Wind power tapered roller bearing retainer slip rate calculation model

Abstract

The invention discloses a wind power tapered roller bearing retainer slip rate calculation model which is simple in structure and can be suitable for various working conditions and structure parameter combinations. A user only needs to input parameters such as the rotating speed of the inner ring, the radial force, the axial force, the inclination angle of the pressing slope surface, the pressing slope depth, the curvature of the pressing slope surface and the pocket gap, and the corresponding slip rate of the retainer can be quickly calculated. The model is verified through multi-body dynamics simulation software, and the result has high accuracy.

Description

Technical Field

[0001] This invention relates to the field of bearing technology, and specifically to a calculation model for the cage slippage rate of a wind turbine tapered roller bearing. Background Technology

[0002] Slippage of wind turbine bearing cages can easily lead to failures such as guide surface wear, cage breakage, bearing jamming, and main shaft breakage. Current research on bearing slippage rate primarily utilizes passive measurement methods, including electromagnetic, optical, vibration, and photoelectric grating methods. For example, Chinese invention publication CN110514443A discloses a non-contact measurement method for the slippage rate of aerospace bearing cages. This method first obtains the actual rotational speed vc′ of the rolling element by collecting mixed magnetic field information from a weak magnetic field detection sensor probe; that is, it obtains the actual rotational speed vc″ of the cage. Based on the actual rotational speed vc″ and the theoretical rotational speed vc, the slippage rate of the cage is then obtained.

[0003] However, the above measurements are all based on the actual operating conditions of the bearing and are mostly used for passive optimization design of the bearing structure, resulting in excessively long product development cycles. Research on the mapping relationship between the bearing pocket pressure slope structure parameters and the slippage rate has not yet been conducted, making it difficult to support proactive bearing structure design. There is an urgent need to establish a cage slippage rate prediction model to guide the structural design of wind turbine tapered roller bearings. Summary of the Invention

[0004] Therefore, this invention aims to overcome the shortcomings of existing technologies and provide a calculation model for the slippage rate of wind turbine tapered roller bearings. To solve the above-mentioned technical problems, this invention introduces a slope surface curvature design into the cage pocket and combines it with multibody dynamics simulation to construct a cage slippage rate calculation model. This model can achieve quantitative prediction of cage slippage behavior and provide a theoretical basis for the optimized design of wind turbine bearing structures.

[0005] To address the aforementioned technical problems, this invention provides a calculation model for the cage slippage rate of wind turbine tapered roller bearings. ,in ; In the formula: The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, This refers to the slope depth. To reduce the curvature of the slope, For the gap of the pocket, These are the weighting coefficients. This is the bias term. ( jTake values ​​from 1 to 35, including the weight coefficients for linear terms, quadratic terms, and cross terms. Specifically: for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients for Cross term weight coefficients, for Cross term weight coefficients for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients for Cross term weight coefficients, for Cross term weight coefficients for Cross term weight coefficients for Cross term weight coefficients, for Cross-term weight coefficients.

[0006] Based on the nonlinear regression model using the sigmoid function described above, the weight coefficients of the cross term and the quadratic term are obtained by minimizing the mean squared error (MSE) loss function between the predicted output and the actual output.

[0007] The BFGS method (Broyden–Fletcher–Goldfarb–Shanno algorithm) is used to adjust the linear combination weights within the Sigmoid function. The regression model is obtained by numerically solving the bias term b.

[0008] Furthermore, the regression model of this invention selects a domestically produced tapered roller bearing for wind turbines as the research object. Based on its actual load and operating conditions, the design parameters of the cage structure that need to be optimized are selected. Combining the reasonable value range of each parameter, the experiment is arranged using an L27 (3~7) orthogonal array according to a seven-factor, three-level orthogonal experimental combination table. The generated 27 sets of data are divided into a modeling set and a validation set in a 6:1 ratio. After randomly shuffling the order, 23 sets of data are selected to establish a simulation model of the cage slippage rate, and the remaining 4 sets are used to verify the effectiveness of this calculation model.

