A method for optimizing a fan conical roller bearing cage structure

Abstract

The application provides a fan conical roller bearing cage structure optimization method to solve the problem of insufficient friction reduction and vibration reduction performance caused by unreasonable cage structure design, comprising: obtaining cage structure parameters; establishing a conical roller bearing dynamics simulation model and verifying the model accuracy; based on the working condition parameters and the structure parameters, performing orthogonal test design, the working condition parameters including the inner ring rotating speed, the radial force and the axial force; taking the working condition parameters and the structure parameters as design variables, taking the minimum value of the slip rate and the sum of the friction forces as the optimization total target, taking the simulation results of the orthogonal test design as the training data of the BP neural network model, and establishing a nonlinear mapping model of the design variables and the optimization target; using the particle swarm algorithm to optimize the established BP neural network model to obtain the best structure parameters; and comparing the slip rate and the friction force of the best structure parameters after optimization with the structure parameters before optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bearings, in particular to a method for optimizing the structure of a retaining cage of a conical roller bearing for a fan. BACKGROUND

[0002] The main bearing of a wind turbine is a core component of a wind turbine generator system, and its performance directly affects the operational stability and service life of the entire machine. Conical roller bearings are widely used in the main shaft system of a fan due to their strong load-carrying capacity, but the retaining cage often becomes a weak link. Unreasonable design of the retaining cage can easily lead to an increase in the slip rate and friction, causing temperature rise, wear, and even damage to the retaining cage, which seriously affects the reliability of the bearing.

[0003] Currently, research on reducing friction and vibration of the retaining cage mainly focuses on structural optimization design. For example, Chinese patent CN118669439A discloses a low-friction rolling bearing retaining cage and a design method thereof. This method improves the lubrication state, reduces friction, and prolongs the service life of the bearing by setting an arc-shaped groove on the pocket and optimizing the position of the lubrication contact point. Although this scheme can improve the lubrication performance to some extent, its optimization still mainly relies on geometric structure adjustment, making it difficult to meet the needs of multi-objective optimization (such as simultaneous optimization of slip rate and friction) under complex working conditions. For example, Chinese patent CN118586108A proposes a method for optimizing the structure of a V-shaped pocket needle bearing retaining cage. This method collects multiple sets of retaining cage optimization parameter data and calculates the corresponding index data, extracts principal component parameters and their weights using principal component analysis, establishes a functional relationship between the principal component parameters and the optimization parameters, and finally constructs a total objective function and solves the optimal solution to ensure the stability and reliability of the retaining cage structure. However, this method mainly relies on statistical correlation and fails to fully consider the coupling effect of slip rate and friction under complex working conditions, and lacks systematic research on key geometric variables. SUMMARY

[0004] The present application aims to overcome the shortcomings of the prior art and provide a method for optimizing the structure of a retaining cage of a conical roller bearing for a fan, to solve the problem of insufficient friction reduction and vibration reduction performance due to unreasonable design of the retaining cage structure, and to quickly determine the optimal structure combination of the retaining cage that meets the dual-objective optimization requirements of "low slip rate + low friction" under complex working conditions, providing important technical support and theoretical basis for high-reliability bearing design in the fields of wind power, rail transportation, and heavy machinery.

[0005] To achieve the above objectives, the present application is implemented through the following technical solutions:

[0006] A method for optimizing the structure of a retaining cage of a conical roller bearing for a fan, comprising the following steps:

[0007] S1, obtain the structure parameters of the cage, the structure parameters including the depth of the pressure slope, the inclination of the pressure slope, the curvature of the pressure slope and the gap between pockets;

[0008] S2, establish a dynamic simulation model of the tapered roller bearing and verify the accuracy of the model;

[0009] S3, based on the working condition parameters of the tapered roller bearing and the structure parameters of the cage, perform an orthogonal test design, the working condition parameters including the rotational speed of the inner ring, the radial force and the axial force;

[0010] S4, take the working condition parameters and the structure parameters as design variables, take the minimum value of the slip rate and the sum of the friction as the overall optimization target, take the simulation results of the orthogonal test design as the training data of the BP neural network model, and establish a nonlinear mapping model of the design variables and the optimization target;

[0011] S5, optimize the established BP neural network model using a particle swarm algorithm to obtain the best structure parameters;

[0012] S6, compare the slip rate and the friction of the optimized best structure parameters and the structure parameters before optimization under different working condition parameters, and if the optimization requirement is not met, adjust the particle swarm algorithm parameters and re-execute step S5.

