A method for analyzing dynamic meshing force of gear pair of dynamic enhanced gear transmission system of wind turbine

Abstract

The application discloses a dynamic meshing force analysis method for gear pairs of a dynamic enhanced gear transmission system of a wind turbine, and belongs to the field of mechanical system dynamics and control technology. First, a geometric entity model of the 1.5MW wind turbine gear transmission system is established to provide a three-dimensional model basis for subsequent establishment of a virtual prototype. Secondly, reasonable constraints are set for the model, and loads are applied to reflect the actual running state. Then, a dynamic enhanced Hertz contact method is used to define the contact type, a new method combining an adaptive contact algorithm and the Hertz contact is proposed, and a Stribeck friction model is introduced to simulate the real working condition, so that the virtual prototype model is established. Further, the contact stiffness of the gear pairs is dynamically fine-tuned based on the feedback mechanism of the PID double-bit control. Therefore, the precision of the dynamic meshing force of the gear pairs of the wind turbine gear transmission system is further improved.

Description

Technical Field

[0001] This invention belongs to the field of mechanical system dynamics and control technology, specifically relating to a method for analyzing the dynamic meshing force of gear pairs in a dynamically enhanced wind turbine gear transmission system. Background Technology

[0002] With the acceleration of the global energy transition, wind power, as a clean and renewable energy technology, is becoming increasingly important. As a core component of wind turbine generators, the gear transmission system directly affects the overall operating efficiency and lifespan of the machine. The gear pair, as a key component in the gear transmission system, has dynamic meshing force characteristics that are one of the key factors affecting system stability and reliability. [1-3] .

[0003] Luo Yongshui et al. [4] Statistical analysis of the dynamic meshing force of gears using the rainflow counting method reveals that the dynamic meshing force exhibits strong time-varying characteristics. (Wang Yefeng) [5] The dynamic meshing force obtained from the lumped parameter model is applied to the finite element model of the internal gear ring to calculate the dynamic response of the internal gear ring, and this is combined with the deformation threshold when multi-tooth meshing occurs. (Xu Fang) [6] By simulating the dynamic model, the dynamic meshing force of each gear pair and the dynamic contact force of each supporting bearing were obtained. Combining the finite element method and Hertzian contact theory, the stress time history of key components was derived. (Lu Hongzhan et al.) [7] A precise modeling method using the parametric equations of involute spur gears was employed to obtain the radius of curvature at the tooth profile contact points. Considering actual loads, the Hertzian contact formula was improved to solve for the gear meshing contact stress. (Lu Zhonghua) [8] Based on Hertzian contact theory, linear coordinate parameters and a Hertzian stress model for gear pairs were established. A formula for calculating 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. (Ren Fei et al.) [9] Based on the ADAMS virtual prototype and Hertzian contact theory, and considering the friction coefficient, a virtual prototype model of the system is constructed to study the kinematic laws of the herringbone planetary gear transmission system, the contact force spectrum characteristics under both healthy and faulty states, and the contact force variation law considering the component support stiffness. Based on the contact force analysis, the system's load-sharing coefficient is calculated, and the system's load-sharing characteristics are analyzed.

[0004] Existing methods for studying the dynamic meshing force of gear pairs have many limitations under complex operating conditions, making it difficult to meet the requirements of efficient and reliable operation of modern wind turbines. Traditional methods for studying the dynamic meshing force of gear pairs are mainly 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 the deformation in the contact area is elastic and that the contact surface is smooth, considering only the normal force. Hertzian contact theory uses analytical methods to calculate 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 actual working conditions. For example, gear pairs are affected by various complex factors during operation, such as random wind loads and variable speed operation. These factors lead to dynamic changes in the deformation of the contact area, contact force, and friction. Traditional Hertzian contact theory cannot fully account for these dynamic changes, thus limiting its applicability in complex working conditions. Summary of the Invention

[0006] In studying the dynamic meshing force of gear pairs in wind turbine gear transmission systems, insufficient simulation accuracy due to various factors is a current challenge. Traditional Hertzian contact theory, a classic elastic contact theory, is used to analyze the stress distribution and deformation behavior of two elastic bodies in contact. However, under complex actual working conditions, the rotation and meshing of gears with the input wind speed leads to time-varying parameters during meshing, necessitating the use of better simulation methods to model real-world conditions. This invention aims to address the problems of existing technologies by proposing a dynamically enhanced method for analyzing the dynamic meshing force of gear pairs in wind turbine gear transmission systems. This invention significantly improves simulation accuracy and adaptability by integrating Hertzian contact theory and adaptive contact theory, and introducing the Stribeck friction model. Furthermore, a feedback mechanism based on PID dual-position control is added to dynamically adjust the contact parameters of the gear pairs to obtain more suitable stiffness, complementing the adaptive contact algorithm.

