Method for analyzing dynamic meshing force of gear pair of dynamically enhanced wind turbine gear transmission system

Abstract

The invention discloses a method for analyzing the dynamic meshing force of a gear pair of a dynamically enhanced wind turbine gear transmission system, and belongs to the technical field of mechanical system dynamics and control. Firstly, a geometric solid model of the 1.5 MW wind turbine gear transmission system is established, and a three-dimensional model basis is provided for subsequently establishing a virtual prototype. Secondly, setting a reasonable constraint for the model, and applying a load to reflect the actual operation state of the model; thirdly, defining a contact type by using a dynamic enhanced Hertz contact method, providing a new method fusing an adaptive contact algorithm and Hertz contact, and introducing a Stribeck friction model to simulate the real working condition of the Stribeck friction model so as to establish a virtual prototype model; furthermore, the contact rigidity of the gear pair is dynamically and finely adjusted based on a feedback mechanism of PID double-position control. Therefore, the precision of the dynamic meshing force of the gear pair of the wind turbine gear transmission system is further improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical system dynamics and control, and in particular relates to a method for analyzing the dynamic meshing force of a gear pair of a dynamically enhanced wind turbine gear transmission system. Background Art

[0002] With the acceleration of global energy transformation, wind power generation as a clean and renewable energy technology has become increasingly important. As the core component of wind turbine generator sets, the performance of wind turbine gear transmission system directly affects the operating efficiency and life of the whole machine. As a key component in the gear transmission system, the dynamic meshing force characteristics of the gear pair are one of the key factors affecting the stability and reliability of the system. [1-3] .

[0003] Luo Yongshui et al. [4] The dynamic meshing force of gears was statistically analyzed by rain flow counting method, and the results showed that the dynamic meshing force has a strong time-varying characteristic. [5] et al. applied the dynamic meshing force obtained by the lumped parameter model to the finite element model of the inner gear ring to calculate the dynamic response of the inner gear ring, and combined it with the deformation threshold when multiple teeth meshed. [6] By simulating the dynamic model, they obtained the dynamic meshing force of each gear pair and the dynamic contact force of each supporting bearing, and combined the finite element method and Hertz contact theory to obtain the stress time history of key components. [7] The involute spur gear parametric equation is used for accurate modeling to obtain the radius of curvature of the tooth profile contact point. Taking into account the actual load, the Hertz contact formula is improved to solve the gear meshing contact stress. [8] Based on the Hertz contact theory, the linear coordinate parameters and Hertz stress model of the gear pair were established, the calculation formula of the tooth surface contact stress at any meshing point on the meshing line was derived, and the influence of different transmission parameters on the tooth surface contact stress was comprehensively analyzed. [9] Based on ADAMS virtual prototyping and Hertz contact theory, a virtual prototype model of the system was constructed, taking into account the friction coefficient. The kinematics of the herringbone planetary gear transmission system were studied, along with the contact force spectrum characteristics in both healthy and faulty states, and the contact force variation when considering component support stiffness. Based on the contact force analysis, the system load sharing coefficient was calculated, and the system's load sharing characteristics were analyzed.

[0004] Existing methods for studying the dynamic meshing forces of gear pairs have numerous limitations under complex operating conditions, making them incapable of meeting the requirements for efficient and reliable operation of modern wind turbines. Traditional methods for studying the dynamic meshing forces of gear pairs are primarily based on Hertzian contact theory. Hertzian contact theory is a classic elastic contact theory used to analyze the stress distribution and deformation behavior of two elastic bodies in contact. This theory assumes that deformation within the contact region is elastic and the contact surfaces are smooth, considering only normal forces. Hertzian contact theory analytically calculates contact stiffness, contact area, and contact stress, providing a theoretical basis for the preliminary design and analysis of gear transmission systems.

