CN112560185A - Method for improving calculation accuracy of radial loading of rim in finite element analysis - Google Patents

Method for improving calculation accuracy of radial loading of rim in finite element analysis Download PDF

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CN112560185A
CN112560185A CN202011533883.4A CN202011533883A CN112560185A CN 112560185 A CN112560185 A CN 112560185A CN 202011533883 A CN202011533883 A CN 202011533883A CN 112560185 A CN112560185 A CN 112560185A
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吴小冬
许磊
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Liuzhou Zhijia Metal Technology Co ltd
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    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention discloses a method for improving the calculation accuracy of rim radial loading in finite element analysis, which comprises the steps of utilizing the resultant force of cosine distribution load to be equal to the radial load transmitted to a wheel by a ground or bench testing machine, and calculating the geometric relation between the distribution pressure at any angle and the radial load of the wheel by integrating the distribution load in a pressure distribution angle; obtaining a relational expression of the distribution pressure and the geometric coordinates of the wheels by utilizing the arctangent relation; the expression is input into finite element analysis software for solving, and a relatively accurate stress value or strain value of the wheel structure is obtained. The method of the invention improves the analysis precision by comparing the correct radial load application mode; the time for calculation derivation and computer analysis is shortened, the derivation form of triangular expansion is replaced by the arc tangent form, unnecessary derivation steps are reduced, the calculation time is reduced by reducing the definition of loads in analysis and the variable iteration times of an analysis expression, and the convergence of a finite element analysis model is accelerated.