[0013] Further, in step S1, when designing the pressure slope structure of the cage, a Bezier curve is used to smooth the pressure slope curve of the cage, so that the curvature of the pressure slope changes continuously along the contact path.

[0014] Further, in step S2, the model accuracy verification method is as follows: under the condition that the load and rotational speed are the same, the average slip rate of the cage is calculated, the dynamic simulation model of the tapered roller bearing is compared with the existing model experimental data, and if the slip rate deviation is within the preset range, it means that the accuracy of the dynamic simulation model of the tapered roller bearing meets the requirements.

[0015] Further, in step S3, the friction value between the tapered roller and the bearing cage is calculated by the following formula:

[0016] ;

[0017] In the formula: is the oil film friction coefficient, is the normal contact force between the roller and the cage in the tapered roller bearing;

[0018] ;

[0019] In the formula: is the oil film parameter, is the full fluid lubrication, is the boundary lubrication, For mixed lubrication, and All measurements were taken using a friction testing machine. s represents the sliding-rolling ratio, and A, B, C, and D are preset coefficients.

[0020] Furthermore, in step S4, the BP neural network model includes:

[0021] The input layer is used to input operating condition parameters and cage structure parameters.

[0022] The hidden layer uses a non-linear activation function.

[0023] The output layer is used to output the slip rate and friction force separately.

[0024] Furthermore, a purely linear transfer function is used between the hidden layer and the output layer.

[0025] Furthermore, the BP neural network model is trained using the trainlm algorithm until the mean squared error is lower than a preset threshold or the maximum number of iterations is reached.

[0026] Furthermore, after the BP neural network model is trained, the coefficient of determination R is used. 2 Verify the fit of the sample:

[0027] ;

[0028] In the formula: This is the actual value. For predicted values, This is the average of the true values.

[0029] Furthermore, in step S5, the BP neural network model is optimized using the particle swarm optimization algorithm, including the following steps:

[0030] The parameters of the particle swarm algorithm are set, including particle swarm size, particle dimension, number of iterations, inertia weight, learning factor, and iteration step size range. The particle swarm dimension includes inner ring rotation speed, radial force, axial force, slope inclination angle, slope curvature, slope depth, and pocket gap.

[0031] Initialize the position and velocity of the particle swarm, where the position of each particle represents its dimension and the velocity represents the direction and step size of movement of that particle dimension in the exploration space.

[0032] The position vector of each particle is input into a trained BP neural network model to predict the corresponding slip rate and friction value.

[0033] The fitness value of each particle is calculated based on the prediction results, and the fitness value is determined by the overall objective function of the parameters to be optimized.

[0034] Update the velocity and position of each particle based on its individual historical best position and the global historical best position;

[0035] Repeat the iteration until the termination condition is met, and output the combination of structural parameters corresponding to the globally optimal position.

[0036] Furthermore, the overall objective function for the parameters to be optimized is:

[0037] ;

[0038] in, Let be the overall objective function that minimizes the sum of the slippage rate and the frictional force. Let slip rate be the objective function. Let the objective function be friction force;

[0039] Design variables:

[0040] ,in, The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, To measure the slope depth, To reduce the curvature of the slope, It is the pocket clearance, and satisfies the following constraints:

[0041] ;

[0042] in, This refers to the limiting speed of the tapered roller bearing. This represents the actual maximum radial force during the operation of the tapered roller bearing. This represents the maximum axial force during the actual operation of the tapered roller bearing. The maximum allowable slope angle of the cage without macroscopic slippage between the cage and the rolling elements. To satisfy the minimum effective thickness of the pocket sidewall and the minimum allowance required for processing the curvature of the bevel surface, the maximum value of the bevel surface depth is required. To determine the maximum value under the condition that the cage and rolling elements form the minimum allowable contact surface area. This is the maximum value at which the rolling elements and the cage do not experience intermittent impacts.