[0009] The technical solution of this invention has the following advantages: 1) The wind turbine tapered roller bearing slippage rate calculation model of this invention has a simple structure and is applicable to various operating conditions and combinations of structural parameters. Users only need to input the inner ring rotational speed. radial force Axial force Slope angle Slope depth Slope curvature and pocket gap By analyzing the parameters, the corresponding cage slippage rate can be quickly calculated. This model has been validated using multibody dynamics simulation software, and the results demonstrate high accuracy.

[0010] 2) The slippage rate calculation model for wind turbine tapered roller bearings proposed in this invention can be used to evaluate the improvement effect of the slope curvature of this type of bearing and provide effective guidance for the optimization design of cage structure parameters. This model is not only applicable to tapered roller bearings, but can also be extended to various types of bearings under other special working conditions, and has strong versatility and engineering applicability. Attached Figure Description

[0011] To more clearly illustrate the specific embodiments of the present invention or the prior art, the accompanying drawings involved in the description will be briefly introduced below. Obviously, the drawings shown herein are only some embodiments of the present invention. For those skilled in the art, other related drawings can be obtained from these drawings without any creative effort.

[0012] Figure 1 Predict slip rate plot for random parameters.

[0013] Figure 2 The retainer of the tapered roller bearing has a sloped structure. Detailed Implementation

[0014] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] like Figure 2 As shown, tapered roller bearings are mainly used to bear combined radial and axial loads, with radial loads being the primary component. The rolling elements undergo both rolling and sliding during movement, resulting in a complex motion trajectory. The cage needs to precisely guide the movement of the rolling elements to ensure uniform load distribution among them. By setting a suitable beveling angle in the cage pockets, the rolling elements can be guided to roll in the correct direction, reducing friction and wear between the rolling elements and between the rolling elements and the raceway. The beveling depth affects the contact between the rolling elements and the cage; a suitable beveling depth ensures good positioning and guidance of the rolling elements within the cage, preventing them from skewing or deviating from their normal trajectory. The curvature of the beveling surface helps to better conform to the rolling element surface during movement, providing stable support and guidance, and improving the overall performance and service life of the bearing.

[0016] The slippage rate model for the tapered roller bearing cage of this invention is as follows: ,in ; In the formula: The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, This refers to the slope depth. To reduce the curvature of the slope, For the gap of the pocket, The weighting coefficients (including the weighting coefficients of the first term, the weighting coefficients of the second term, and the weighting coefficients of the cross term) j Take values ​​from 1 to 35, specifically: for Weight coefficient of first-order term, for First-order term weight coefficient, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for First-order term weight coefficient, for Weight coefficient of first-order term, for Weight coefficient of first-order term, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Quadratic term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross term weight coefficients, for Cross-term weight coefficients). For bias terms; Based on the nonlinear regression model using the sigmoid function described above, the weight coefficients of the cross term and the quadratic term are obtained by minimizing the mean squared error (MSE) loss function between the predicted output and the actual output.

[0017] Let the original sample be After normalization, the following features are constructed: Linear term (7-dimensional, j=1-7): The linear term of the original parameters, used to capture the basic linear relationship between each parameter and the slippage rate. The eigenvector of the linear term is... ; Quadratic terms (nonlinear terms, 7-dimensional, j=8-14): The squared terms of each parameter, used to capture the nonlinear effects of each parameter itself.

[0018] eigenvectors of nonlinear terms ; Interaction terms (multiplication terms, 21-dimensional, j=15-35): Terms in which different parameters are multiplied pairwise, used to capture the interaction between parameters.

[0019] Cross term feature vector ; To predict slip rate, T represents transpose, which converts a row vector into a column vector; These are all weight coefficients (including the weight coefficients of the first term, the second term, and the cross term). It is an extended vector composed of first-order, second-order, and cross-term features.

[0020] Given a total of N samples, each sample has an input feature vector. Corresponding to the true normalized slip rate label The objective function is defined as mean squared error (MSE): because Since it is a nonlinear function, the weighting coefficients mentioned above cannot be solved directly using analytical methods. (Including the weighting coefficients of the first-order, second-order, and cross-terms) and bias terms These parameters cannot be directly solved using traditional analytical methods. This invention employs numerical optimization algorithms (such as the BFGS method) for iterative fitting to approximate the optimal parameters.

