CN115356104A - Parameterized evaluation and prediction method for hub bearing rigidity - Google Patents
Parameterized evaluation and prediction method for hub bearing rigidity Download PDFInfo
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Abstract
The invention relates to a parameterized evaluation and prediction method for hub bearing stiffness, which comprises the following steps: step 1, parameterizing a structure influencing the rigidity of a hub bearing, establishing a design space of the rigidity parameter of the hub bearing, and determining a series of design schemes; step 2, establishing a finite element simulation model by adopting a method of simulating a rigidity test, and carrying out rigidity simulation on a series of design schemes by using the finite element simulation model; step 3, constructing a neural network model for predicting and evaluating the rigidity of the hub bearing according to the simulation result of the step 2 and carrying out training; and 4, verifying the accuracy of the neural network model established in the step 3 and developing prediction. The method can quickly predict the product rigidity in the design link without performing rigidity test on all designed products, greatly improves the design efficiency, reduces the cost, has short period and is beneficial to the development of various small-batch products.
Description
Technical Field
The invention belongs to the technical field of hub bearing development, and particularly relates to a parameterized evaluation and prediction method for the rigidity of a hub bearing.
Background
The rigidity analysis of the traditional bearing is usually based on the Hertz contact theory, a bearing total stress balance equation is established, and the rigidity (CN 107153734B) is obtained by solving the deformation of the bearing through iteration. At present, the common method is that the indexes such as service life and the like are preferentially met during design, the rigidity index is not considered for the moment, then a sample is trial-manufactured, and then a special device is adopted to carry out a rigidity test (CN 101886979B) to verify whether a designed product meets the rigidity requirement or not. The method has higher cost and longer period, and is not beneficial to the development of various small-batch products.
Disclosure of Invention
The invention aims to provide a parameterized estimation and prediction method for the rigidity of a hub bearing aiming at the defects of the prior art, and the method can greatly improve the design efficiency of the hub bearing.
A parameterized evaluation and prediction method for the rigidity of a hub bearing comprises the following steps:
and 4, verifying the precision of the neural network model trained in the step 3, and carrying out rigidity prediction.
Further, in step 1, the parameters affecting the rigidity of the hub bearing include internal structural parameters and external structural parameters.
Further, the internal structure parameters comprise the pitch circle diameter of the steel balls, the center distance of the steel balls, the number of steel balls, a contact angle, the position of an outer groove, the position of an inner groove, the diameter of the steel balls and the axial clearance.
Further, the external structural parameters comprise the comprehensive wall thickness of the inner flange determined by four parameters and the comprehensive wall thickness of the outer flange determined by three parameters.
Further, step 1 specifically includes:
designing upper and lower limits of each parameter to form a design space, forming a basic design scheme by taking an intermediate value in each parameter design space as a basic value, uniformly sampling in a design range, changing a single factor, and forming a series of design schemes.
Further, the method for establishing the finite element simulation model in the step 2 comprises the following steps:
the hub bearing adopts a 1/2 model, an upper fixed sleeve is connected with an inner flange plate through a bolt, an outward transmission method is fixedly connected with a base through a pressing block, and a contact part adopts binding constraint; applying bolt load pre-tightening at the bolt connection part, applying fixed pre-tightening load at the shaft end riveting part of the inner flange, and applying axial load at the position of the tail end of the loading arm away from the radius of the central tire; establishing a plurality of analysis steps to apply different axial loads so as to obtain the rigidity under different loads; after the simulation calculation is completed, the axial displacement and the distance of the two fixed points of the upper fixed sleeve and the fixed point of the lower loading sleeve are extracted, and the rigidity of the hub bearing is obtained through calculation.
Further, in step 3, the method for establishing the neural network model comprises:
randomly selecting a part of samples from simulation result samples as a training set, and taking the rest samples as test samples; and generating an input vector by using a design scheme, taking the corresponding rigidity values under different loads as output vector values, taking the root mean square error of the predicted value of the output vector and the expected value of the output vector as input data of a neural network error back propagation algorithm, carrying out cyclic reciprocating training on the neural network model, and continuously adjusting the weight and the error until the error between the output predicted value and the expected value is smaller than a set threshold value and the sum of squares of the errors reaches the minimum, thereby obtaining the trained neural network model.
Further, in step 4, a test input vector is generated by the test sample in step 3, the test input vector is input into the trained neural network model, the output value of the test input vector is the predicted value of the stiffness of the design scheme, and the predicted value of the stiffness is compared with the measured value to verify the accuracy of the model.