[0043] The technical solution provided by this invention has the following advantages compared with the prior art:

[0044] 1. The optimization objective is "low slip rate + low friction" as the dual objective function, which breaks through the limitation of the past that only a single performance index is used as the objective;

[0045] 2. Two key geometric parameters, the curvature and depth of the slope surface, were introduced into the optimization variables. Combined with factors such as rotational speed, radial force, axial force, hole clearance and slope inclination angle, a complete working condition-structure optimization variable system was constructed.

[0046] 3. In terms of optimization methods, a BP neural network is used to establish a nonlinear mapping relationship between input parameters and performance indicators, and a particle swarm optimization algorithm is combined to achieve global optimization, thereby improving prediction accuracy and avoiding the tendency of traditional methods to get trapped in local optima.

[0047] 4. This invention can quickly determine the optimal cage structure combination that meets the dual objectives of "low slippage rate + low friction" under complex working conditions, providing important technical support and theoretical basis for the design of high-reliability bearings in fields such as wind power, rail transit and heavy-duty machinery. Attached Figure Description

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0049] Figure 1 This is a flowchart of the method for optimizing the cage structure of the tapered roller bearing for wind turbines according to the present invention;

[0050] Figure 2 A schematic diagram of the cage pressure slope structure for a tapered roller bearing in a wind turbine;

[0051] Figure 3 Schematic diagram of the improved cage pressure slope structure for Bézier curves;

[0052] Figure 4 This is a schematic diagram comparing the experimental data of the tapered roller bearing model of this invention with the model in the reference.

[0053] Figure 5 A schematic diagram showing the comparison of friction before and after optimization using Bézier curves;

[0054] Figure 6 Here is a flowchart of the BP neural network model;

[0055] Figure 7 Here is a flowchart of the particle swarm optimization algorithm;

[0056] Figure 8 Comparison chart before and after slippage rate optimization;

[0057] Figure 9 Comparison chart before and after friction optimization. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0059] A method for optimizing the cage structure of a tapered roller bearing for wind turbines, such as... Figure 1 and Figure 2 As shown, it includes the following steps:

[0060] S1. Obtain the structural parameters of the cage, including the slope depth, slope angle, slope curvature, and pocket clearance.

[0061] Specifically, when designing the cage pressure slope structure of the tapered roller bearing for the wind turbine, Bézier curves are used in the design, such as... Figure 3 As shown, this embodiment includes the following steps:

[0062] S11. A second-order Bézier curve is generated from three points: the starting point, the control point, and the ending point. By adjusting the control point, the curvature of the Bézier curve can be varied. It is mainly used to design relatively simple curves. The formula describing the points on a second-order Bézier curve is as follows:

[0063] Here, the starting point P0, the control point P1, and the ending point P2 are three points, and β represents any point P2 chosen between P0 and P1. That is, proportion. This represents a point on the Bézier curve with a scale of β.

[0064] S12. The Bézier curve subdivision algorithm is used to smooth the cage pressure slope curve, thereby solving the Bézier curve fitting distortion problem. The principle of the Bézier curve subdivision algorithm is to split the original Bézier curve into two Bézier curves.