[0007] The technical solution adopted by this invention to solve its technical problem is as follows:

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

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

[0010] To impose constraints reflecting the actual operating state on the established geometric solid model, apply loads and input loads;

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

[0012] Furthermore, the establishment of the geometric solid model of the 1.5MW wind turbine gear transmission system specifically includes: using the 1.5MW wind turbine gear transmission system as the three-dimensional modeling object, with Young's modulus E = 200 GPa, Poisson's ratio = 0.3, and mass density = 7850 kg / m³. 3 Other specific parameters are shown in the table below.

[0013]

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

[0015] Furthermore, the process of applying constraints reflecting the actual operating state to the established geometric solid model, and applying loads and input loads, specifically includes: in the first-stage transmission system, the planet carrier and the sun gear form a ground-based revolute pair, each planet gear forms a revolute pair relative to the planet carrier, while the ring gear is fixed to the ground; for the second and third-stage transmissions, the gears are constrained on the drive shaft, which itself rotates around the ground; in addition, the mutual contact between gears is simulated using solid-solid contact pairs, a drive pair is installed on the planet carrier at the input end to achieve power transmission, and a load is applied to the output end; after completing the addition of constraints in the model, corresponding dynamic drives are applied, including integrating drive pairs on the planet carrier at the input end while configuring corresponding rated load torque at the output end.

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

[0017] The theoretical formula for Hertzian contact is expressed as:

[0018]

[0019] In the formula, F n δ 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 the meshing gear pairs at the maximum penetration depth, δ e This is the corrected equivalent permeability; This is the integral of the contact penetration amount over time.

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

[0021]

[0022]

[0023]

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

[0025]

[0026] In the formula, "+" in "±" indicates external meshing, and "-" indicates internal meshing; d1 represents the pitch circle diameter of the driving gear; u represents the gear ratio between the two meshing gears; α t Indicates the end-face 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, and this dynamic interaction can be accurately described by the concept of contact damping.

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

[0029] ① Adjustment based on contact force

[0030] The contact stiffness is adjusted according to the change in contact force:

[0031]

[0032]

[0033] F n K 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 change in deformation:

[0036]

[0037]

[0038] In the formula, K new For the adjusted contact stiffness, C new For the adjusted contact damping, d max，new F is the adjusted maximum penetration depth. max and F min δ represents the upper and lower threshold values ​​of the contact force. max and δ min : Upper and lower limits of deformation.

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

[0040]

[0041] In the formula, μ coulomb μ is the Coulomb friction coefficient. lubricated v is the coefficient of friction under hydrodynamic lubrication. min and v max Let μ be the initial and final velocities of the Stribeck curve, respectively. static It is the static friction coefficient.

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

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

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

[0045] In the formula, F sim (t) represents the contact force obtained from the simulation, F ref e(t) is the reference contact force, and e(t) is the change in error over time.

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

[0047] Define two sets of suitable PID two-position controller parameters, including the proportional gain K. p Integral gain K i Differential gain K d The initial values ​​are set based on experience and then optimized through experiments or simulations.

[0048] Calculate the integral term: The integral term is used to accumulate the change of error over time.

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

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

[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, used to represent 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 amount.

[0057] ③ The PID two-position control algorithm is implemented through user-defined functions to dynamically adjust the contact stiffness;

[0058] Adjusting contact stiffness using a PID two-position controller:

[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 existing research methods. The comparison results show that the relative error of the present invention is reduced compared with existing research methods, and is closer to the actual situation, demonstrating the superiority of the present invention.

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

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

[0064] (1) By adaptively adjusting contact parameters and friction coefficient, this 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 heavy-load conditions, the contact stiffness and damping are adaptively adjusted to ensure accurate calculation of contact force; under high-speed light-load conditions, the friction coefficient is dynamically adjusted to capture changes in friction behavior. This invention can effectively capture the changing patterns of contact force, deformation, and sliding speed, improving the reliability and realism of simulation results.