Compared with the prior art, the invention has the beneficial effects that: according to the method, the structure influencing the rigidity of the hub bearing is extracted in a parameterization mode, a design space is established, rigidity simulation is carried out through finite element simulation, sample data of structural parameters and rigidity values are obtained, then a BP neural network model is established, and finally the rigidity of a product is rapidly predicted in a design link without carrying out rigidity test on all products, so that the design efficiency is greatly improved, the cost is reduced, the period is short, and the development of multiple varieties of small-batch products is facilitated.
Drawings
FIG. 1 is a flow chart of a parameterized evaluation and prediction method for hub bearing stiffness according to an embodiment of the invention;
FIG. 2 is an internal design parameter of a hub-bearing arrangement in accordance with an embodiment of the present invention;
FIG. 3 is an external design parameter of the hub bearing arrangement in accordance with the present embodiment;
FIG. 4 is a hub bearing stiffness simulation finite element model according to an embodiment of the present invention;
FIG. 5 is a neural network model according to an embodiment of the present invention;
FIG. 6 is a graph of the fitness of a training set according to an embodiment of the present invention;
FIG. 7 is a graph of the fitness of a test set according to an embodiment of the present invention.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the following embodiments of the present invention, and it should be understood that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.
The present invention is further illustrated by the following examples, which are not to be construed as limiting the invention.
As shown in fig. 1, an embodiment of the present invention provides a method for predicting the parameterized evaluation of the stiffness of a hub bearing, including the following steps:
in the step, according to the structural characteristics of the hub bearing, parameterizing a structure which possibly influences the rigidity, and providing internal structural parameters and external structural parameters which influence the rigidity of the hub bearing; wherein, the internal structure parameter contains 8 variables: the pitch circle diameter Dwp of the steel ball, the center distance Po of the steel ball, the number Z of steel balls and the contact angle alpha 0 Outer groove position He, inner groove position Hi, steel ball diameter Dw, axial clearance Ga, as shown in FIG. 2;
the external structural parameters comprise 7 variables, namely the comprehensive wall thickness delta of the inner flange i1 、δ i2 、δ i3 、δ i4 (wherein δ i3 Angle value), the overall wall thickness delta of the outer flange e1 、δ e2 、δ e3 As shown in fig. 3;
according to the design experience and the basic specification of the hub bearing unit, determining a hub bearing rigidity parameter design space, namely determining a design space of internal parameters and a design space of external parameters, wherein the design space of the internal parameters is as follows:
the design space for the external parameters is as follows:
and then, the basic design scheme is formed by taking the intermediate value of each parameter design space as a basic value. The sampling is uniform in the design range, single factors are changed, a series of design schemes are formed, and meanwhile, the bearing geometric relation among the associated parameters is guaranteed. Total N total design scenarios, where Li is the number of levels of the ith factor;
specifically, in this embodiment, 15 stiffness influence parameters are determined according to a product result, and values of the parameters are respectively:
Dwp＝{61,63.875,66.875,69.625,72.5}
Po＝{20,23,26,29,32}
Z＝{12,13,14,15,16,17}
α＝{32°,34°,36°,38°,40°,42°,44°,46°,48°}
He＝{9,10.75,12.5，14.25,16}
Hi＝{2,4,6，8,10}
Dw＝{10,10.5,11，12.5,13,13.494,14}
Ga＝{0,-0.02,-0.04，-0.06,-0.08}
δ i1 ＝{8.185,10.184,12.184，14.184,16.184}
δ i2 ＝{49,53,57,61,65}
δ i3 ＝{6.22°,9.72°,13.22°,16.72°，20.22°}
δ i4 ＝{10.27，14.27,18.27,22.27,26.27}
δ e1 ＝{4.328,5.328,6.328,7.328,8.328}
δ e2 ＝{9,10，11,12,13}
δ e3 ＝{16.9,18.9,20.9,22.9,24.9,26.9}
the basic design scheme is as follows:
{Dwp，Po，Z，α，He，Hi，Dw，Ga，δ i1 ，δ i2 ，δ i3 ，δ i4 ，δ e1 、δ e2 、δ e3 }＝{66.875，26，14，36°，12.5,6，12.5,0，12.184，57，13.22°，18.27，6.328，11,20.9}
the samples were sampled uniformly within the design value range, and a single factor was changed to constitute a series of design solutions, for a total of 69 solutions.