[0065] S13. The subdivision function of a second-order Bézier curve can be defined as:

[0066] ;

[0067] ;

[0068] In the formula, the parameter μ represents the distortion rate. Let C represent the column vector of control points in the original Bézier curve, A1 be the transformation matrix of the first Bézier curve, and A2 be the transformation matrix of the second Bézier curve. This is the result obtained after applying the transformation matrix A1, representing the set of control points for the first new Bézier curve after segmentation. It is the result obtained after applying the transformation matrix A2, representing the set of control points for the second new Bézier curve after segmentation;

[0069] The transformation matrices with respect to μ given by A1 and A2 are represented as follows:

[0070] , ;

[0071] Assuming the column vectors of the control points of the first and second subdivided Bézier curves are C1 and C2 respectively, then: , ;

[0072] Establish a coordinate system for the cage's slope surface, with the cage's inner diameter and the bottom of the pocket wall as the origin, the tangent to the cage's inner diameter as the horizontal axis, and the outer diameter of the cage as the vertical axis. Control points ,end These are the three points of the original Bézier curve. Through the above formula, we obtain three subdivided points, V0, V1, and V2. P0, V0, and V2 form the control points of a second-order Bézier curve, and V1, V2, and P2 form the control points of another second-order Bézier curve. In this way, the original Bézier curve is split into two Bézier curves. By adjusting the parameter μ, the fitting curve formed by combining the two subdivided Bézier curves will become closer and closer to the trajectory formed by connecting P0, P1, and P2.

[0073] Where V0 is a point taken on the line segment from P0 to P1 at a ratio of μ, representing the tangent direction at the starting point of the original curve; V1 is a point taken on the line segment from P1 to P2 at the same ratio, representing the tangent direction at the ending point of the original curve; V2 is a point taken on the line segment from V0 to V1 at the same ratio, which is the curve obtained after the original curve's subdivision points at parameter μ are processed by the Bézier curve subdivision algorithm; from Figure 3 As can be seen from the data, the smaller the value of μ, the closer the final curve is to the trajectory of the original control point. The curve is denoted as a function... Maintain the curvature of the frame-pressed slope. Then it is: ;

[0074] For slope depth : ;

[0075] For the slope inclination angle : ;

[0076] For pocket gap : In the formula The average diameter of the rolling element. This represents the average width of the pocket.

[0077] S2. Establish a dynamic simulation model of tapered roller bearings and verify the accuracy of the model.

[0078] Specifically, a three-dimensional geometric model of the tapered roller bearing for the main shaft of the wind turbine was created using SolidWorks and then imported into Adams for dynamic modeling. By setting boundary conditions with the outer ring fixed and the inner ring rotating, and by applying contact constraints between the various components of the bearing, the motion behavior of the cage under working conditions was simulated and analyzed using different contact parameters and a suitable solver.

[0079] The rotational speed data of the tapered roller bearing cage of the wind turbine was extracted using Adams post-processing, and then calculated according to the formula. Calculate the slip ratio, where, To maintain the actual rotational speed of the cage, To the theoretical rotational speed of the cage;

[0080] To verify the accuracy of the tapered roller bearing dynamic model established in this invention, a 32212 type tapered roller bearing was used as the object. Based on the load and speed conditions described in the literature [A dynamic analysis of tapered roller bearings under fully flooded conditions part 2: results], the average cage slippage rate was calculated and compared with the experimental data in that literature. The comparison curves of the simulation data and experimental results of the cage model of this invention under different working conditions are shown below. Figure 4 As shown, the slippage rate deviation is within 3%, which verifies the accuracy of the model of the present invention.

[0081] By employing a Bezier curve parametric design on the cage's bevel surface, the curvature of the bevel surface continuously varies along the contact path, achieving a smooth transition of local curvature. This design effectively reduces relative sliding and local embedding between the cage and rolling elements, lowering friction and frictional energy consumption. Simulation verification shows that, using a domestically produced tapered roller bearing for a wind turbine, based on the actual load and operating conditions, the average friction between the rolling elements and the cage is reduced by 3.33%. Figure 5 As shown.

[0082] S3. Set the operating parameters of the tapered roller bearing and the structural parameters of the cage for orthogonal experimental design. The operating parameters include the inner ring speed, radial force, and axial force. The structural parameters include the slope depth, slope angle, slope curvature, and pocket clearance.