Description

Method for improving calculation accuracy of radial loading of rim in finite element analysis
Technical Field
The invention relates to the technical field of finite element analysis of wheels, in particular to a method for improving the calculation accuracy of radial loading of a rim in finite element analysis.
Background
In the present finite element analysis of the wheel, because the material used by the tire is complex, the tire model is not easy to be simulated in the analysis, and in order to obtain a more accurate analysis result of the wheel, the equivalent treatment of the force applied by the tire on the wheel is necessary. The existing method for analyzing and calculating the stress of the hub by using a finite element method comprises the following two methods:
uniformly dividing a pressure distribution angle where a distributed load is located into 16 areas, and performing one-by-one loading analysis on corresponding single areas by solving the force of each area, for example, the fatigue crack position estimation of automobile wheel spokes is performed in the No. 6 of volume 30 of the university of Chinese book, 11 months in 2009;
secondly, the geometric relation between the distributed pressure at any angle and the radial load of the wheel is solved by integrating the distributed load in the pressure distribution angle, the obtained expression is expanded by using a triangular formula to obtain a more complex relational expression between the distributed pressure and a geometric coordinate, and the more complex relational expression is input into finite element analysis software (Abaqus) for solving, for example, application of ABAQUS in radial fatigue simulation analysis of steel wheels, which is published by Changan automobile engineering research institute.
However, the two methods have some defects, the accuracy of the calculation model in the method 1 is low, because the pressure distribution angle for distributing the load is uniformly divided into 16 areas, according to the approximate value research, the accuracy of two digits after the decimal point can be obtained only when the central angle is less than 0.17 degrees, and the 80-degree pressure angle only divides 16 areas and obviously does not meet the loading accuracy requirement, and then 16 loads are loaded one by one, which also causes low analysis efficiency; in the method 2, the geometric relational expression of the distributed pressure and the radial load of the wheel is expanded by using a triangular formula, the derivation is complicated, and the time is wasted, and the relational expression after the triangular formula is expanded is used for analysis, so that variables are quoted for many times, and the solving time of a computer is prolonged.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above and/or other problems associated with the prior art methods for improving the accuracy of rim radial loading calculations in finite element analysis.
Therefore, the problem to be solved by the invention is how to solve the problems that the existing method for improving the calculation accuracy of rim radial loading in finite element analysis is inaccurate in accuracy and long in calculation derivation and computer analysis time.
In order to solve the technical problems, the invention provides the following technical scheme: a method for improving the calculation accuracy of radial loading of a rim in finite element analysis comprises the steps of utilizing the resultant force of cosine distribution loads to be equal to the radial load transmitted to a wheel by a ground or bench testing machine, and integrating the distribution loads in pressure distribution angles to obtain the geometric relation between the distribution pressure at any angle and the radial load of the wheel; obtaining a relational expression of the distribution pressure and the geometric coordinates of the wheels by utilizing the arctangent relation; the expression is input into finite element analysis software for solving, and a relatively accurate stress value or strain value of the wheel structure is obtained.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: the pressure distribution to each load surface can be calculated as follows:
Figure BDA0002849676240000021
in the formula: theta is the pressure W on each loading surfacerWith maximum load W0Angle between them, theta0Is the pressure profile angle.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: the resultant force of the cosine distributed load and the ground or bench tester are transmitted to the vehicleRadial load F of the wheeldEqual, so the following formula is available:
Figure BDA0002849676240000022
the finishing formula (2) is as follows:
Figure BDA0002849676240000023
in the formula: r isbIs the bead seat radius, b is the bead seat width;
substituting formula (1) for formula (3) to obtain:
Figure BDA0002849676240000024
integrating the above formula to obtain:
Figure BDA0002849676240000025
finishing the formula to obtain:
Figure BDA0002849676240000031
the distributed pressure W can be obtained by substituting formula (6) for formula (1)rRadial load F with wheeldThe equation of (c):
Figure BDA0002849676240000032
in the formula FdIs the wheel radial load.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: according to Fd=FvK, substituting the obtained product into formula (7) to obtain the distribution pressure W on the bead seatr
Figure BDA0002849676240000033
In the formula: k is the strengthening test coefficient, FvIs the rated load.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: establishing a local coordinate system by taking the X axis as a rotating axis of the wheel, wherein the local coordinate system can be obtained as follows:
Figure BDA0002849676240000034
substituting formula (9) into formula 8 to obtain:
Figure BDA0002849676240000035
namely:
Figure BDA0002849676240000036
in the formula: fvThe unit of (a) is N; the unit of b is mm; r isbThe unit of (a) is mm; the unit of θ is rad.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: the wheel and the test condition parameter rb、b、K、FvAnd theta0Substituting the formula (10) into a formula (10), and inputting the formula (10) after the parameters are substituted into finite element analysis software to realize the radial load W of the wheel0Cosine loading on shoulder.
As a preferable aspect of the method for improving the rim radial loading calculation accuracy in finite element analysis according to the present invention, wherein: the finite element analysis software used was the Abaqus software.
As a preferred scheme of the method for improving the calculation accuracy of the rim radial loading in finite element analysis, the method isWherein: the method comprises the following steps of setting a function expression in a set (10) by using an analytic field command in Abaqus software:
Figure BDA0002849676240000041
and applying an applied load W0The values of (2) are submitted for calculation.
The invention has the beneficial effects that:
1. the analysis precision is improved by comparing the correct radial load application mode;
2. the time for calculation derivation and computer analysis is shortened, the derivation form of triangular expansion is replaced by the arc tangent form, unnecessary derivation steps are reduced, the calculation time is reduced by reducing the definition of loads in analysis and the variable iteration times of an analysis expression, and the convergence of a finite element analysis model is accelerated.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
figure 1 is a radial loading diagram illustrating the method of improving the rim radial loading calculation accuracy in finite element analysis of example 1.
Figure 2 is a mathematical model of a wheel illustrating the method of example 1 to improve the accuracy of rim radial loading calculations in finite element analysis.
Figure 3 is a diagram of a wheel mesh model for the method of improving the rim radial loading calculation accuracy in finite element analysis of example 1.