[0005] However, the assumptions of Hertzian contact theory are often difficult to meet in real-world operating conditions. For example, gear pairs are subject to a variety of complex factors during operation, such as random wind loads and variable speed operation. These factors can lead to dynamic changes in deformation, contact force, and friction in the contact area. Traditional Hertzian contact theory cannot fully account for these dynamic changes, limiting its applicability in complex operating conditions. Summary of the Invention

[0006] When studying the dynamic meshing force of the gear pairs of the wind turbine gear transmission system, the lack of simulation accuracy caused by various factors is a challenge currently faced. The traditional Hertz contact theory is a classic elastic contact theory used to analyze the stress distribution and deformation behavior of two elastic bodies in the contact state. However, under actual complex working conditions, the gears rotate and mesh with the input wind speed, resulting in various parameters in the meshing process also being in a time-varying state. It is necessary to consider using better simulation methods to simulate real working conditions. The present invention aims to solve the above problems of the prior art and proposes a dynamically enhanced method for analyzing the dynamic meshing force of the gear pairs of the wind turbine gear transmission system. The present invention significantly improves the simulation accuracy and adaptability by integrating the Hertz contact theory with the adaptive contact theory and introducing the Stribeck friction model. At the same time, a feedback mechanism based on PID two-position control is added to dynamically adjust the contact parameters of the gear pairs to obtain a more appropriate stiffness, which complements the adaptive contact algorithm.

[0007] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0008] A method for analyzing the dynamic meshing force of a gear pair of a dynamically enhanced wind turbine gear transmission system comprises the following steps:

[0009] Establish a geometric solid model of the 1.5MW wind turbine gear transmission system;

[0010] Apply constraints, loads and input loads to the established geometric solid model to reflect its actual operating state;

[0011] By integrating the adaptive contact algorithm with the Hertzian contact and introducing the Stribeck friction model, a dynamically enhanced Hertzian contact method is obtained to define the contact. A PID two-position control feedback mechanism is added to dynamically fine-tune the contact stiffness of the gear pair, which complements the adaptive contact algorithm. The dynamic meshing force response curve of the gear pair is obtained by simulation.

[0012] Furthermore, the geometric entity model of the 1.5MW wind turbine gear transmission system is established, specifically including: taking the 1.5MW wind turbine gear transmission system as the three-dimensional modeling object, Young's modulus E = 200GPa, Poisson's ratio = 0.3, mass density = 7850kg / m 3 , other specific parameters are shown in the following table

[0013]

[0014] According to the parameters given in the table, the parts are modeled and assembled in the 3D modeling software to obtain the geometric solid model of the 1.5MW wind turbine gear transmission system.

[0015] Furthermore, the established geometric entity model is subjected to constraints reflecting its actual operating state, and loads and input loads are applied, specifically including: in the primary transmission system, the planetary carrier and the sun gear constitute a ground rotating pair, each planetary gear forms a rotating pair relative to the planetary carrier, and the ring gear is fixed to the ground; for the secondary and tertiary transmissions, the gears are restricted to the transmission shaft, and the transmission shaft itself rotates around the ground; in addition, the mutual contact between the gears is simulated using a solid-solid contact pair, a drive pair is installed on the planetary carrier at the input end to realize power transmission, and a load is added to the output end; after completing the constraint addition in the model, the corresponding dynamic drive is applied, including integrating the drive pair on the planetary carrier at the input end and configuring the corresponding rated load torque at the output end.

[0016] Furthermore, the fusion of the adaptive contact algorithm and the Hertzian contact specifically includes:

[0017] The theoretical formula of Hertz contact is expressed as:

[0018]

[0019] Where, F n is the normal contact force between meshing gear teeth; K is the contact stiffness coefficient between meshing gear pairs; δ is the pure contact penetration between meshing gears; d max C is the maximum permissible penetration depth between meshing gears; max To achieve the maximum contact damping between meshing gear pairs when the maximum penetration depth is reached, δ e is the corrected equivalent penetration; is the integral of contact penetration over time.

[0020] The Hertz contact theory parameters include contact stiffness coefficient, contact damping coefficient, and maximum penetration depth. The contact stiffness coefficient can be expressed as:

[0021]

[0022]

[0023]

[0024] Where: R1 and R2 are the pitch circle radii of the two meshing gears; E1 and E2 are the elastic moduli of the two meshing gears; E* is the combined elastic modulus; v1 and v2 are the Poisson's ratios of the materials used for the two meshing gears; for two meshing helical gears, the contact stiffness coefficient is expressed as:

[0025]

[0026] In the formula, “+” in “±” indicates external meshing, “-” indicates internal meshing; d1 is the pitch circle diameter of the driving gear; u is the gear ratio of the two meshing gears; α t Indicates the end pressure angle; α' t Indicates the end face engagement angle; β b Indicates the gear helix angle;

[0027] During the meshing process of gear pairs, energy conversion and loss phenomena are significant. This dynamic interaction can be accurately described by the concept of contact damping.