[0083] Specifically, this invention selects a domestically produced tapered roller bearing for wind turbines. Based on the actual load and operating conditions, it identifies the cage structure design parameters that need optimization. Combining the reasonable value ranges of each parameter, a seven-factor, three-level combination table is constructed as shown in Table 1. L27(3 7 Orthogonal experimental design:

[0084]

[0085] Table 1. Factors in Orthogonal Experiments

[0086] To obtain more accurate and engineering-guiding values ​​of the frictional force between the rolling elements and the cage, this invention uses the Adams multibody dynamics simulation platform to obtain the normal contact force between the rollers and the cage in tapered roller bearings for wind turbine main shafts. The oil film friction coefficient is calculated according to the following formula. :

[0087] ,

[0088] in, For oil film parameters, For complete flow lubrication, For boundary lubrication, For mixed lubrication, and All measurements were taken using a friction testing machine. s is the sliding-rolling ratio, and A, B, C, and D are correlation coefficients. For information on A, B, C, and D, please refer to the literature "Research on the Rheological Properties of Aviation Lubricating Oil and its Influence on Lubrication Performance".

[0089] According to the formula The method of calculating the frictional force between the cage and the rollers can accurately characterize the influence of lubrication conditions on frictional force, thereby establishing a frictional force model that is closer to the actual working conditions.

[0090] Through orthogonal experiments, the cage slippage rate and the frictional force between the rolling elements and the cage corresponding to 27 groups can be obtained, as shown in Table 2:

[0091]

[0092] Table 2. Orthogonal experimental data.

[0093] S4. Using the working condition parameters and structural parameters as design variables, and the minimum value of the sum of slippage rate and friction force as the overall optimization objective, the simulation results of the orthogonal experimental design are used as training data for the BP neural network model to establish a nonlinear mapping model between the design variables and the optimization objective.

[0094] Specifically, in combination Figure 6 The orthogonal experiment included 27 sets of sample data in Table 2. The results of different working conditions and structural parameters were used as training samples for the BP neural network. The network input layer had 7 neurons, corresponding to 7 input parameters; the output layer had 2 neurons, outputting the slip rate and friction force respectively. To fit the nonlinear characteristics of the system, a three-layer network structure was adopted. The BP neural network was constructed using the newff function in Matlab. The activation function of the hidden layer was the tansig nonlinear function with a fast convergence speed. A pure linear transfer function was used between the hidden layer and the output layer to ensure that the output value is not limited by the range and can generate arbitrary real numbers. The trainlm algorithm was used during training. This algorithm combines the advantages of gradient descent and Newton's method and is suitable for feedforward networks with hundreds of connection weights, with high training efficiency and convergence speed.

[0095] Based on the input-output range characteristics of the activation function tansig, the normalization function premnmx is first used to normalize the 27 sets of sample data, mapping the data to the interval [−1, 1], as shown in the following formula:

[0096] ;

[0097] In the formula: This is the upper limit of the normalized target interval, which is 1 here; This is the lower bound of the normalized target interval, which is -1 here; The minimum value in the original input data; The maximum value in the original input data; This represents the data value after normalization. It represents any data value in the original input data.

[0098] In addition, to improve the generalization ability of the neural network model, the randperm function in Matlab was used to randomly shuffle the 27 sets of sample data. Since the input data sample size was small, a 6:1 ratio of training and testing data was used. Therefore, 23 sets of samples were selected as training data to build the BP neural network prediction model, and the remaining 4 sets were used for model validation to evaluate its prediction accuracy and stability on unseen samples. The mean squared error (MSE) was used as the loss function. In the formula This is the actual value. Here, n represents the predicted value, and n is the number of samples. Figure 6 middle This represents the network output error corresponding to the q-th training sample, calculated based on the mean squared error (MSE) criterion. q represents the q-th sample currently being trained (or the q-th iteration / training step). The training stopping condition is set jointly by the maximum number of iterations and the error threshold. The maximum number of iterations is set to 10,000, the learning rate is set to 0.01, and the minimum expected error ε is set to 10. -8 , Training stops when the value is less than ε or when the maximum number of iterations is reached.