in this embodiment, as shown in fig. 4, for 69 design solutions, a finite element simulation model is established by using a test method for simulating a stiffness test. Specifically, the 1/2 model is adopted integrally to save calculated amount, the inner flange plate 4 is connected with the upper fixing sleeve 1 through the bolt 2, the external transmission method 5 is connected with the base fixing 3 through the pressing block, and binding constraint is adopted during simulation. And applying a 50KN bolt load to the joint of the bolt 2 for pre-tightening. And applying a pre-tightening load of 30KN to the riveting position of the shaft end of the inner flange to simulate the influence of the riveting clamping force. And applying axial force axial load Fa to the tail end (the position with the tire rolling radius of 318 mm) of the loading arm of the upper fixed sleeve 1, and establishing three analysis steps, wherein the axial load is 1.5KN,4KN and 8KN respectively. After the simulation calculation is finished, extracting the axial displacement and the distance of two fixed points A, B of an upper fixed sleeve (inner flange) and a fixed point C, D of a lower loading sleeve, and calculating the rigidity K of the hub bearing according to the following formula:
wherein, Δ Z AB Indicating A, B relative axial displacement; Δ X AB Indicating the distance between A, B.
ΔZ CD Indicating the relative axial displacement between C, D; Δ X CD Indicating the distance between C, D.
in this step, see fig. 5, a certain proportion of samples are randomly selected from the simulation result samples in step 2 as a training set, and the rest are used as test samples. Determining an input vector and an output vector, in the embodiment, generating the input vector by using a design scheme of the selected influence factors, wherein k is a matrix vector of 15, k is the number of samples in a training set, and 15 is the number of nodes in an input layer; and taking the corresponding rigidity values under different loads as output vector values, namely k × m matrix vectors, wherein m is the classification number of the axial loads, namely the number of nodes of the output layer.
Setting an error threshold according to the actual prediction precision requirement; establishing a BP neural network model of a single hidden layer, and the number n of nodes of the hidden layer k The following empirical formula is used for determination:
n is the number of nodes of the input layer, and m is the number of nodes of the output layer.
The hidden layer transfer function adopts Tansig, the output layer transfer function adopts Purelin, and the mapminmax is adopted to normalize the data to be between [ -1,1 ].
Training network
The network was trained using bayesian regularization (trainbr). And taking the root mean square error of the predicted value of the output vector and the expected value of the output vector as input data of a back propagation algorithm of the error of the BP neural network, carrying out cyclic reciprocating training on the BP neural network model, and continuously adjusting the weight and the error of the network until the error between the predicted value of the output and the expected value is smaller than a set threshold value and the sum of squares of the errors reaches the minimum value, thereby obtaining the trained BP neural network model. After the trained model is stored, when the rigidity of the hub bearing is subsequently designed, the stored model is loaded, and a vector is input, so that a rigidity predicted value can be obtained.
In this embodiment, 61 samples are selected as a training set, 8 samples are selected as a test set (accounting for 11.6%), an input vector is a matrix of 61 × 15, an output vector is a matrix of 61 × 3, the number of iterations is set to 1000, and the learning rate is set to 0.005.
After multiple times of training, the model is optimized, the mean square error MSE =141.67, the goodness of fit R =0.99984 of the training set is good, and the fitting degree is shown in FIG. 6.
And 4, verifying the precision of the neural network model established in the step 3.
In the step, according to a design scheme, a randomly selected test set is used for prediction verification to generate a test input vector, the test input vector is input into a trained BP neural network model, and the output of the test input vector is the rigidity prediction value of the design scheme. Furthermore, in order to verify the prediction accuracy of the method, a certain sample can be taken for rigidity test and compared with a predicted value.
In this embodiment, 8 samples are used as a test set, and prediction is performed, wherein mean square error MSE =2068.51, goodness of fit R =0.9985, and the degree of fit is better as shown in fig. 7. The predicted value is compared with the target value, see table 1, and it can be seen from table 1 that the absolute error and the relative error between the predicted value and the target value are as follows, and the predicted relative error is less than 2%, which indicates that the BP neural network model trained in step 3 has high prediction accuracy.