[0028] An adaptive contact algorithm is introduced to monitor the contact force changes during the meshing process in real time, thereby dynamically adjusting the above three parameters. The specific adjustment methods are as follows:

[0029] ① Adjustment based on contact force

[0030] The contact stiffness adjusts to changes in the contact force:

[0031]

[0032]

[0033] F n represents the contact force, K represents the stiffness coefficient, and C represents the damping coefficient.

[0034] ② Adjustment based on deformation

[0035] The contact stiffness and maximum penetration depth are adjusted according to the deformation:

[0036]

[0037]

[0038] Where K new is the adjusted contact stiffness, C new is the adjusted contact damping, d max，new is the maximum penetration depth after adjustment, F max and F min are the upper and lower thresholds of the contact force, δ max and δ min : Upper and lower thresholds of deformation.

[0039] More specifically, the Stribeck curve in the Stribeck friction model is expressed as:

[0040]

[0041] Where μ coulomb is the Coulomb friction coefficient, μ lubricated is the friction coefficient under hydrodynamic lubrication, v min and v max are the starting and ending velocities of the Stribeck curve, μ static is the static friction coefficient.

[0042] Furthermore, the feedback mechanism of adding PID two-position control to dynamically fine-tune the contact stiffness of the gear pair specifically includes:

[0043] ①Define the performance index. The performance index is the contact force error, which is expressed as:

[0044] e(t)=F sim (t)-F ref (t)

[0045] Where, F sim (t) is the contact force obtained by simulation, F ref (t) is the reference contact force, and e(t) is the error variation over time.

[0046] ② Initialize PID two-position controller parameters and calculate parameters

[0047] Define two sets of appropriate PID two-position controller parameters, including proportional gain K p , integral gain K i , differential gain K d , the initial value is set based on experience and subsequently optimized through experiments or simulations;

[0048] Calculate the integral term: The integral term is used to calculate the cumulative error over time.

[0049] integral(t)=integral(t-Δt)+e(t)·Δt

[0050] integral(t) is the integral term, which is used to accumulate the change of error over time; Δt is the time change.

[0051] Calculate the differential term: The differential term is used to capture the rate of change of the error

[0052]

[0053] derivative(t) is the differential term, which represents the rate of change of the error.

[0054] Calculate the adjustment amount: Calculate the adjustment amount according to the PID formula:

[0055] ΔK(t)=K p ·e(t)+K i integral(t)+K d ·derivative(t)

[0056] ΔK(t) is the stiffness coefficient adjustment.

[0057] ③ Implement PID dual-position control algorithm through user-defined functions to dynamically adjust contact stiffness;

[0058] Use a PID two-position controller to adjust the contact stiffness:

[0059]

[0060] K old is the stiffness coefficient before adjustment, and e is the nonlinear spring force index of the meshing gear material.

[0061] The above scheme also includes: simulating and calculating the dynamic meshing force response curve of the gear pair, calculating its relative error with the actual value, and comparing it with the existing research method. The comparison results show that the relative error of the present invention is reduced compared with the existing research method, which is closer to the actual situation, reflecting the superiority of the present invention.

[0062] The present invention also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, the steps of the above-mentioned method for analyzing the dynamic meshing force of a gear pair of a dynamically enhanced wind turbine gear transmission system are implemented.

[0063] Compared with the existing technology, the present invention has the following beneficial technical effects:

[0064] (1) By adaptively adjusting contact parameters and friction coefficients, the present invention can more accurately simulate the dynamic response of gear pairs under complex working conditions such as random wind loads. For example, under low-speed and heavy-load conditions, the contact stiffness and damping are adaptively adjusted to ensure accurate calculation of contact force; under high-speed and light-load conditions, the friction coefficient is dynamically adjusted to capture changes in friction behavior. The present invention can effectively capture the changing patterns of contact force, deformation, and sliding speed, improving the reliability and authenticity of simulation results.

[0065] (2) Since the stiffness coefficient is a key factor affecting the simulation results of gear meshing force, the present invention dynamically adjusts the contact stiffness of the gear pair through the feedback mechanism of PID two-position control, and can monitor the simulation results in real time and compare them with the target value to improve the simulation accuracy.