[0099] The predictive performance of the training samples is evaluated using the correlation coefficient R, which measures the linear correlation between the predicted output and the target value; the fit of the validation samples is measured using the coefficient of determination R. 2 Characterization:

[0100] In the formula This is the average of the true values.

[0101] A backpropagation neural network is constructed to predict parameters (rotational speed, radial force, axial force, beveling depth, beveling angle, beveling curvature, and pocket clearance) that simultaneously affect cage slippage rate and friction between rolling elements and cage. The coefficient of determination R0 for both parameters is calculated. 2 The result is close to 95%, indicating a close relationship between the predicted and output data, and reflecting a relatively accurate functional relationship between the cage slippage rate and the friction between the rolling elements and the cage.

[0102] S5. Optimize the established BP neural network model using the particle swarm optimization (PSO) algorithm to obtain the optimal structural parameters. Specifically, use the PSO algorithm to perform a global optimum solution on the constructed BP neural network model, finding the parameter combination that minimizes the cage slippage rate and the friction between the rolling elements and the cage. Figure 7 The details are as follows:

[0103] The parameters of the particle swarm optimization (PSO) algorithm are set, including the particle swarm size (number of particles), particle dimensions (7 parameters: rotational speed, radial force, axial force, slope inclination angle, slope curvature, slope depth, and pocket gap), number of iterations, inertia weight, learning factor, and iteration step size range. Then, the position and velocity of each particle are randomly initialized; the position of each particle is a combination of these 7 parameters, and the velocity represents the direction and step size of movement of this set of parameters in the search space. For each particle, the values ​​of its 7 parameters are input into a pre-trained backpropagation (BP) neural network model. The BP neural network outputs two values: slip rate and friction force. Then, based on these two values ​​and combined with the overall objective function, the fitness function value is calculated; the smaller the value, the better the parameter combination corresponding to the particle.

[0104] More specifically, the overall objective function for the parameters to be optimized is as follows:

[0105] ;

[0106] in, Let be the overall objective function that minimizes the sum of the slippage rate and the frictional force. Let slip rate be the objective function. Let the objective function be friction force;

[0107] Design variables:

[0108] ,in, The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, To measure the slope depth, To reduce the curvature of the slope, It is the pocket clearance, and satisfies the following constraints:

[0109] ,in The limiting speed of the tapered roller bearing is 500 r / min in this embodiment;

[0110] , The actual maximum radial force of the tapered roller bearing is 10000N in this embodiment.

[0111] ,in The actual maximum axial force of the tapered roller bearing is 5000N. In this embodiment, the actual maximum axial force of the tapered roller bearing is 5000N.

[0112] ,in The bearing cage pressure slope angle is limited. The theoretical basis is that the cage's guiding mechanism for the rolling elements depends on the coupling relationship between the normal force and the tangential drag force generated by the pressure slope. According to the principles of contact mechanics and tribology, when the slope angle is too large, the tangential component of the contact force will decrease sharply, resulting in insufficient traction force, which cannot overcome the motion inertia of the rolling elements, thus causing macroscopic slippage. In this embodiment, the limit slope angle that ensures the contact force vector is always within the effective drag force range is π / 4.

[0113] ,in The bearing cage bevel depth is limited. The bevel depth needs to achieve a reasonable balance between improving the guiding ability of the rolling elements and the overall strength of the cage. If the bevel depth is too large, it will significantly weaken the effective thickness of the pocket sidewall, reduce its bending stiffness and impact resistance, and fail to meet the minimum allowance required for the bevel curvature machining. Based on the cage thickness, safety margin requirements, and material allowance constraints for bevel curvature machining, the limit value of the bevel depth is determined to be 4mm after comprehensive consideration. This limit value constitutes the maximum allowable boundary of the bevel depth. Exceeding this range will result in the structural strength and machining process failing to meet the design requirements.

