Parametric evaluation prediction method for hub bearing stiffness

Abstract

The present application relates to a kind of parameterized evaluation prediction methods of wheel hub bearing stiffness, comprising: step 1, the structural parameterization of the influence wheel hub bearing stiffness is parameterized, the design space of wheel hub bearing stiffness parameter is established, and a series of design schemes are determined;Step 2, the method for establishing finite element simulation model is simulated stiffness test test, and the stiffness simulation of series design scheme is carried out using finite element simulation model;Step 3, according to the simulation result of step 2, construct the neural network model for predicting and evaluating wheel hub bearing stiffness and carry out training;Step 4, the accuracy of the neural network model established in step 3 is verified and prediction is carried out.The present application can quickly predict the product stiffness in the design link, without needing to carry out stiffness test to all design products, greatly improve the design efficiency, reduce cost, short cycle, conducive to the development of multi-species small batch products.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of wheel hub bearing development, and particularly relates to a parameterized evaluation and prediction method for wheel hub bearing stiffness. BACKGROUND

[0002] The stiffness analysis of conventional bearings is usually based on the Hertz contact theory, and the overall force balance equation of the bearing is established to obtain the stiffness by iteratively solving the bearing deformation (CN107153734B). This method only considers the contact deformation of the raceway and the steel ball, and the inner and outer rings of the bearing are regarded as rigid bodies. However, for a wheel hub bearing unit, the inner and outer flange structures are relatively complex, and regarding them as rigid bodies will bring a large analysis error, especially compared with the test results. Currently, the common practice is to prioritize meeting the life and other indicators during design, and temporarily not considering the stiffness indicators, then samples are manufactured, and special equipment is used to carry out stiffness testing (CN101886979B) to verify whether the designed product meets the stiffness requirements. This method has high cost and long cycle, which is not conducive to the development of multi-variety and small-batch products. SUMMARY

[0003] The present application aims to overcome the shortcomings of the prior art and provide a parameterized evaluation and prediction method for wheel hub bearing stiffness, which can greatly improve the design efficiency of wheel hub bearings.

[0004] A parameterized evaluation and prediction method for wheel hub bearing stiffness, comprising the following steps:

[0005] Step 1: parameterize the structural parameters affecting the stiffness of the wheel hub bearing, establish a design space of the stiffness parameters of the wheel hub bearing, and determine a series of design schemes;

[0006] Step 2: establish a finite element simulation model by using a simulated stiffness test method, and use the finite element simulation model to perform stiffness simulation on the series of design schemes;

[0007] Step 3: construct a neural network model for predicting and evaluating the stiffness of the wheel hub bearing according to the simulation results of Step 2, and perform training;

[0008] Step 4: verify the accuracy of the trained neural network model of Step 3, and perform stiffness prediction.

[0009] Further, in Step 1, the parameters affecting the stiffness of the wheel hub bearing include internal structural parameters and external structural parameters.

[0010] Further, the internal structural parameters include the diameter of the steel ball pitch circle, the center distance of the steel ball, the number of steel balls, the contact angle, the outer groove position, the inner groove position, the diameter of the steel ball, and the axial play.

[0011] Further, the external structure parameters include an inner flange comprehensive wall thickness determined by four parameters and an outer flange comprehensive wall thickness determined by three parameters.

[0012] Further, the step 1 further specifically includes:

[0013] The upper and lower limits of each parameter form a design space, and a basic design scheme is formed based on the middle values of the design space of each parameter; uniform sampling is performed in the design range, a single factor is changed, and a series of design schemes are formed.

[0014] Further, the method for establishing the finite element simulation model in the step 2 is:

[0015] The hub bearing adopts a 1 / 2 model, the upper fixed sleeve is connected with the inner flange plate through bolts, the lower fixed sleeve is fixedly connected with the base through a pressing block, and binding constraints are adopted at the contact positions; bolt load pre-tightening is applied at the bolt connection positions, fixed pre-tightening load is applied at the riveting position of the inner flange shaft end, and an axial load is applied at the end of the loading arm at a distance of the center tire radius; a plurality of analysis steps are established to apply different axial loads to obtain the stiffness under different loads; after the simulation calculation is completed, the axial displacement amounts and distances of the two fixed points of the upper fixed sleeve and the fixed point of the lower fixed sleeve are extracted, and the stiffness of the hub bearing is obtained through calculation.