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

[0066] (3) This invention can adapt to various working conditions, such as random wind load, variable speed operation, and temperature changes, and has wide applicability. Through a dynamic adjustment mechanism, the stability and accuracy of the model under different working conditions are ensured. Attached Figure Description

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

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

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

[0070] Figure 4 This is a comparison chart of the simulation results of the present invention and the simulation results of existing methods. Detailed Implementation

[0071] First, based on the parameters of a physical 1.5MW wind turbine, this invention establishes a geometric solid model of the gear transmission system of the 1.5MW wind turbine, providing a three-dimensional model foundation for the subsequent establishment of a virtual prototype model. Second, reasonable constraints and loads are applied to the model to reflect its actual operating state. Next, a dynamic enhanced Hertzian contact method is used to define the contact type, proposing a method that integrates adaptive contact algorithms and Hertzian contact. Simultaneously, the Stribeck friction model is introduced to simulate its actual working conditions. A virtual prototype model is established, and a PID two-position control feedback mechanism is added to dynamically adjust the contact parameters of the gear pair, complementing the adaptive contact algorithm. Finally, simulation results comparing this invention with existing methods demonstrate the superiority of this invention.

[0072] This invention integrates Hertzian contact with adaptive contact algorithms, introduces the Stribeck friction model, and incorporates a feedback mechanism of PID two-position control, thereby improving simulation accuracy.

[0073] The present invention will now be described in more detail:

[0074] (1) Three-dimensional modeling of the gear transmission system of a 1.5MW wind turbine:

[0075] This invention takes the gearbox transmission system of a 1.5MW wind turbine generator set as the research object, and its detailed structural diagram is shown below. Figure 2 As shown, the system adopts a three-stage gear transmission configuration. Figure 2 In the diagram, 1 is the gear ring, 2 is the planetary carrier input shaft, 3 is the planetary gear, 4 is the sun gear, 5 is the medium-speed stage large gear, 6 is the medium-speed stage small gear, 7 is the high-speed stage large gear, and 8 is the high-speed stage small gear; according to... Figure 2 A transmission system consisting of a single-stage planetary gear drive and a two-stage parallel shaft gear drive was constructed. Its operating principle is as follows: wind energy drives the wind turbine blades to rotate, and then, through the coupling between the turbine and the main shaft, the planetary carrier rotates. In the single-stage planetary gear system, the planetary carrier acts as the input component, while the sun gear serves as the output power source, driving the subsequent two stages of parallel shafts. Finally, the system effectively drives the generator to produce electricity through the third-stage output section. The Young's modulus E = 200 GPa, Poisson's ratio = 0.3, and mass density is 7850 kg / m³. 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] Based on the parameters given in the table, the modeling and assembly of each part are performed in 3D modeling software to obtain a 3D solid model of the 1.5MW wind turbine gear transmission system, as shown below. Figure 3 As shown.

[0079] (2) Based on the 3D solid model, constraints, drives, and loads are added, contact is 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 based on the virtual prototype model, specifically including:

[0080] For a 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 principle of the gear transmission system, a series of precise constraints need to be set to reflect its actual operating state: In the first-stage transmission system, the planet carrier and the sun gear form a ground-based rotating pair, and each planet gear forms a rotating pair relative to the planet carrier, while 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 gears is simulated using a solid-solid contact pair, and a drive pair (time-varying speed at the input end) is installed on the planet carrier at the input end to realize power transmission. To more realistically recreate the working scenario of the gearbox, a load should be added to the output end to comprehensively evaluate the system's performance. After adding constraints to the model, the corresponding dynamic drive needs to be applied precisely. To simulate the gearbox's performance in the actual working environment, while integrating the drive pair on the planetary carrier at the input end, the corresponding rated load torque needs to be configured 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 Nm.

[0081] (3) A method combining Hertzian contact and adaptive contact algorithms is used to define contact types, and the Stribeck friction model is introduced to more accurately describe the actual motion behavior of gears. The theoretical formula for Hertzian contact is expressed as follows:

[10] :

[0082]

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

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

[0085]

[0086]

[0087]

[0088] In the formula: 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 in the two meshing gears, and E* is the comprehensive elastic modulus.

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

[0090]

[0091] In the formula: "±" indicates external meshing, and "-" indicates internal meshing; d1 is the pitch circle diameter of the driving gear; u is the gear ratio between 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 gear pairs, energy conversion and loss phenomena are significant. This dynamic interaction can be accurately described by the concept of contact damping, or estimated based on empirical rules in traditional engineering practice. The damping coefficient of this invention is taken as 1% of the stiffness coefficient.