[0114] ,in To limit the curvature of the bearing cage's pressure slope, firstly, according to the stress concentration theory in elasticity, the radius of curvature (the reciprocal of curvature) is a key geometric parameter determining the stress concentration factor. An excessively small radius of curvature will generate extremely high local stress at the edge of the contact area, significantly reducing the structure's fatigue limit. Secondly, from a geometric perspective, curvature and depth are coupled; excessive curvature, under a given depth constraint, cannot form an effective contact surface, thus losing the geometric meaning of the "pressure slope." Therefore, in this embodiment, the upper limit of the optimized design domain for the pressure slope curvature, determined after balancing stress concentration suppression with ensuring geometric functionality, is 0.5 mm. -1 ;

[0115] ,in The bearing cage pocket clearance is limited. In multibody system dynamics, clearance is one of the main factors that cause nonlinear vibration. Excessive pocket clearance will cause the motion relationship between the rolling elements and the cage to change from controlled guidance to intermittent impact. In order to maintain the stability of the cage and avoid harmful impact, the limit value set in this embodiment is 0.25mm.

[0116] During the iteration process, each particle continuously updates its velocity and position based on its individual historical best value and global best value, thereby achieving a global search of the parameter space. When the fitness function meets the set convergence condition or reaches the maximum number of iterations, the particle that minimizes the comprehensive performance index can be obtained, thus obtaining the optimal parameter combination that minimizes slippage rate and friction.

[0117] The main parameter settings for the particle swarm optimization algorithm are as follows:

[0118] (1) Population size m: that is, the number of particles in the population. If the number is too small, it is easy to fall into a local optimum, and if it is too large, it will increase the computational cost. Taking all factors into consideration, the population size is set to 40 in this invention.

[0119] (2) Maximum number of iterations: This is the termination condition of the algorithm, set to 100 iterations to ensure a balance between optimization accuracy and efficiency;

[0120] (3) Maximum speed Vmax: controls the maximum step size of the particle in the search space, which affects the search capability of the algorithm. In this invention, it is set to 10% of the range of independent variable values ​​to achieve better global search capability.

[0121] (4) Inertia weight w: used to balance local search and global search capabilities, set to a fixed value of 0.5 to improve algorithm stability;

[0122] (5) Acceleration factors c1 and c2: represent individual learning factor and social learning factor respectively, which determine the search behavior of particles. In this invention, both are set to 2 to enhance the global optimal search capability.

[0123] In this embodiment, the parameter combination obtained by the above method for the cage slippage rate and the minimum friction between the rolling elements and the cage is as follows: bevel angle 14°, bevel depth 3.796 mm, pocket clearance 0.15 mm, and bevel curvature 0.41 mm. -1 .

[0124] S6. Compare the slippage rate and friction of the optimized structural parameters with those of the original structural parameters under different working conditions.

[0125] Simulations were performed on the cage structures before and after optimization under different speeds and load conditions, and the performance differences were compared and analyzed. If the performance of the tapered roller bearing corresponding to the optimized structure was not better than that of the unoptimized structure, the parameters such as the maximum number of iterations of the particle swarm optimization algorithm were readjusted, and the optimization process was re-executed. Specifically, the slippage rate and friction of the bearing cage under the optimal structural parameters were calculated for 27 operating conditions and compared with the slippage rate and friction of the bearing cage under the original structural parameters for the same 27 operating conditions. This compared whether the structural combination could meet the optimization requirements under each operating condition. Since there were 6 identical operating conditions among the 27 operating conditions, 21 sets of tests were ultimately compared, in accordance with the instruction manual. Figure 8 , Figure 9 The optimized tapered roller bearing for the wind turbine has lower friction and slippage rate than the unoptimized bearing, indicating that the optimized bearing has achieved the effect of reducing cage friction and vibration.