[0066] (3) The present invention can adapt to a variety of working conditions, such as random wind loads, variable speed operation, temperature changes, etc., and has wide applicability. Through the dynamic adjustment mechanism, the stability and accuracy of the model under different working conditions are ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 A flowchart of a method for analyzing the dynamic meshing force of a gear pair in a dynamically enhanced wind turbine gear transmission system;

[0068] Figure 2 This is the structural diagram of the gear transmission system of a 1.5MW wind turbine;

[0069] Figure 3 This is a three-dimensional solid model diagram of the 1.5MW wind turbine gear transmission system;

[0070] Figure 4 The figure is a comparison chart of the simulation results of the present invention and the simulation results of the existing method. DETAILED DESCRIPTION

[0071] First, based on the parameters of a physical 1.5MW wind turbine, the present invention establishes a geometric entity model of the gear transmission system of a 1.5MW wind turbine, providing a three-dimensional model foundation for the subsequent establishment of a virtual prototype model. Secondly, reasonable constraints are imposed on the model and loads are applied to reflect its actual operating status. Then, the dynamic enhanced Hertz contact method is used to define the contact type, and a method of integrating the adaptive contact algorithm and Hertz contact is proposed. At the same time, the Stribeck friction model is introduced to simulate its actual working conditions, and a virtual prototype model is established. The feedback mechanism of PID two-position control is added to dynamically adjust the contact parameters of the gear pair to complement the adaptive contact algorithm. Finally, the simulation results of the present invention are compared with those of the existing methods, which shows the superiority of the present invention.

[0072] The present invention integrates the Hertz contact and adaptive contact algorithms, introduces the Stribeck friction model, and adds a PID two-position control feedback mechanism to improve the simulation accuracy.

[0073] The solution of the present invention is described in more detail below:

[0074] (1) 3D modeling of the 1.5MW wind turbine gear transmission system:

[0075] The present invention takes the gearbox transmission system of a 1.5MW wind turbine as the research object, and its detailed structure is shown in the following figure. Figure 2 As shown, the system adopts a three-stage gear transmission configuration. Figure 2 1 is the ring gear, 2 is the planetary carrier input shaft, 3 is the planetary gear, 4 is the sun gear, 5 is the medium-speed gear, 6 is the medium-speed gear, 7 is the high-speed gear, and 8 is the high-speed gear. Figure 2 A transmission system consisting of a first-stage planetary gear transmission and a two-stage parallel shaft gear transmission is constructed. The principle of its motion is as follows: wind energy drives the blades of the wind turbine to rotate, and then the planetary carrier is driven to rotate by the coupling between the wind wheel and the main shaft. In the configuration of the first-stage planetary gear system, the planetary carrier plays the role of an input component, while the sun gear serves as an output power source, driving the operation of the subsequent two-stage parallel shafts. Finally, the system effectively drives the generator to generate electricity through the third-stage output part. The Young's modulus E = 200GPa, the Poisson's ratio = 0.3, the mass density is 7850kg / m3, and other parameters are shown in Table 1 below:

[0076] Table 1 Basic parameters of the gearbox transmission system of a 1.5MW wind turbine

[0077]

[0078] According to the parameters given in the table, the modeling and assembly steps of each part are carried out in the 3D modeling software to obtain the 3D solid model of the 1.5MW wind turbine gear transmission system. Figure 3 shown.

[0079] (2) Based on the three-dimensional solid model, constraints, drives, and loads are added, contacts are set, and an adaptive contact algorithm and Stribeck friction model are introduced to establish a virtual prototype model; the dynamic meshing force response curve of the gear pair is obtained by simulation and solution based on the virtual prototype model, including:

[0080] For the 1.5MW wind turbine gear transmission system, the fundamental reason why the system can achieve effective motion and power transmission is that there is a precise interaction mechanism between the various components within the system. Based on the dynamic principles of the gear transmission system, a series of precise constraints need to be set to reflect its actual operating status: in the first-stage transmission system, the planetary carrier and the sun gear form a ground rotating pair, each planetary gear forms a rotating pair relative to the planetary carrier, and the ring gear is fixed to the ground; for the second and third-stage transmissions, the gears are constrained on the drive shaft, and the drive shaft itself rotates around the ground; in addition, the mutual contact between the gears is simulated using a solid-solid contact pair, and a drive pair (time-varying speed at the input end) is installed on the planetary carrier at the input end to achieve power transmission. To more realistically reproduce the working scenario of the gearbox, a load should be added to the output end to fully consider the performance of the system. After completing the constraints in the model, the corresponding dynamic drive needs to be accurately applied. To simulate the performance of the gearbox in an actual working environment, by integrating a drive pair on the input planetary carrier, it is necessary to configure the corresponding rated load torque at the output end to ensure the comprehensiveness and accuracy of the test conditions. Based on the actual working conditions, the load is set to 5300 Newton meters (N·M).