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

[0094] In actual operating conditions, the system's input speed and torque often vary with wind speed. Hertzian contact sets the contact stiffness coefficient, contact damping coefficient, and maximum penetration depth to constant values, which cannot accurately describe the contact situation under the complex operating conditions of the wind turbine gear transmission system. Therefore, an adaptive contact algorithm is introduced to monitor the changes in contact force during meshing in real time, thereby dynamically adjusting the above three parameters. The specific adjustment method is as follows:

[0095] In adaptive contact algorithms, defined functions (UDFs) are used to dynamically adjust contact parameters, such as contact stiffness, damping, and friction coefficient. The specific adjustment formulas are as follows:

[0096] ① Adjustment based on contact force

[0097] The contact stiffness is adjusted according to the change in contact force:

[0098]

[0099]

[0100] F nK represents 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 change in deformation:

[0103]

[0104]

[0105] In the formula, K new For the adjusted contact stiffness, C new For the adjusted contact damping, d max，new F is the adjusted maximum penetration depth. max and F min δ represents the upper and lower threshold values ​​of the contact force. max and δ min These are the upper and lower threshold values ​​for the deformation amount.

[0106] Because Hertzian contact theory simplifies the friction model by default, and in actual wind turbine gear transmission processes, the gearbox is lubricated and quite complex, which directly affects the meshing force, this invention introduces the Stribeck friction model to better simulate the friction behavior of gear pairs under actual operating conditions. The Stribeck curve shows the relationship between the coefficient of friction (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 coefficient of friction approaches the static coefficient of friction (μstatic). At this point, friction is mainly controlled by boundary lubrication, and the hydrodynamic effect of the lubricant can be ignored.

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

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

[0111] The Stribeck curve can be represented as:

[0112]

[0113] In the formula, μcoulomb μ is the Coulomb friction coefficient. lubricated v is the coefficient of friction under hydrodynamic lubrication. min and v max These represent the initial and final velocities of the Stribeck curve, respectively. μ static It is the static friction coefficient.

[0114] The Stribeck curve is achieved 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] ① Define 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] In the formula, F sim (t) represents the contact force obtained from the simulation, F ref e(t) represents the reference contact force, and e(t) represents the change in error over time. The defined error threshold is e(t). threshold =1.0.

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

[0121] Define two sets of suitable PID two-position controller parameters (proportional gain K) p Integral gain K i Differential gain K d The initial values ​​can be set based on experience and can be 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, error parameters are monitored in real time. When the error exceeds the threshold, the high-gain group is activated; when the error is less than the threshold, the low-gain group is activated.

[0125] Calculate the integral term:

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

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

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

[0129] Calculate the differential term:

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

[0131]

[0132] derivative(t) is the differential term, used to represent the rate of change of the error.

[0133] Calculate the adjustment amount:

[0134] Calculate the adjustment amount based on 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 amount.

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

[0138]

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

[0140] ④ Implement PID two-position control algorithm

[0141] The above formula is implemented using user-defined functions (UDFs) to achieve a PID two-position control algorithm and dynamically adjust the contact stiffness.

[0142] Through feedback control, simulation results can be monitored in real time and compared with target values, and model parameters can be dynamically adjusted to improve 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 according to the current contact state, while PID two-position control fine-tunes contact stiffness through a feedback mechanism to ensure the accuracy of the simulation results. The combination of the two can significantly improve the accuracy and adaptability of the simulation model, providing stronger support for the design optimization and performance improvement of gear transmission systems.

[0144] (4) Taking a high-speed gear pair as an example, the dynamic meshing force response curve of the gear pair is obtained through simulation calculation, and compared with the simulation results of existing methods (e.g., Figure 4 As shown in the figure, red represents the simulation diagram obtained by the method of the present invention, and blue represents the simulation diagram obtained by the existing method. The figure shows that the method of the present invention, compared with the existing method, reduces many sudden changes caused by random wind. The relative errors between these methods and the actual values ​​are calculated. The comparison results show that the relative error of the present invention is significantly reduced compared to the existing research methods, resulting in less sudden system response, smoother operation, and closer resemblance to actual conditions, demonstrating the superiority of the present invention. Table 2 compares the dynamic meshing force obtained by the present invention and the actual values ​​obtained by the existing method, taking 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 impact under variable working conditions [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 meshing stiffness of gear pairs considering 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. Study 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. Reliability study 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 load on gear transmission system of wind turbine under random wind action [J]. China Mechanical Engineering, 2016, 27, (3): 290-295.

