Wind power tapered roller bearing cage slip rate calculation model

Abstract

The application discloses a wind power conical roller bearing cage slip rate calculation model, and the wind power conical roller bearing slip rate calculation model is simple in structure and applicable to various working conditions and structural parameter combinations. A user only needs to input an inner ring rotating speed, a radial force, an axial force, a pressure slope surface inclination, a pressure slope depth, a pressure slope surface curvature and a pocket gap parameter, and corresponding cage slip rate can be quickly calculated. The model has been verified by multi-body dynamics simulation software, and the result has high accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bearings, in particular to a wind power conical roller bearing cage slip rate calculation model. BACKGROUND

[0002] Wind power bearing cage slip is prone to cause guide surface wear, cage fracture, bearing jamming, spindle fracture and other faults. At present, the research on bearing slip rate is mainly passive measurement method, mainly including electromagnetic measurement method, optical measurement method, vibration measurement method and photoelectric grating measurement method. For example, the Chinese invention with publication number CN110514443A discloses a non-contact measurement method for aviation bearing cage slip rate. The actual speed vc' of the rolling body is obtained through the mixed magnetic field information collected by the weak magnetic detection sensor probe, that is, the actual speed vc" of the cage is obtained, and the slip rate of the cage is obtained according to the actual speed vc" of the cage and the theoretical speed vc.

[0003] However, the above-mentioned slip rate measurement is based on the actual working state of the bearing, which is mainly used for passive optimization design of bearing structure, resulting in too long product development cycle. The mapping relationship between the cage pocket pressure slope surface structure parameters and the slip rate has not been studied, which is difficult to support active design of bearing structure. It is urgent to establish a cage slip rate prediction model to guide the design of wind power conical roller bearing structure. SUMMARY

[0004] Therefore, the present application aims to overcome the shortcomings of the prior art and provide a wind power conical roller bearing cage slip rate calculation model. In order to solve the above technical problems, the present application introduces the curvature design of the pressure slope surface in the cage pocket of the cage, and combines with multi-body dynamics simulation to construct the cage slip rate calculation model. The model can realize the quantitative prediction of the slip behavior of the cage, and provide a theoretical basis for the optimization design of the wind power bearing structure.

[0005] In order to solve the above technical problems, the present application provides a wind power conical roller bearing cage slip rate calculation model,

[0006] wherein

[0007] ;

[0008] In the formula: is the inner ring speed, is the radial force, is the axial force, is the pressure slope angle, is the pressure slope depth, is the pressure slope curvature, is the pocket gap, is the weight coefficient, is a bias term. Wherein ( j takes 1~35) contains a linear term weight coefficient, a quadratic term weight coefficient and a cross term weight coefficient, specifically: is a linear term weight coefficient, is a linear term weight coefficient, is a linear term weight coefficient, is a linear term weight coefficient, is a linear term weight coefficient, is a linear term weight coefficient, is a linear term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a quadratic term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, is a cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient, For cross term weight coefficient.

[0009] The solving of the cross term and quadratic term weight coefficients of the nonlinear regression model based on the above Sigmoid function is obtained by minimizing the mean square error (MSE) loss function between the predicted output and the real output.

[0010] The linear combination weight coefficients and the bias term b inside the Sigmoid function are numerically solved by using the BFGS method (Broyden-Fletcher-Goldfarb-Shanno algorithm), and the regression model is obtained.

[0011] Further, the regression model of the application selects a domestic wind turbine conical roller bearing as the research object, screens the cage structure design parameters to be optimized according to the actual load and operating condition, and combines the reasonable value range of each parameter to arrange the test according to the orthogonal test combination table of seven factors and three levels by using the L27(3~7) orthogonal table. The generated 27 groups of data are divided into modeling set and verification set according to the proportion of 6:1, and after the order is randomly disturbed, 23 groups of data are selected to establish the simulation model of the cage slip rate, and the remaining 4 groups are used to verify the effectiveness of the calculation model.

[0012] The technical scheme of the application has the following advantages:

[0013] 1) The wind power conical roller bearing slip rate calculation model of the application has a simple structure and can be applied to various working conditions and structural parameter combinations. The user only needs to input the inner ring rotating speed , radial force , axial force , pressure slope angle , pressure slope depth , pressure 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.

[0014] 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

[0015] 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.

[0016] Figure 1 Predict slip rate plot for random parameters.

[0017] Figure 2 The retainer for tapered roller bearings has a sloped structure. Detailed Implementation

[0018] 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.

[0019] 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.

[0020] The slippage rate model for the tapered roller bearing cage of this invention is as follows:

[0021] wherein

[0022] ;

[0023] wherein: is the inner ring rotation speed, is the radial force, is the axial force, is the pressure slope angle, is the pressure slope depth, is the pressure slope curvature, is the pocket gap, is the weight coefficient (including the first-order weight coefficient, the second-order weight coefficient, and the cross-term weight coefficient, j is 1-35, and specifically: is the first-order weight coefficient, is the first-order weight coefficient, is the first-order weight coefficient, is the first-order weight coefficient, is the first-order weight coefficient, is the first-order weight coefficient, is the first-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the second-order weight coefficient, is the cross-term weight coefficient, is the cross-term weight coefficient, is the cross-term weight coefficient, is the cross-term weight coefficient, is the cross-term weight coefficient, is the cross-term weight coefficient, 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, bias term;

[0024] The cross-term and quadratic term weight coefficients of the above-mentioned Sigmoid function-based nonlinear regression model are obtained by minimizing the mean square error (MSE) loss function between the predicted output and the real output.