[0021] For the prediction of each sample, we have: Calculate the loss function The partial derivatives with respect to each parameter are used to determine the trend of the loss function and the direction of its fastest descent under the current parameter values: For weighting coefficients ( j =1~35): For bias term b: In the formula: Indicates the first i The input feature vector for each sample is a column vector containing 7 elements. It represents all parameters input into the model in the i-th simulation; N is the total number of samples; i represents the sample index. , used to iterate through all samples; The j-th extended feature of the i-th sample is the original input feature vector. The j-th eigenvalue in the 35-dimensional eigenvector obtained after feature engineering (including quadratic and cross terms); This represents the predicted slip rate for the i-th sample, which is determined by the model based on the input. The calculated output value; This represents the actual slip rate of the i-th sample, which is obtained through simulation. Let represent the linear weighted sum of the i-th sample.

[0022] The BFGS method (Broyden–Fletcher–Goldfarb–Shanno algorithm) is used to adjust the linear combination weights within the Sigmoid function. The regression model is obtained by numerically solving the bias term b. Specific Implementation Example 1: Specifically, this embodiment selects a domestically produced tapered roller bearing for wind turbines as the research object for the calculation model of cage slippage rate. Based on its actual load and operating conditions, the cage structure design parameters that need to be optimized are selected. Combined with the reasonable value range of each parameter, a seven-factor, three-level orthogonal experimental combination table is constructed as shown in Table 1, and the experiment is arranged using an L27 (3^7) orthogonal array. The generated 27 sets of data are divided into a modeling set and a validation set at a ratio of 6:1. After randomizing the order, 23 sets of data are selected to establish a simulation model of cage slippage rate, and the remaining 4 sets are used to verify the effectiveness of this calculation model. Table 1 shows the orthogonal experimental factor level table; Table 2 shows the corresponding simulation data table.

[0024] Table 1: Factor Level Table for Orthogonal Experiment

[0025] Table 2: Simulation Data Table Test No. Rotational speed (r / min) Radial force (N) Axial force (N) Slope angle (°) Slope compressing depth (mm) Slope curvature (mm⁻¹) Pocket clearance (mm) Slippage rate (%) 1 150 3000 500 14 3.20 0.083 0.10 7.43 2 150 3000 1000 16 3.55 0.350 0.15 5.26 3 150 3000 1500 18 3.80 0.500 0.18 5.71 4 150 5000 500 14 3.55 0.350 0.18 6.3 5 150 5000 1000 16 3.80 0.500 0.10 7.31 6 150 5000 1500 18 3.20 0.083 0.15 8.09 7 150 10000 500 16 3.20 0.500 0.15 8.46 8 150 10000 1000 18 3.55 0.083 0.18 6.79 9 150 10000 1500 14 3.80 0.350 0.10 7.3 10 300 3000 1000 14 3.80 0.350 0.18 0.83 11 300 3000 1000 16 3.20 0.500 0.10 9.89 12 300 3000 1000 18 3.55 0.083 0.15 3.89 13 300 5000 1500 14 3.55 0.083 0.18 1.85 14 300 5000 1500 16 3.80 0.350 0.10 5.03 15 300 5000 1500 18 3.20 0.500 0.15 8.7 16 300 10000 500 14 3.80 0.500 0.15 3.05 17 300 10000 500 16 3.20 0.083 0.18 2.39 18 300 10000 500 18 3.55 0.350 0.10 7.06 19 450 3000 500 18 3.55 0.350 0.10 6.05 20 450 3000 1000 14 3.80 0.500 0.15 3.94 21 450 3000 1500 16 3.20 0.083 0.18 1.78 22 450 5000 500 16 3.55 0.083 0.18 1.92 23 450 5000 1000 18 3.20 0.350 0.10 7.65 24 450 5000 1500 14 3.80 0.500 0.15 3.95 25 450 10000 500 18 3.80 0.500 0.15 3.53 26 450 10000 1000 14 3.20 0.083 0.18 2.74 27 450 10000 1500 16 3.55 0.350 0.10 6.27 Referring to Table 2, using 23 sets of simulation data as sample data, and applying the aforementioned BFGS method (which assigns weights to the linear combination coefficients within the Sigmoid function),... The weight coefficients of the regression model are obtained by numerically solving for the bias term b. The formula for the cage slippage rate model is shown below: ,in (1) Furthermore, to verify the accuracy of the tapered roller bearing cage slippage rate calculation model, the radial force was added to the operating parameters of the remaining four sets of data. axial force Rotation speed and pocket gap Slope angle Slope depth Slope curvature Substitute the result into formula (1) and then substitute it into the formula. The predicted slip rate can then be calculated. .like Figure 1 As shown, Figure 1 middle,z The log-odds ratio of the model represents a linear combination of the input features (the seven original features and their polynomial extensions). The curve in the figure represents the mapping relationship from z to s slip rate (sigmoid function), which is equivalent to a composite function. The remaining four sets of simulation data points float near the cage slip rate calculation model curve, indicating that the predicted values ​​and simulation values ​​are in good agreement, thus verifying the accuracy of the calculation model's predictions.