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

[0155] [8] Lü 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 a 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 gear pairs in a dynamically enhanced wind turbine gear transmission system, characterized in that, Includes the following steps: Establish a geometric solid model of the gear transmission system of a 1.5MW wind turbine; To impose constraints reflecting the actual operating state on the established geometric solid model, apply loads and input loads; By integrating the adaptive contact algorithm with Hertzian contact and introducing the Stribeck friction model, a dynamically enhanced Hertzian contact method is obtained to define the contact. A feedback mechanism of PID two-position control 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. The fusion of the adaptive contact algorithm with Hertzian contact specifically includes: The theoretical formula for Hertzian contact is expressed as: In the formula, F n δ represents 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. This refers to the maximum permissible penetration depth between meshing gears; To achieve the maximum contact damping between the meshing gear pairs at the maximum penetration depth, This is the corrected equivalent permeability; This is the integral of the contact penetration amount over time. Hertzian contact theory parameters include three: contact stiffness coefficient, contact damping coefficient, and maximum penetration depth. The contact stiffness coefficient can be expressed as: In the formula: R1 and R2 are the pitch circle radii of the two meshing gears, respectively; E1 and E2 are the elastic moduli of the two meshing gears, respectively; E* is the combined elastic modulus; v1 and v2 are the Poisson's ratios of the materials used in the two meshing gears, respectively; for two meshing helical gears, the expression for their contact stiffness coefficient is: In the formula, "+" indicates external meshing and "-" indicates internal meshing; d1 represents the pitch circle diameter of the driving gear; u represents the gear ratio between the two meshing gears; α t Indicates the end face pressure angle; 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, and this dynamic interaction can be accurately described by the concept of contact damping. An adaptive contact algorithm is introduced to monitor the changes in contact force during meshing in real time, thereby dynamically adjusting the above three parameters. The specific adjustment method is as follows: ① Adjustment based on contact force The contact stiffness is adjusted according to the change in contact force: Indicates contact force. Indicates the stiffness coefficient. Indicates the damping coefficient; ② Adjustment based on deformation The contact stiffness and maximum penetration depth are adjusted according to the change in deformation: In the formula, K new For the adjusted contact stiffness, C new For the adjusted contact damping, d max，new F is the adjusted maximum penetration depth. max and F min δ represents the upper and lower threshold values ​​of the contact force. max and δ min : Upper and lower limits of deformation; The feedback mechanism incorporating PID dual-position control to dynamically fine-tune the contact stiffness of the gear pair specifically includes: ① Define the performance index, which is the contact force error, expressed as: In the formula, F sim (t) represents the contact force obtained from the simulation, F ref (t) is the reference contact force. This represents the change in error over time. ② Initialize the PID two-position controller parameters and calculate the parameters. Define two sets of suitable PID two-position controller parameters, including the proportional gain K. p Integral gain K i Differential gain K d The initial values ​​are set based on experience and then optimized through experiments or simulations. Calculate the integral term: The integral term is used to accumulate the change of error over time. integral(t)=integral(t−Δt)+e(t)·Δt integral(t) is the integral term, and Δt is the change in time. Calculate the differential term: The differential term is used to capture the rate of change of the error. For differential terms; 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 amount; ③ Implement a PID two-position control algorithm through user-defined functions to dynamically adjust contact stiffness. Adjusting contact stiffness using a PID two-position controller: is the stiffness coefficient before adjustment, and e is the nonlinear spring force index of the meshing gear material.

2. The method for analyzing the dynamic meshing force of gear pairs in a dynamically enhanced wind turbine gear transmission system according to claim 1, characterized in that: The establishment of the geometric solid model of the 1.5MW wind turbine gear transmission system specifically includes: using the 1.5MW wind turbine gear transmission system as a three-dimensional modeling object, with Young's modulus E=200GPa, Poisson's ratio=0.3, and mass density=7850kg / m³. 3 Other specific parameters are shown in the table below. Based on the parameters given in the table, the various parts are modeled and assembled in 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 in a dynamically enhanced wind turbine gear transmission system according to claim 1, characterized in that: The process involves applying constraints reflecting the actual operating state to the established geometric solid model, and applying loads and input loads. Specifically, in the first-stage transmission system, the planet carrier and sun gear form a ground-based revolute pair, with each planet gear forming a revolute pair relative to the planet carrier, while the ring gear is fixed to the ground. For the second and third-stage transmissions, the gears are constrained on the drive shaft, which itself rotates around the ground. Furthermore, the contact between gears is simulated using solid-to-solid contact pairs. A drive pair is installed on the planet carrier at the input end to achieve power transmission, and a load is applied to the output end. After adding constraints to the model, corresponding dynamic drives are applied, including integrating a drive pair on the planet carrier at the input end while configuring a corresponding rated load torque at the output end.

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

5. 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, it implements the steps of the method for analyzing the dynamic meshing force of a gear pair in a dynamically enhanced wind turbine gear transmission system as described in any one of claims 1 to 4.

Images