tangential deviation of the sun gear, f′ i_r is the single-tooth tangential deviation of the ring gear, f′ i_pi is the single-tooth tangential deviation of the planet gear, w m_spi is the meshing frequency between the sun gear and the planet gear, w m_rpi is the meshing frequency between the ring gear and the planet gear, is the initial phase between the sun gear and the planet gear, is the initial phase between the ring gear and the planet gear, and t is time.

7. The modeling method according to claim 6, characterized in that, The error excitation force generated by the meshing error of the gear pair is: In the above formula, F sp is the error excitation force generated by the gear meshing error between the sun gear and the planet gear, F rp is the error excitation force generated by the gear meshing error between the internal gear ring and the planet gear, is the gear meshing error between the sun gear and the planet gear, is the gear meshing error between the internal gear ring and the planet gear, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding up towards positive infinity, ξ spi is the contact ratio between the sun gear and the planet gear, ξ rpi is the contact ratio between the internal gear ring and the planet gear, Λ is the positioning matrix, Θ spi is the tooth meshing judgment coefficient between the sun gear and the planet gear, Θ rpi is the tooth meshing judgment coefficient between the internal gear ring and the planet gear, K spi is the comprehensive meshing stiffness between the sun gear and the planet gear, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gear, V spi is the meshing vector between the sun gear and the planet gear, V rpi is the meshing vector between the internal gear ring and the planet gear; The exciting force generated by the virtual vibration linear displacement of the internal gear ring is as follows: In the above formula, is the virtual vibration linear displacement of the internal gear ring, N p is the number of planet gears, N r is the number of teeth of the internal gear ring, ceil(·) is rounding towards positive infinity, ξ rpi is the contact ratio between the internal gear ring and the planet gears, Λ is the positioning matrix, Θ rpi is the tooth engagement judgment coefficient between the internal gear ring and the planet gears, K rpi is the comprehensive meshing stiffness between the internal gear ring and the planet gears, V rpi is the meshing vector between the internal gear ring and the planet gears.

8. The modeling method according to claim 1, wherein Establishing the dynamic model of the planetary gear train includes assembling various mass matrices, stiffness matrices, and damping matrices of the sun gear, internal gear ring, planet carrier, and planetary gear according to the degrees of freedom of the sun gear, internal gear ring, planet carrier, and planetary gear nodes and their coupling relationships; the dynamic model of the planetary gear train is: In the above formula, M is the sum of M C , M r and M s , where M C , M r , and M s are the mass matrices of the planet carrier, internal gear ring, and shaft segment respectively; C is the sum of C c , C r and C s , where C c , C r , and C s are the damping matrices of the planet carrier, internal gear ring, and shaft segment respectively; K is the sum of K c , K r , K sp , K rp , K cp , and K s , where K s , K r , and K s are the stiffness matrices of the planet carrier, internal gear ring, and shaft segment respectively, K sp is the meshing stiffness between the sun gear and the planet gear after decomposition, K rp is the meshing stiffness between the internal gear ring and the planet gear after decomposition, K cp is the coupling stiffness matrix between the pin shaft condensation point and the corresponding planet gear node; F is the sum of F sp , F rp , T in , and T out , is the virtual vibration linear displacement excitation of the internal gear ring, F sp is the error excitation force generated by the gear meshing error between the sun gear and the planet gear, F rp is the error excitation force generated by the gear meshing error between the internal gear ring and the planet gear, T in is the input torque, T out is the load, and X sys is the generalized displacement vector of the coupled system in the global coordinate system.

9. A gearbox of a wind turbine, characterized in that, The planet carrier, internal gear ring, sun gear, planetary gear, and shaft segment in the gearbox are designed by using the modeling method described in any one of claims 1 - 8.

Images