[0081] (3) The contact type is defined by combining the Hertz contact and adaptive contact algorithms, and the Stribeck friction model is introduced to more accurately describe the actual motion behavior of the gear. The theoretical formula of Hertz contact is expressed as

[10] :

[0082]

[0083] Where: F n is the normal contact force between meshing gear teeth; K is the contact stiffness coefficient between meshing gear pairs; δ is the pure contact penetration between meshing gears; δ e is the corrected equivalent penetration; nonlinear spring force index of meshing gear material; d max C is the maximum permissible penetration depth between meshing gears; max To achieve the maximum contact damping between meshing gear pairs at maximum penetration depth, is the integral of contact penetration over time.

[0084] The Hertz contact theory parameters include contact stiffness coefficient, contact damping coefficient, and maximum penetration depth. The contact stiffness coefficient can be expressed as:

[0085]

[0086]

[0087]

[0088] Where: R represents the equivalent contact radius, R1 and R2 are the pitch circle radii of the two meshing gears, E1 and E2 are the elastic moduli of the two meshing gears, v1 and v2 are the Poisson's ratios of the materials used for the two meshing gears, and E* is the comprehensive elastic modulus.

[0089] For two meshing helical gears, the contact stiffness coefficient expression is:

[0090]

[0091] Where: "+" in "±" indicates external meshing, "-" indicates internal meshing; d1 is the pitch circle diameter of the driving gear; u is the gear ratio of the two meshing gears; α t -End face pressure angle; α' t - end face engagement angle; β b - Gear helix angle.

[0092] During the meshing process of the gear pair, energy conversion and loss phenomena are significant. This dynamic interaction can be accurately described by the concept of contact damping, or estimated based on the empirical rules in traditional engineering practice. The damping coefficient of the present invention is taken as 1% of the stiffness coefficient.

[0093] Considering that too large or too small a penetration depth may lead to failure of the simulation process, the present invention selects a maximum penetration depth of 0.1 mm based on the material properties and geometric parameters of the meshing gears to ensure that the simulation model can reflect the complex characteristics of the real working conditions.

[0094] In actual working conditions, the input speed and torque of the system often change with wind speed. In Hertz contact, the contact stiffness coefficient, contact damping coefficient, and maximum penetration depth are set to fixed values, which cannot accurately describe the contact conditions under complex working conditions of the wind turbine gear transmission system. The adaptive contact algorithm is introduced to monitor the contact force changes during the meshing process in real time, thereby dynamically adjusting the above three parameters. The specific adjustment method is as follows:

[0095] In the adaptive contact algorithm, a user-defined function (UDF) is used to dynamically adjust contact parameters, such as contact stiffness, damping, and friction coefficient. The specific adjustment formula is expressed as:

[0096] ① Adjustment based on contact force

[0097] The contact stiffness adjusts to changes in the contact force:

[0098]

[0099]

[0100] F nrepresents the contact force, K represents the stiffness coefficient, and C represents the damping coefficient.

[0101] ② Adjustment based on deformation

[0102] The contact stiffness and maximum penetration depth are adjusted according to the deformation:

[0103]

[0104]

[0105] Where K new is the adjusted contact stiffness, C new is the adjusted contact damping, d max，new is the maximum penetration depth after adjustment, F max and F min are the upper and lower thresholds of the contact force, δ max and δ min are the upper and lower thresholds of deformation.

[0106] Since the Hertz contact theory simplifies the friction model by default, and in the actual wind turbine gear transmission process, the gearbox is lubricated and the situation is relatively complex, which has a direct impact on the meshing force. Therefore, this paper introduces the Stribeck friction model to better simulate the friction behavior of the gear pair under actual working conditions. The Stribeck curve shows the relationship between the friction coefficient (μ) and the sliding velocity (v), especially the friction behavior under lubricated conditions. The curve is generally divided into three main regions:

[0107] ① Static friction zone (low speed zone):

[0108] At very low sliding speeds, the friction coefficient approaches the static friction coefficient (μstatic). At this point, friction is dominated by boundary lubrication and the hydrodynamic effects of the lubricant can be ignored.