[0025] Let the original sample be After normalization, the following features are constructed:

[0026] Linear term (linear term, 7 dimensions, j=1-7): linear term of original parameters, used to capture the basic linear relationship between each parameter and the slip rate, and the linear term feature vector is ;

[0027] Quadratic term (nonlinear term, 7 dimensions, j=8-14): square term of each parameter, used to capture the nonlinear effect of each parameter itself.

[0028] Nonlinear term feature vector ;

[0029] Cross term (multiplication term, 21 dimensions, j=15-35): term of multiplication of different parameters, used to capture the interaction between parameters.

[0030] cross term feature vector ;

[0031]

[0032]

[0033]

[0034] For prediction of slip rate, T represents transposition, converting row vector to column vector; For all weight coefficients (including weight coefficients of linear terms, quadratic terms and cross terms), For the extended vector composed of linear, quadratic and cross term features.

[0035] Given the total number of samples N, each sample has an input feature vector , corresponding to the real normalized slip rate label , define the objective function as mean square error (MSE):

[0036]

[0037] Since is a nonlinear function, the above weight coefficients (including weight coefficients of linear terms, quadratic terms and cross terms) and bias term cannot be directly solved by traditional analytical methods. The present application uses numerical optimization algorithm (such as BFGS method) for iterative fitting to approximate the optimal parameters.

[0038] For the prediction of each sample, we have:

[0039]

[0040]

[0041] Calculate the loss function The partial derivative of each parameter to determine the trend of the loss function at the current parameter value and the direction of the fastest descent:

[0042] For weight coefficients ( j =1~35):

[0043]

[0044] For bias term b:

[0045]

[0046] wherein: represents the input feature vector of the i-th sample, which is a column vector containing 7 elements i represents all the parameters input to the model in the i-th simulation; N is the total number of samples; i represents the sample index, , is used to traverse all samples; the j-th extended feature of the i-th sample, which is the j-th feature value in the 35-dimensional feature vector obtained after feature engineering (including quadratic terms, cross terms) on the original input feature vector represents the predicted slip rate of the i-th sample, which is the output value calculated by the model according to the input represents the true slip rate of the i-th sample, which is obtained by simulation; represents the linear weighted sum of the i-th sample.

[0047] The BFGS method (Broyden-Fletcher-Goldfarb-Shanno algorithm) is used to numerically solve the linear combination weight coefficients and the bias term b inside the Sigmoid function to obtain the regression model. Specific embodiment 1:

[0049] Specifically, the wind power conical roller bearing retainer slip rate calculation model of this embodiment selects a domestic wind turbine conical roller bearing as the research object, screens out the retainer structure design parameters that need to be optimized according to its actual load and operating conditions, and combines the reasonable value range of each parameter to construct a seven-factor three-level orthogonal test combination table as shown in Table 1. The L27(3^7) orthogonal table is used to arrange the test. The generated 27 groups of data are divided into modeling set and verification set according to the ratio of 6:1. After randomly shuffling the order, 23 groups of data are selected to establish the simulation model of the retainer slip rate, and the remaining 4 groups are used to verify the effectiveness of the calculation model. Table 1 shows the orthogonal test factor level table; Table 2 is the corresponding simulation data table.

[0050] Table 1: Orthogonal test factor level table

[0051]

[0052] Table 2: Simulation data table

[0053] Test No. Rotational speed (r / min) Radial force (N) Axial force (N) Pitch angle (°) Pitch depth (mm) Pitch curvature (mm"1) Pocket clearance (mm) Slip 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

[0054] Combined with Table 2, 23 groups of simulation data are used as sample data, and the above-mentioned BFGS method (the linear combination weight coefficients​​​ 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:

[0055] ,in

[0056] (1)

[0057] 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.

[0058] 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.

[0059] The application effectively solves the problem of long calculation time of the existing simulation method. Traditional rigid body simulation needs at least one day from modeling to completing the simulation of 1 second. If a more accurate rigid-flexible coupling model is used, it may take a week or even longer to complete the simulation of the same length. In addition, each modeling needs to rely on three-dimensional software such as SolidWorks to redraw, and if multiple variables need to be adjusted, the parameter modification process will also consume a lot of time. In view of the above problems, the application creatively introduces the pressure slope curvature parameter, expands the design consideration of the wind power conical roller bearing retainer structure to seven types of parameters, and can combine multi-body dynamics simulation or actual sample data to establish a calculation model of the retainer slip rate, thereby realizing the quantitative prediction of the slip behavior, providing theoretical support for improving the wind power bearing structure design. At the same time, the application also constructs an efficient prediction calculation formula, and designers only need to substitute the relevant parameters to quickly obtain the prediction results, which greatly reduces the range of structure parameters that need to be deeply verified. This method significantly reduces the repeated modeling and simulation time, saves a lot of computing resources, and effectively improves the design efficiency.

[0060] The application can provide a beneficial design idea reference for designers, effectively assist them in judging whether to introduce pressure slope curvature design in the bearing, and provide data support for analyzing the influence of the design on the retainer slip rate. The wind power conical roller bearing calculation model established by the application can accurately calculate the slip rate of the retainer, thereby scientifically evaluating the necessity of pressure slope curvature improvement, and providing guidance for the optimization design of the key structure parameters of the retainer.

[0061] It should be noted that the above examples are only used to clearly illustrate the technical solutions of the application, and do not constitute a limitation on the specific embodiments. For those skilled in the art, on the basis of the above description, other different forms of changes or modifications can also be made. It is not necessary or possible to list all possible embodiments here. Any obvious changes or variations based on the application should be considered to be within the scope of protection of the application.

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. As an offset term, 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 .

2. The wind turbine tapered roller bearing cage slippage rate calculation model according to claim 1, 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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