[0126] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the cage structure of a tapered roller bearing for wind turbines, characterized in that, Includes the following steps: S1. Obtain the structural parameters of the cage, including the slope depth, slope angle, slope curvature, and pocket clearance. S2. Establish a dynamic simulation model of tapered roller bearings and verify the accuracy of the model; S3. Orthogonal experimental design based on the operating parameters of tapered roller bearings and the structural parameters of cages, wherein the operating parameters include inner ring speed, radial force, and axial force; S4. Using the working condition parameters and structural parameters as design variables, and the minimum value of the sum of slippage rate and friction force as the optimization objective, the simulation results of the orthogonal experimental design are used as the training data of the BP neural network model to establish a nonlinear mapping model between the design variables and the optimization objective. S5. Optimize the established BP neural network model using the particle swarm optimization algorithm to obtain the optimal structural parameters, including the following steps: The parameters of the particle swarm optimization algorithm are set, including particle swarm size, particle dimension, number of iterations, inertia weight, learning factor, and iteration step size range. The particle swarm dimension includes the structural parameters and operating parameters of the cage. Initialize the position and velocity of the particle swarm, where the position of each particle represents its dimension and the velocity represents the direction and step size of movement of that particle dimension in the exploration space. The position vector of each particle is input into a trained BP neural network model to predict the corresponding slip rate and friction value. The fitness value of each particle is calculated based on the prediction results. The fitness value is determined by the overall objective function of the parameters to be optimized. The overall objective function of the parameters to be optimized is: ； in, Let be the overall objective function that minimizes the sum of the slippage rate and the frictional force. Let slip rate be the objective function. Design variables for the objective function of friction force. ,in, The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, To measure the slope depth, To reduce the curvature of the slope, This refers to the gap between the pockets. Update the velocity and position of each particle based on its individual historical best position and the global historical best position; Repeat the iteration until the termination condition is met, and output the combination of structural parameters corresponding to the globally optimal position; S6. Compare the slip rate and friction of the optimized structural parameters with those of the original structural parameters under different working conditions. If the optimization requirements are not met, adjust the particle swarm algorithm parameters and re-execute step S5.

2. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, In step S1, when designing the cage pressure slope structure, a Bezier curve is used to smooth the cage pressure slope curve, so that the curvature of the pressure slope changes continuously along the contact path.

3. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, In step S2, the model accuracy verification method is as follows: Under the condition of keeping the load and speed the same, calculate the average slip rate of the cage, compare the dynamic simulation model of the tapered roller bearing with the experimental data of the existing model, and if the slip rate deviation is within the preset range, it indicates that the accuracy of the dynamic simulation model of the tapered roller bearing meets the requirements.

4. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, In step S3, the frictional force between the tapered roller and the bearing cage is calculated using the following formula: ； In the formula: The coefficient of friction of the oil film. This refers to the normal contact force between the rollers and the cage in a tapered roller bearing. ； In the formula: For oil film parameters, For complete flow lubrication, For boundary lubrication, For mixed lubrication, and All measurements were taken using a friction testing machine. s The sliding ratio is denoted by A, B, C, and D, which are preset coefficients.

5. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, In step S4, the BP neural network model includes: The input layer is used to input operating condition parameters and cage structure parameters. The hidden layer uses a non-linear activation function. The output layer is used to output the slip rate and friction force separately. Furthermore, a purely linear transfer function is used between the hidden layer and the output layer.

6. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, The BP neural network model is trained using the trainlm algorithm until the mean square error is lower than a preset threshold or the maximum number of iterations is reached.

7. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, After the BP neural network model is trained, the coefficient of determination R is used. 2 Verify the fit of the sample: ； In the formula: This is the actual value. For predicted values, This is the average of the true values.

8. The method for optimizing the cage structure of a tapered roller bearing for wind turbines according to claim 1, characterized in that, In step S5, design variables The following constraints must be met: ； in, This refers to the limiting speed of the tapered roller bearing. This represents the actual maximum radial force during the operation of the tapered roller bearing. This represents the maximum axial force during the actual operation of the tapered roller bearing. The maximum allowable slope angle of the cage without macroscopic slippage between the cage and the rolling elements. To satisfy the minimum effective thickness of the pocket sidewall and the minimum allowance required for processing the curvature of the bevel surface, the maximum value of the bevel surface depth is required. To determine the maximum value under the condition that the cage and rolling elements form the minimum allowable contact surface area. This is the maximum value at which the rolling elements and the cage do not experience intermittent impacts.

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