[0016] Further, in the step 3, the method for establishing the neural network model is:

[0017] A part of the simulation result samples are randomly selected as a training set, and the rest are used as test samples; an input vector is generated according to the design scheme, the stiffness values under different loads corresponding to the input vector are used as output vector values, the root mean square error between the predicted values of the output vector and the expected values of the output vector is used as the input data of the error back propagation algorithm of the neural network, and the neural network model is repeatedly trained to continuously adjust the weights and errors until the error between the predicted values and the expected values of the output is less than a set threshold and the sum of squares of the error is minimized, and the trained neural network model is obtained.

[0018] Further, in the step 4, a test input vector is generated from the test samples in the step 3, the test input vector is input into the trained neural network model, the output value of the neural network model is the stiffness predicted value of the design scheme, and the stiffness predicted value is compared with the measured value to verify the accuracy of the model.

[0019] Compared with the prior art, the beneficial effects of the present application are that: the present application extracts the parameters of the structure affecting the stiffness of the hub bearing, establishes a design space, carries out stiffness simulation through finite element simulation, obtains sample data of the structure parameters and the stiffness values, and finally realizes the rapid prediction of the product stiffness in the design link, without the need for stiffness testing of all products, which greatly improves the design efficiency, reduces the cost, shortens the cycle, and is beneficial to the development of multi-variety and small-batch products. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 A flow chart of a parameterized evaluation prediction method for hub bearing stiffness of an embodiment of the present application;

[0021] Figure 2 Internal design parameters of a hub bearing structure of an embodiment of the present application;

[0022] Figure 3 External design parameters of a hub bearing structure of an embodiment of the present application;

[0023] Figure 4 A hub bearing stiffness simulation finite element model of an embodiment of the present application;

[0024] Figure 5 A neural network model of an embodiment of the present application;

[0025] Figure 6 A fitting degree of a training set of an embodiment of the present application;

[0026] Figure 7 A fitting degree of a test set of an embodiment of the present application. DETAILED DESCRIPTION

[0027] The technical solutions in the present application will be described clearly and completely below in conjunction with the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without any creative work fall within the protection scope of the present application.

[0028] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0029] The present application will be further described below in conjunction with specific embodiments, but is not limited to the embodiments.

[0030] As shown in the accompanying drawings, Figure 1 a parameterized evaluation prediction method for hub bearing stiffness is provided, including the following steps:

[0031] Step 1, parameterize the structure parameters affecting the hub bearing stiffness, establish a design space of hub bearing stiffness parameters, and determine a series of design schemes;

[0032] In this step, according to the structural characteristics of the hub bearing, the structural parameters that may affect the stiffness are parameterized, and the internal structural parameters and external structural parameters that affect the stiffness of the hub bearing are proposed; wherein the internal structural parameters include 8 variables: steel ball pitch circle diameter Dwp, steel ball center distance Po, steel ball number Z, contact angle a0, outer groove position He, inner groove position Hi, steel ball diameter Dw, and axial clearance Ga, as shown in Figure 2

[0033] The external structural parameters include 7 variables, that is, the inner flange comprehensive wall thickness δ i1 , δ i2 , δ i3 , δ i4 (wherein δ i3 is an angle value), the outer flange comprehensive wall thickness δ e1 , δ e2 , δ e3 , as shown in Figure 3

[0034] According to the design experience and basic specifications of the hub bearing unit, the hub bearing stiffness parameter design space is determined, that is, the design space of the internal parameters and the design space of the external parameters are determined, and the design space of the internal parameters is as follows:

[0035]

[0036] The design space of the external parameters is as follows:

[0037]

[0038] Then, the basic design scheme is composed based on the middle value of each parameter design space as the basic value. Uniform sampling is performed in the design range, a single factor is changed, a series of design schemes are composed, and the related parameters meet the bearing geometric relationship at the same time. There are N total design schemes, wherein Li is the level number of the ith factor;

[0039]

[0040] Specifically, in this embodiment, 15 stiffness influence parameters are determined according to the product results, and the values of each parameter are respectively:

[0041] Dwp={61, 63.875, 66.875, 69.625, 72.5}

[0042] Po={20, 23, 26, 29, 32}

[0043] Z={12, 13, 14, 15, 16, 17}

[0044] ​​a = {32°, 34°, 36°, 38°, 40°, 42°, 44°, 46°, 48°}

[0045] He = {9, 10.75, 12.5, 14.25, 16}

[0046] Hi = {2, 4, 6, 8, 10}

[0047] Dw = {10, 10.5, 11, 12.5, 13, 13.494, 14}

[0048] Ga = {0, -0.02, -0.04, -0.06, -0.08}

[0049] delta i1 = {8.185, 10.184, 12.184, 14.184, 16.184}

[0050] delta i2 = {49, 53, 57, 61, 65}

[0051] delta i3 = {6.22°, 9.72°, 13.22°, 16.72°, 20.22°}

[0052] delta i4 = {10.27, 14.27, 18.27, 22.27, 26.27}

[0053] delta e1 = {4.328, 5.328, 6.328, 7.328, 8.328}

[0054] delta e2 = {9, 10, 11, 12, 13}

[0055] delta e3 = {16.9, 18.9, 20.9, 22.9, 24.9, 26.9}

[0056] The basic design scheme is:

[0057] {Dwp, Po, Z, a, He, Hi, Dw, Ga, delta i1 , delta i2 , delta i3 , delta i4 , delta e1 , delta e2 , delta e3} = {66.875, 26, 14, 36°, 12.5, 6, 12.5, 0, 12.184, 57, 13.22°, 18.27, 6.328, 11, 20.9}

[0058] In the design value range, uniform sampling, changing a single factor, constituting a series of design schemes, a total of 69 schemes.

[0059] Step 2, the method of simulating the stiffness test test is used to establish a finite element simulation model, and the finite element simulation model is used to simulate the stiffness of the series of design schemes;

[0060] In this embodiment, as Figure 4 For the 69 design schemes, the finite element simulation model is established by using the test method of simulating the stiffness test. Specifically, the whole is adopted 1 / 2 model to save the calculation amount, the inner flange 4 is connected with the upper fixed sleeve 1 through the bolt 2, the outer flange 5 is fixed with the base 3 through the pressing block, and the binding constraint is adopted during simulation. A pre-tightening load of 50KN is applied at the bolt connection of the bolt 2. A pre-tightening load of 30KN is applied at the riveting end of the inner flange to simulate the influence of the riveting clamping force. An axial force axial load Fa is applied at the end of the loading arm of the upper fixed sleeve 1 (at a tire rolling radius of 318mm). Three analysis steps are established, and the axial loads are 1.5KN, 4KN and 8KN respectively. After the simulation calculation is completed, the axial displacement amounts and distances of the two fixed points A and B of the upper fixed sleeve (inner flange) and the fixed points C and D of the lower loading sleeve are extracted, and the stiffness K of the hub bearing is calculated by the following formula:

[0061]

[0062] Wherein, ΔZ AB represents the relative axial displacement amount between A and B; ΔX AB represents the distance between A and B.

[0063] ΔZ CD represents the relative axial displacement amount between C and D; ΔX CD represents the distance between C and D.

[0064] Step 3, constructing a neural network model for predicting and evaluating the stiffness of the hub bearing according to the simulation results of step 2;

[0065] In this step, see Figure 5 , a certain proportion of samples are randomly selected from the simulation result samples of step 2 as a training set, and the rest are used as test samples. Determine the input vector and output vector. In this embodiment, the input vector is generated by the selected design scheme of the influencing factor, which is a k*15 matrix vector, k is the number of training set samples, and 15 is the number of input layer nodes; the stiffness value under different loads is used as the output vector value, which is a k*m matrix vector, m is the number of axial load classification, that is, the number of output layer nodes.

[0066] According to the actual prediction accuracy requirement, the error threshold is set; a BP neural network model with single hidden layer is established, the number of hidden layer nodes nk The following empirical formula is used to determine:

[0067]

[0068] n is the number of input layer nodes, and m is the number of output layer nodes.

[0069] The hidden layer transfer function uses Tansig, the output layer transfer function uses Purelin, and the data is normalized to [-1, 1] by using mapminmax.

[0070] Training the network

[0071] The network is trained by using the Bayesian regularization method (trainbr). The root mean square error between the predicted value of the output vector and the expected value of the output vector is used as the input data of the BP neural network error back propagation algorithm, and the BP neural network model is trained repeatedly, and the weights and errors of the network are adjusted until the error between the predicted value and the expected value of the output is less than the set threshold and the sum of the squares of the errors is minimized, and the trained BP neural network model is obtained. The trained model is saved, and when the hub bearing stiffness is designed in the subsequent, the saved model is loaded, and the input vector is input, and the stiffness prediction value can be obtained.

[0072] In this embodiment, 61 samples are selected as the training set, 8 samples are selected as the test set (accounting for 11.6%), the input vector is a 61*15 matrix, the output vector is a 61*3 matrix, the number of iterations is set to 1000 times, and the learning rate is set to 0.005.

[0073] After multiple training, the model is optimized, the mean square error MSE is 141.67, the goodness of fit of the training set R is 0.99984, and the fitting degree is good, as shown in Figure 6 .

[0074] Step 4, verify the accuracy of the neural network model established in step 3.