[0109] ② Mixed lubrication zone (medium speed zone): As the sliding speed increases, the friction coefficient gradually decreases. This is because the lubricant begins to form a hydrodynamic film, partially separating the contact surfaces and thus reducing friction.

[0110] ③ Hydrodynamic lubrication zone (high speed zone): At higher sliding speeds, the friction coefficient tends to a lower stable value (μlubricated). At this point, the lubricant completely separates the contact surface, and friction is mainly controlled by the internal friction of the lubricant.

[0111] The Stribeck curve can be expressed as:

[0112]

[0113] Where μcoulomb is the Coulomb friction coefficient, μ lubricated is the friction coefficient under hydrodynamic lubrication, v min and v max are the starting and ending velocities of the Stribeck curve respectively. static is the static friction coefficient.

[0114] Implement the Stribeck curve using a custom friction model (UDF).

[0115] A feedback mechanism based on PID two-position control is added to dynamically adjust the contact parameters of the gear pair.

[0116] ①Define performance indicators

[0117] The performance indicator is the contact force error, which can be expressed as:

[0118] e(t)=F sim (t)-F ref (t) (11)

[0119] Where, F sim (t) is the contact force obtained by simulation, F ref (t) is the reference contact force, and e(t) is the error variation over time. The error threshold is defined as e threshold =1.0.

[0120] ② Initialize PID two-position controller parameters and calculate parameters

[0121] Define two sets of appropriate PID two-position controller parameters (proportional gain K p , integral gain K i , differential gain K d The initial value can be set based on experience and can be subsequently optimized through experiments or simulations.

[0122] High gain group: K p =1.0,K i =0.1, K d =0.01.

[0123] Low gain group: K p =0.5, K i =0.05, K d =0.01.

[0124] During the simulation process, the error parameters are monitored in real time. When the error is greater than the threshold, the high gain group is called, and when the error is less than the threshold, the low gain group is called.

[0125] Calculate the integral term:

[0126] The integral term is used to accumulate the error over time

[0127] integral(t)=integral(t-Δt)+e(t)·Δt (12)

[0128] integral(t) is the integral term, which is used to accumulate the change of error over time; Δt is the time change.

[0129] Compute the differential term:

[0130] The derivative term is used to capture the rate of change of the error:

[0131]

[0132] derivative(t) is the differential term, which represents the rate of change of the error.

[0133] Calculate the adjustment:

[0134] Calculate the adjustment amount according to the PID formula:

[0135] ΔK(t)=K p ·e(t)+K i integral(t)+K d ·derivative(t) (14)

[0136] ΔK(t) is the stiffness coefficient adjustment.

[0137] ③The contact stiffness adjusted using the PID two-position controller can be expressed as:

[0138]

[0139] K old is the stiffness coefficient before adjustment.

[0140] ④Implement PID dual-position control algorithm

[0141] Through the user-defined function (UDF), the above formula is implemented in code to realize the PID two-position control algorithm and dynamically adjust the contact stiffness.

[0142] Through feedback control, the simulation results can be monitored in real time and compared with the target values, and the model parameters can be dynamically adjusted to improve the simulation accuracy.

[0143] By combining adaptive contact and PID two-position control, more accurate and stable simulation results can be achieved under different operating conditions. Adaptive contact dynamically adjusts contact parameters based on the current contact state, while PID two-position control fine-tunes contact stiffness through a feedback mechanism to ensure accurate simulation results. This combination significantly improves the accuracy and adaptability of simulation models, providing stronger support for design optimization and performance improvement of gear transmission systems.

[0144] (4) Taking the high-speed gear pair as an example, the dynamic meshing force response curve of the gear pair is obtained by simulation calculation and compared with the simulation result diagram of the existing method (such as Figure 4 As shown in the figure, the red figure is the simulation figure obtained by the method of the present invention, and the blue figure is the simulation figure obtained by the existing method. It can be seen from the figure that the method of the present invention reduces many mutations caused by random wind compared with the existing method. The relative errors between these and the actual values are calculated. The comparison results show that the relative errors of the present invention are significantly reduced compared with the existing research methods, the system mutation response is reduced, the operation is smoother, and it is closer to the actual situation, which reflects the superiority of the present invention. Table 2 compares the dynamic meshing force and actual values obtained by simulation of the present invention and the existing method using a high-speed gear pair as an example:

[0145] Table 2 Comparison of simulation results

[0146]

[0147] References

[0148] [1] Feng Haisheng, Wang Liqin, Zheng Dezhi, et al. Dynamic meshing force analysis of gears considering variable working condition impact [J]. Vibration. Testing and Diagnosis, 2015, 35, (2): 212-217, 394.