Figure 4 is a local coordinate system of the method of improving the accuracy of rim radial loading calculations in finite element analysis of example 1.
Figure 5 is a cosine loading of radial load for the method of improving the accuracy of rim radial loading calculation in finite element analysis of example 1.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Example 1
Referring to fig. 1 to 5, a first embodiment of the present invention provides a method for improving the calculation accuracy of radial loading of a rim in finite element analysis, where the method for improving the calculation accuracy of radial loading of a rim in finite element analysis includes:
the resultant force of cosine distribution load is equal to the radial load transmitted to the wheel by the ground or bench testing machine, and the geometrical relation between any angle distribution pressure and the radial load of the wheel is solved by integrating the distribution load in the pressure distribution angle, wherein the meaning of the pressure distribution angle is as follows: the pressure applied to the wheel in the radial direction by the ground or the bench testing machine is transmitted to the bead seat of the rim by the tire, the area covered by the pressure on the bead seat is in the shape of an arc, the two ends of the arc and the corresponding circle center form a sector area, and the sector area is a circle center angle. This central angle is then defined as the pressure profile angle. It should be explained that, in the finite element analysis software Abaqus, a region load is required to be applied to the position of the wheel bead seat, the region load changes along with the position change, and at this time, the region load needs to be loaded through a relational expression, so that the geometric relationship between the distributed load in the pressure distribution angle and the radial load of the wheel is obtained by integrating the distributed load in the pressure distribution angle.
Obtaining a relational expression of the distribution pressure and the geometric coordinates of the wheels by utilizing the arctangent relation; the expression is input into finite element analysis software for solving, and a relatively accurate stress value or strain value of the wheel structure is obtained.
It should be noted that distributing the load is distributing the pressure.
The force applied by the ground or bench testing machine to the wheel during the running or bench test of the automobile can be equivalent to the distributed pressure applied to the bead seat of the rim, and the load is distributed on the bead seat in 80 DEG cosine, as shown in figure 1, wherein W is0Is the maximum pressure loaded on the rim; wrPressure distributed over the loading surface; theta0Is a pressure distribution angle; r isbIs the bead seat radius; b is the bead seat width.
According to a study of the document "An introduction of stress and displacement distribution in An aluminum alloy automatic mobile rim", the pressure distribution on each loading surface can be calculated as follows:
Figure BDA0002849676240000061
in the formula: theta is the pressure W on each loading surfacerWith maximum load W0Angle between them, theta0Is the pressure profile angle.
Resultant force of cosine distributed loads and radial load F transmitted to wheel by ground or bench testing machinedEqual, so the following formula is available:
Figure BDA0002849676240000062
the finishing formula (2) is as follows:
Figure BDA0002849676240000063
in the formula: r isbIs the bead seat radius, b is the bead seat width;
substituting formula (1) for formula (3) to obtain:
Figure BDA0002849676240000064
integrating the above formula to obtain:
Figure BDA0002849676240000065
finishing the formula to obtain:
Figure BDA0002849676240000066
the distributed pressure W can be obtained by substituting formula (6) for formula (1)rRadial load F with wheeldThe equation of (c):
Figure BDA0002849676240000067
in the formula FdIs the wheel radial load.
According to Fd=FvK, substituting the obtained product into formula (7) to obtain the distribution pressure W on the bead seatr
Figure BDA0002849676240000071
In the formula: k is the strengthening test coefficient, FvIs the rated load.
In the finite element analysis, the mathematical model of the wheel needs to be divided into mesh models, as shown in fig. 2 and 3. The wheel uses the X axis as a rotating axis to establish a local coordinate system, and the Y-Z plane is a plane where the wheel is located in the radial direction. Defining boundary conditions, defining the coordinate relation between the loading direction and the application position of the load, as shown in fig. 4, and obtaining under the local coordinate system:
Figure BDA0002849676240000072
substituting formula (9) into formula 8 to obtain:
Figure BDA0002849676240000073
comparing formula (10) with formula (1) to obtain:
Figure BDA0002849676240000074
in the formula: fvThe unit of (a) is N; the unit of b is mm; r isbThe unit of (a) is mm; the unit of θ is rad.
The wheel and the test condition parameter rb、b、K、FvAnd theta0Substituting the formula (10) into a formula (10), and inputting the formula (10) after the parameters are substituted into finite element analysis software to realize the radial load W of the wheel0And (4) cosine loading on the tire shoulder, judging whether the wheel structure is reasonable or not according to the obtained stress value or strain value of the wheel structure, and if not, changing the wheel structure or the wheel material. Wheel and rated load F in test condition parametersvThe value is selected according to the vehicle type. The strengthening experiment coefficient K is a national standard specified value; total bead seat width b, bead seat radius rbPressure distribution angle theta0The values are selected according to the national standard specified range corresponding to the wheel size.
The finite element analysis software uses Abaqus software to set the function expression in the set (10) using analytical field commands:
Figure BDA0002849676240000081
and applying an applied load W0The values of (2) are submitted for calculation.
In the actual analysis, the wheel and test condition parameters are as follows:
TABLE 1 wheel and test Condition parameters
Figure BDA0002849676240000082
In Table 1, except for the rated load FvBesides, the other parameters are specific data of thirteen-inch wheels and rated load FvAccording to the maximum load of a certain type of car.
According to GB/T5334-2005, F is obtainedd=FvK. Substituting the table value to obtain Fd3865.14 × 2 × 7730.28N, and the parameter rbB and theta0Substituting the formula (10) to obtain the distribution pressure W on the bead seatrComprises the following steps:
Figure BDA0002849676240000083
local coordinates established with the X-axis as the axis of rotation will
Figure BDA0002849676240000084
Substituted into formula (11) to obtain:
Figure BDA0002849676240000085
in the finite element analysis software Abaqus, the function in the set (12) is expressed using the analytical field command
Figure BDA0002849676240000086
And applying an applied load W0The value of (c): 1.686979521, submitted to calculation, so as to achieve the wheel radial load W0Along with cosine loading under different tire shoulder positions, the loading form is shown in fig. 5, the wheel can be submitted for calculation after the loading is finished, and the wheel has a reasonable structure after judgment.
In conclusion, the method of the invention improves the analysis precision by comparing the correct radial load application mode, shortens the time of calculation derivation and computer analysis, replaces the derivation form of triangular expansion with the arc tangent form, reduces unnecessary derivation steps, reduces the calculation time by reducing the load definition in analysis and the variable iteration times of the analysis expression, and accelerates the convergence of the finite element analysis model.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.