[0026] For the implementation of the above simulation model, there are currently two mainstream technical approaches in the industry: one is to perform multibody dynamics simulation based on existing commercial simulation software (such as ADAMS), and the other is to build a custom model by writing code such as Python. ADAMS supports both rigid body simulation and rigid-flexible coupling simulation, the latter of which takes into account the flexibility effect of components and can more realistically reflect actual working conditions. The rigid-flexible coupling simulation model used in this invention has been made flexible for the cage. This model is quite similar to existing technologies in some structural aspects, and specific details will not be elaborated here.

[0027] This invention effectively solves the problem of excessively long computation time in existing simulation methods. Traditional rigid body simulation requires at least one day from modeling to completing a one-second simulation; if a more accurate rigid-flexible coupling model is used, completing a simulation of the same duration may even take a week or longer. Furthermore, each modeling requires redrawing using 3D software such as SolidWorks, and if multiple variables need adjustment, the parameter modification process also consumes a significant amount of time. To address these pain points, this invention creatively introduces the slope curvature parameter, expanding the design considerations for wind turbine tapered roller bearing cage structures to seven types of parameters. It can also combine multibody dynamics simulations or actual sample data to establish a calculation model for cage slippage rate, thereby achieving quantitative prediction of slippage behavior and providing theoretical support for improving wind turbine bearing structural design. Simultaneously, this invention also constructs an efficient prediction calculation formula, allowing designers to quickly obtain prediction results simply by substituting relevant parameters, significantly narrowing the range of structural parameters requiring in-depth verification. This method significantly reduces repetitive modeling and simulation time, saves substantial computational resources, and effectively improves design efficiency.

[0028] This invention provides designers with valuable design insights, effectively assisting them in determining whether to incorporate a slope curvature design into bearings, and offering data support for analyzing the impact of this design on cage slippage rate. Using the wind turbine tapered roller bearing calculation model established by this invention, the cage slippage rate can be accurately calculated, thereby scientifically assessing the necessity of slope curvature improvement and providing guidance for the optimized design of key cage structural parameters.

[0029] It should be noted that the above embodiments are only used to clearly illustrate the technical solutions of the present invention, and are not intended to limit its specific implementation. For those skilled in the art, other variations or modifications can be made based on the above description. It is neither possible nor necessary to list all possible implementations here. Any obvious variations or modifications derived from the present invention should be considered to still fall within the protection scope of the present invention.

Claims

1. A calculation model for the slippage rate of a wind turbine tapered roller bearing cage, characterized in that, ,in, In the formula: The inner ring speed, Radial force, It is an axial force. To reduce the slope angle, This refers to the slope depth. To reduce the curvature of the slope, For the gap of the pocket, ( j Take 1 to 35 as the weighting coefficient. This is a bias term.

2. The wind turbine tapered roller bearing cage slippage rate calculation model according to claim 1, characterized in that, The calculation model for the slippage rate of the wind turbine tapered roller bearing cage is suitable for operating conditions with inner ring speeds ranging from 150-450 r / min, radial forces from 3000-10000 N, and axial forces from 500-1500 N; and structural parameters including pocket clearance from 0.1 mm to 0.18 mm, slope inclination angle from 14° to 18°, slope depth from 3.2 mm to 3.8 mm, and slope curvature of 0.083 mm. -1 -0.5mm -1 .

3. The wind turbine tapered roller bearing cage slippage rate calculation model according to claim 2, characterized in that, The weight coefficients of the first-order, cross-term, and quadratic terms are solved by minimizing the mean squared error loss function between the predicted output and the sample output.

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