[0075] In this step, according to the design scheme, the test set is randomly selected for prediction verification, the test input vector is generated, the test input vector is input into the trained BP neural network model, and the output is the stiffness prediction value of the design scheme. Further, in order to verify the prediction accuracy of the present application, a certain sample can be taken for stiffness test, and compared with the predicted value.

[0076] In this embodiment, 8 samples are used as the test set for prediction, the mean square error MSE of the test set is 2068.51, the goodness of fit R is 0.9985, and the fitting degree is good, as shown in Figure 7The predicted value is compared with the target value, and Table 1 shows that the absolute error and relative error of the predicted value and the target value are as follows: the relative error of the prediction is less than 2%, which indicates that the prediction accuracy of the trained BP neural network model in step 3 is high.

[0077] Table 1 Comparison of predicted value and target value

[0078]

[0079]

[0080] Further, three design schemes are taken to make samples, and stiffness tests are carried out, and the comparison between the test value and the predicted value is shown in Table 2. As shown in Table 2, the relative error between the test value and the predicted value is less than 10%, the error is large at a small load (1.5 KN), and the maximum error is 8.6%, the accuracy is high at a large load (8 KN), and the error is less than 5%, which indicates that the accuracy of the neural network model established in step 3 can meet the engineering design requirements.

[0081] Table 2 Comparison of predicted value and test value

[0082]

[0083] The above are only the preferred embodiments of the present application, and do not limit the embodiments and protection scope of the present application. It should be realized by those skilled in the art that any equivalent replacement and obvious changes made according to the content of the present application should be included in the protection scope of the present application.

Claims

1. A parametric evaluation and prediction method for the stiffness of a wheel hub bearing, characterized in that, Includes the following steps: Step 1: Parameterize the structures that affect the stiffness of the wheel hub bearing, establish the design space for the stiffness parameters of the wheel hub bearing, and determine a series of design schemes; Step 2: Establish a finite element simulation model using the method of simulated stiffness testing, and use the finite element simulation model to perform stiffness simulation on a series of design schemes; Step 3: Based on the simulation results of Step 2, construct a neural network model for predicting and evaluating the stiffness of wheel hub bearings, and conduct training. Step 4: Verify the accuracy of the neural network model trained in Step 3 and perform stiffness prediction. In step 1, the parameters affecting the stiffness of the wheel hub bearing include internal structural parameters and external structural parameters. Internal structural parameters include the pitch circle diameter of the steel balls, the center distance between the steel balls, the number of steel balls, the contact angle, the position of the outer groove, the position of the inner groove, the diameter of the steel balls, and the axial clearance; External structural parameters include the combined wall thickness of the flange and the combined wall thickness of the outer flange; The method for establishing the finite element simulation model in step 2 is as follows: The wheel hub bearing uses a 1 / 2 model. The upper fixed sleeve is connected to the inner flange by bolts, and the outer flange is fixedly connected to the base by pressure blocks. Binding constraints are applied at the contact points. Bolt load preload is applied at the bolt connection, fixed preload is applied at the riveting point at the shaft end of the inner flange, and axial load is applied at the end of the loading arm at a distance from the center tire radius. Multiple analysis steps are established to apply different axial loads to obtain the stiffness under different loads. After the simulation calculation is completed, the axial displacement and distance of the two fixed points of the upper fixed sleeve and the fixed point of the lower loading sleeve are extracted, and the stiffness of the wheel hub bearing is obtained by calculation.

2. The parametric evaluation and prediction method for wheel hub bearing stiffness according to claim 1, characterized in that, Step 1 also includes: The upper and lower limits of each parameter are designed to form a design space. The intermediate value within the design space of each parameter is used as the base value to form a basic design scheme. Samples are taken evenly within the design range, and a single factor is changed to form a series of design schemes.

3. The parametric evaluation and prediction method for hub bearing stiffness according to claim 1, characterized in that, In step 3, the method for establishing the neural network model is as follows: A portion of the simulation results samples are randomly selected as the training set, and the rest are used as test samples. The input vector is generated using the design scheme, and the stiffness values ​​under different loads are used as the output vector values. The root mean square error between the predicted and expected values ​​of the output vector is used as the input data for the backpropagation algorithm of the neural network error. The neural network model is trained iteratively, and the weights and errors are continuously adjusted until the error between the predicted and expected values ​​is less than a set threshold and the sum of squared errors is minimized, thus obtaining the trained neural network model.

4. The parametric evaluation and prediction method for wheel hub bearing stiffness according to claim 3, characterized in that, In step 4, a test input vector is generated from the test samples in step 3. The test input vector is then input into the trained neural network model, and its output value is the stiffness prediction value of the design scheme. The stiffness prediction value is compared with the measured value to verify the accuracy of the model.

Images