Claims (8)

1. A method for improving the calculation accuracy of rim radial loading in finite element analysis is characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
the resultant force of the cosine distributed load is equal to the radial load transmitted to the wheel by the ground or bench testing machine, and the geometric relation between the distributed pressure at any angle and the radial load of the wheel is solved by integrating the distributed load in the pressure distribution angle;
obtaining a relational expression of the distribution pressure and the geometric coordinates of the wheels by utilizing the arctangent relation;
the expression is input into finite element analysis software for solving, and a relatively accurate stress value or strain value of the wheel structure is obtained.
2. A method for improving rim radial load calculation accuracy in finite element analysis according to claim 1 wherein: the pressure distribution to each load surface can be calculated as follows:
Figure FDA0002849676230000011
in the formula: theta is the pressure W on each loading surfacerWith maximum load W0Angle between them, theta0Is the pressure profile angle.
3. A method of improving rim radial loading calculation accuracy in finite element analysis according to claim 2The method is characterized in that: resultant force of cosine distributed loads and radial load F transmitted to wheel by ground or bench testing machinedEqual, so the following formula is available:
Figure FDA0002849676230000012
the finishing formula (2) is as follows:
Figure FDA0002849676230000013
in the formula: r isbIs the bead seat radius, b is the bead seat width;
substituting formula (1) for formula (3) to obtain:
Figure FDA0002849676230000014
integrating the above formula to obtain:
Figure FDA0002849676230000015
finishing the formula to obtain:
Figure FDA0002849676230000021
the distributed pressure W can be obtained by substituting formula (6) for formula (1)rRadial load F with wheeldThe equation of (c):
Figure FDA0002849676230000022
in the formula FdIs the wheel radial load.
4. A handle as claimed in claim 3The method for calculating the accuracy of the radial loading of the rim in the high finite element analysis is characterized in that: according to Fd=FvK, substituting the obtained product into formula (7) to obtain the distribution pressure W on the bead seatr
Figure FDA0002849676230000023
In the formula: k is the strengthening test coefficient, FvIs the rated load.
5. A method of improving the rim radial loading calculation accuracy in finite element analysis according to claim 4 wherein: establishing a local coordinate system by taking the X axis as a rotating axis of the wheel, wherein the local coordinate system can be obtained as follows:
Figure FDA0002849676230000024
substituting formula (9) into formula (8) to obtain:
Figure FDA0002849676230000025
namely:
Figure FDA0002849676230000026
in the formula: fvThe unit of (a) is N; the unit of b is mm; r isbThe unit of (a) is mm; the unit of θ is rad.
6. A method of improving the rim radial loading calculation accuracy in finite element analysis according to claim 5 wherein: the wheel and the test condition parameter rb、b、K、FvAnd theta0Substituting the formula (10) into a formula (10), and inputting the formula (10) after the parameters are substituted into finite element analysis software to realize the radial load W of the wheel0Cosine loading on shoulder.
7. A method of improving the rim radial loading calculation accuracy in finite element analysis according to claim 6 wherein: the finite element analysis software used was the Abaqus software.
8. A method of improving rim radial load calculation accuracy in finite element analysis according to claim 7 wherein: using a function expression in an analytic field command set (10) in the Abaqus software:
Figure FDA0002849676230000031
and applying an applied load W0The values of (2) are submitted for calculation.
CN202011533883.4A 2020-12-22 2020-12-22 Method for improving calculation accuracy of radial loading of rim in finite element analysis Pending CN112560185A (en)

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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102855359A (en) * 2012-09-11 2013-01-02 北京航空航天大学 Optimized design method for variable-thickness rims of automobile wheels
CN109002676A (en) * 2018-10-11 2018-12-14 安徽合力股份有限公司 A kind of emulation modelling method of wheel rim

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102855359A (en) * 2012-09-11 2013-01-02 北京航空航天大学 Optimized design method for variable-thickness rims of automobile wheels
CN109002676A (en) * 2018-10-11 2018-12-14 安徽合力股份有限公司 A kind of emulation modelling method of wheel rim

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
徐鹏: "汽车钢制车轮有限元分析与疲劳寿命预测", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 *

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