[0149] [2] He Zeyin, Yi Feng, Yang Zhen, et al. Analytical algorithm for time-varying mesh stiffness of gear pairs taking into account impact and load [J]. Journal of Hunan University (Natural Science Edition), 2024, 51, (12): 38-46.

[0150] [3] Xiao Qian, Wang Danhong, Chen Daoyun, et al. Analysis of dynamic contact characteristics of high-speed train transmission gears considering the influence of inter-tooth sliding [J]. Journal of Mechanical Engineering, 2021, 57, (10): 87-94.

[0151] [4] Luo Yongshui, Zhou Minqiang, Chen Qi, et al. Research on dynamic characteristics of transmission system of megawatt-class wind turbine generator set [J]. Vibration and Shock, 2015, 34, (21): 113-118.

[0152] [5] Lu Zhicheng, Zhou Jianxing, Cui Quanwei, et al. Research on reliability of wind turbine gear transmission system based on dynamics[J]. Acta Energiae Solaris Sinica, 2023, 44, (9): 397-404.

[0153] [6] Xu Fang, Zhou Zhigang. Calculation and statistical analysis of dynamic loads of wind turbine gear transmission system under random wind action[J]. China Mechanical Engineering, 2016, 27, (3): 290-295.

[0154] [7] Lü Hongzhan, Hou Zhiyong, Wang Junzheng, et al. Contact analysis, calculation and simulation research of involute cylindrical gears[J]. Journal of Southeast University (English Edition), 2024, 40, (1): 68-79.

[0155] [8] Lv Zhonghua. Analysis of contact stress characteristics of gear pairs based on Hertz theory[J]. Journal of Lanzhou Institute of Technology, 2023, 30, (3): 5-8.

[0156] [9] Ren Fei, Wang Dexi, Shi Guiqin, et al. Dynamic simulation and fault characteristic analysis of double-ring herringbone planetary gear transmission system based on ADAMS [J]. Journal of Henan Polytechnic University (Natural Science Edition), 2022, 41, (1): 114-121.

[10] Peng Yulin, Wei Jing, Zhang Aiqiang, et al. Vibration characteristics of planetary gear transmission under pitting fault [J]. Journal of Chongqing University, 2025, 48, (1): 10-20.

Claims

1. A method for analyzing the dynamic meshing force of a gear pair of a dynamically enhanced wind turbine gear transmission system, characterized in that: The following steps are involved: Establish a geometric solid model of the 1.5MW wind turbine gear transmission system; Apply constraints, loads and input loads to the established geometric solid model to reflect its actual operating state; By integrating the adaptive contact algorithm with the Hertzian contact and introducing the Stribeck friction model, a dynamically enhanced Hertzian contact method is obtained to define the contact. A PID two-position control feedback mechanism is added to dynamically fine-tune the contact stiffness of the gear pair, which complements the adaptive contact algorithm. The dynamic meshing force response curve of the gear pair is obtained by simulation.

2. The method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to claim 1, characterized in that: The geometric entity model of the 1.5MW wind turbine gear transmission system is established, specifically including: taking the 1.5MW wind turbine gear transmission system as the three-dimensional modeling object, Young's modulus E = 200GPa, Poisson's ratio = 0.3, mass density = 7850kg / m 3 , other specific parameters are shown in the following table According to the parameters given in the table, the parts are modeled and assembled in the 3D modeling software to obtain the geometric solid model of the 1.5MW wind turbine gear transmission system.

3. The method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to claim 1 is characterized in that: The established geometric entity model is subjected to constraints reflecting its actual operating state, and loads and input loads are applied, specifically including: in the primary transmission system, the planet carrier and the sun gear form a ground rotating pair, each planetary gear forms a rotating pair relative to the planet carrier, and the ring gear is fixed to the ground; for the secondary and tertiary transmissions, the gears are constrained on the transmission shaft, and the transmission shaft itself rotates around the ground; in addition, the mutual contact between the gears is simulated using a solid-solid contact pair, a drive pair is installed on the planet carrier at the input end to achieve power transmission, and a load is added to the output end; after completing the addition of constraints in the model, the corresponding dynamic drive is applied, including integrating the drive pair on the planet carrier at the input end and configuring the corresponding rated load torque at the output end.