TABLE 1 comparison of predicted values to target values
Further, 3 design schemes are taken to prepare samples, the stiffness test is carried out, the test values and the predicted values are compared as shown in the following table 2, and as can be seen from the table 2, the relative error between the test values and the predicted values is less than 10%, the error is large when the load is small (1.5 KN), the maximum error is 8.6%, the precision is high when the load is large (8 KN), the precision is less than 5%, and the precision of the neural network model established in the step 3 can meet the engineering design requirements.
TABLE 2 comparison of predicted values with test values
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes in form and detail may be made without departing from the spirit and scope of the invention.
Claims (8)
1. A method for parameterized evaluation and prediction of hub bearing stiffness is characterized by comprising the following steps:
step 1, parameterizing a structure influencing the rigidity of a hub bearing, establishing a design space of the rigidity parameter of the hub bearing, and determining a series of design schemes;
step 2, establishing a finite element simulation model by adopting a method of simulating a rigidity test, and carrying out rigidity simulation on a series of design schemes by using the finite element simulation model;
step 3, constructing a neural network model for predicting and evaluating the rigidity of the hub bearing according to the simulation result of the step 2, and carrying out training;
and 4, verifying the precision of the neural network model trained in the step 3 and carrying out rigidity prediction.
2. The parametric estimation and prediction method for the rigidity of the hub bearing according to claim 1, wherein in step 1, the parameters affecting the rigidity of the hub bearing comprise internal structural parameters and external structural parameters.
3. The method for evaluating and predicting the stiffness parameterization of the hub bearing according to claim 2, wherein the internal structural parameters comprise steel ball pitch circle diameter, steel ball center distance, steel ball number, contact angle, outer groove position, inner groove position, steel ball diameter and axial play.
4. The parametric estimation and prediction method for the rigidity of the hub bearing according to claim 1, wherein the external structural parameters comprise an inner flange comprehensive wall thickness determined by four parameters and an outer flange comprehensive wall thickness determined by three parameters.
5. The parametric estimation and prediction method for the rigidity of the hub bearing according to claim 1, wherein the step 1 specifically comprises the following steps:
designing upper and lower limits of each parameter to form a design space, forming a basic design scheme by taking an intermediate value in each parameter design space as a basic value, uniformly sampling in a design range, changing a single factor, and forming a series of design schemes.
6. The parametric estimation and prediction method for the rigidity of the hub bearing according to claim 1, wherein the method for establishing the finite element simulation model in the step 2 comprises the following steps:
the hub bearing adopts a 1/2 model, an upper fixed sleeve is connected with an inner flange plate through a bolt, an outward transmission method is fixedly connected with a base through a pressing block, and a contact part adopts binding constraint; applying bolt load pre-tightening at the bolt connection part, applying fixed pre-tightening load at the shaft end riveting part of the inner flange, and applying axial load at the position of the tail end of the loading arm away from the radius of the central tire; establishing a plurality of analysis steps to apply different axial loads so as to obtain the rigidity under different loads; after the simulation calculation is completed, the axial displacement and the distance of the two fixed points of the upper fixed sleeve and the fixed point of the lower loading sleeve are extracted, and the rigidity of the hub bearing is obtained through calculation.
7. The parameterized estimation and prediction method for hub bearing stiffness according to claim 1, wherein in step 3, the method for establishing the neural network model comprises:
randomly selecting a part of samples from simulation result samples as a training set, and taking the rest samples as test samples; and generating an input vector by using a design scheme, taking the corresponding rigidity values under different loads as output vector values, taking the root mean square error of the predicted value of the output vector and the expected value of the output vector as input data of a neural network error back propagation algorithm, carrying out cyclic reciprocating training on the neural network model, and continuously adjusting the weight and the error until the error between the output predicted value and the expected value is smaller than a set threshold value and the sum of squares of the errors reaches the minimum, thereby obtaining the trained neural network model.
8. The parameterized hub bearing stiffness estimation and prediction method according to claim 7, wherein in step 4, the test input vector is generated from the test sample in step 3, the test input vector is input into the trained neural network model, the output value of the test input vector is the predicted value of the stiffness of the design, and the predicted value of the stiffness is compared with the measured value to verify the accuracy of the model.
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| CN116522510A (en) * | 2023-06-28 | 2023-08-01 | 中信戴卡股份有限公司 | Inversion method and system for tire material parameters for wheel performance simulation |
| CN116522510B (en) * | 2023-06-28 | 2023-09-01 | 中信戴卡股份有限公司 | Inversion method and system for tire material parameters for wheel performance simulation |
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