4. The method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to claim 1, characterized in that: The fusion of the adaptive contact algorithm and the Hertzian contact algorithm specifically includes: The theoretical formula of Hertz contact is expressed as: Where, F n is the normal contact force between meshing gear teeth; K is the contact stiffness coefficient between meshing gear pairs; δ is the pure contact penetration between meshing gears; d max C is the maximum permissible penetration depth between meshing gears; max To achieve the maximum contact damping between meshing gear pairs when the maximum penetration depth is reached, δ e is the corrected equivalent penetration; is the integral of contact penetration over time; The Hertz contact theory parameters include contact stiffness coefficient, contact damping coefficient, and maximum penetration depth. The contact stiffness coefficient can be expressed as: Where: R1 and R2 are the pitch circle radii of the two meshing gears; E1 and E2 are the elastic moduli of the two meshing gears; E* is the combined elastic modulus; v1 and v2 are the Poisson's ratios of the materials used for the two meshing gears; for two meshing helical gears, the contact stiffness coefficient is expressed as: In the formula, "+" in "±" indicates external meshing, and "-" indicates internal meshing; d1 is the pitch circle diameter of the driving gear; u is the gear ratio of the two meshing gears; α t Indicates the end pressure angle; α' t Indicates the end face engagement angle; β b Indicates the gear helix angle; During the meshing process of gear pairs, energy conversion and loss phenomena are significant. This dynamic interaction can be accurately described by the concept of contact damping. An adaptive contact algorithm is introduced to monitor the contact force changes during the meshing process in real time, thereby dynamically adjusting the above three parameters. The specific adjustment methods are as follows: ① Adjustment based on contact force The contact stiffness adjusts to changes in the contact force: F n represents the contact force, K represents the stiffness coefficient, and C represents the damping coefficient; ② Adjustment based on deformation The contact stiffness and maximum penetration depth are adjusted according to the deformation: Where K new is the adjusted contact stiffness, C new is the adjusted contact damping, d max，new is the maximum penetration depth after adjustment, F max and F min are the upper and lower thresholds of the contact force, δ max and δ min : Upper and lower thresholds of deformation.

5. A method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to claim 1 or 4, characterized in that: The Stribeck curve in the Stribeck friction model is expressed as: Where μ coulomb is the Coulomb friction coefficient, μ lubricated is the friction coefficient under hydrodynamic lubrication, v min and v max are the starting and ending velocities of the Stribeck curve, μ static is the static friction coefficient.

6. The method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to claim 1, characterized in that: The PID two-position control feedback mechanism is added to dynamically fine-tune the contact stiffness of the gear pair, specifically including: ①Define the performance index. The performance index is the contact force error, which is expressed as: e(t)=F sim (t)-F ref (t) Where, F sim (t) is the contact force obtained by simulation, F ref (t) is the reference contact force, e(t) is the error variation over time; ② Initialize PID two-position controller parameters and calculate parameters Define two sets of appropriate PID two-position controller parameters, including proportional gain K p , integral gain K i , differential gain K d , the initial value is set based on experience and subsequently optimized through experiments or simulations; Calculate the integral term: The integral term is used to calculate the cumulative error over time. integral(t)=integral(t-Δt)+e(t)·Δt Integral(t) is the integral term, Δt is the time variation; Calculate the differential term: The differential term is used to capture the rate of change of the error derivative(t) is the differential term; Calculate the adjustment amount: Calculate the adjustment amount according to the PID formula: ΔK(t)=K p ·e(t)+K i ·integral(t)+K d ·derivative(t) ΔK(t) is the stiffness coefficient adjustment; ③ Implement PID dual-position control algorithm through user-defined functions to dynamically adjust contact stiffness Use a PID two-position controller to adjust the contact stiffness: K old is the stiffness coefficient before adjustment, and e is the nonlinear spring force index of the meshing gear material.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the computer program, the steps of the method for analyzing the dynamic meshing force of gear pairs of a dynamically enhanced wind turbine gear transmission system according to any one of claims 1 to 6 are implemented.

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