WO2023246244A1 - 一种降低车轮风阻的轮辐开口轮廓形状的方法 - Google Patents

一种降低车轮风阻的轮辐开口轮廓形状的方法 Download PDF

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WO2023246244A1
WO2023246244A1 PCT/CN2023/087752 CN2023087752W WO2023246244A1 WO 2023246244 A1 WO2023246244 A1 WO 2023246244A1 CN 2023087752 W CN2023087752 W CN 2023087752W WO 2023246244 A1 WO2023246244 A1 WO 2023246244A1
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wheel
spoke opening
opening profile
profile shape
wind resistance
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PCT/CN2023/087752
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English (en)
French (fr)
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周海超
黄婷慧
焦东琦
张铃欣
王国林
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江苏大学
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Definitions

  • the invention relates to an optimization method for reducing the wheel spoke opening profile shape, and in particular to a method for reducing the wheel spoke opening profile shape for reducing wheel wind resistance, and belongs to the technical field of vehicle engineering.
  • the wheel area contributes up to 25-30% to the aerodynamic resistance of the car.
  • the flow field in the wheel area is jointly affected by the flow from the side and bottom of the car, as well as the flow field in the engine compartment. It has relatively strong mutual interference with the body, the bottom structure and the ground, and wheel rotation will also affect this flow.
  • the flow field in the area generates energy input, making the flow field structure in the wheel area more complex.
  • Existing research also shows that different opening shapes of car wheel rims will have a direct impact on wheel aerodynamic resistance and car aerodynamic resistance.
  • the arrangement of the openings on the wheel web has a great influence on the aerodynamic characteristics: when the total opening area is the same, appropriately increasing the number of openings is beneficial to improving the aerodynamic characteristics; as the total opening area increases, the wheel itself
  • the resistance coefficients all show irregular changes to a certain extent. Therefore, taking the wheel spoke as the optimization object, without changing the wheel opening area, and reducing the aerodynamic resistance of a single wheel as the optimization goal, the small arc radius R 1 , the large arc radius R 2 , and the small arc radius of a single spoke hole are selected.
  • the arc tangents L 1 and L 2 and the corresponding circumferential angle ⁇ are design variables.
  • the optimal hyper-Latin cubic design, RBF approximation model and adaptive simulated annealing algorithm (ASA) are comprehensively used to optimize the spoke holes, and the optimal spoke shape is obtained.
  • the present invention provides a method for reducing the wheel wind resistance and the shape of the wheel spoke opening profile.
  • the method takes the reduction of the aerodynamic resistance of a single wheel as the optimization goal and can effectively avoid the formation of the wheel spokes.
  • the blindness problem existing in the opening profile design process can effectively reduce the wheel spoke opening profile design cycle, thereby improving the improvement efficiency.
  • it can also improve the aerodynamic characteristics of the wheel area to achieve the purpose of reducing vehicle resistance.
  • a method for reducing the wheel spoke opening profile shape that reduces wheel wind resistance including the following steps:
  • Step 1 Establish an initial wheel model, and draw a three-dimensional model of the wheel based on the selected number of wheel spokes and the initial value of the wheel spoke opening profile shape;
  • the spoke opening profile shape parameters include the small arc radius R 1 and the large arc radius R 2 , the small arc tangents L 1 and L 2 and the corresponding circumferential angle ⁇ of the large arc;
  • Step 2 Construct an initial wheel wind resistance calculation model, build a wheel wind resistance calculation model based on the above-mentioned three-dimensional model of the wheel, and conduct simulation analysis to obtain the initial wheel aerodynamic drag coefficient value;
  • Step 3 Design the test plan. On the premise that the wheel spoke opening area remains unchanged, select the wheel opening profile shape as the variable, set the value range of the variable, and use the aerodynamic resistance coefficient of the wheel as the target response value; use statistical sampling
  • the experimental design method is used to design the wheel spoke opening profile shape, conduct wheel wind resistance simulation analysis on the models under different spoke opening profile shapes, and obtain the aerodynamic drag coefficient value under each spoke opening profile shape;
  • Step 4 Construct the functional relationship between the wheel spoke opening profile shape and its aerodynamic drag coefficient value based on the test data in step 3, and verify its accuracy.
  • Step 5 Use the optimization algorithm to obtain the wheel spoke opening profile shape when the aerodynamic drag coefficient value is the smallest.
  • step one a three-dimensional model of the initial wheel is constructed, and the initial wheel opening ratio is selected to be between 20% and 80%.
  • the wheel wind resistance calculation model construction method in the second step is a fluid dynamics calculation method, a three-dimensional virtual wind tunnel model of the wheel and the road is constructed, and the three-dimensional model is imported into the meshing software to generate the fluid domain grid and boundary around the wheel.
  • Layer mesh use computational fluid dynamics analysis software to set the velocity inlet, pressure outlet and wheel wall motion mode to achieve simulation analysis of wheel aerodynamic wind resistance.
  • the value range of the wheel spoke opening profile shape in step three is that the small arc radius R 1 is 5.41 mm ⁇ 10.46 mm, the large arc radius R 2 is 41.58 mm ⁇ 58.68 mm, and the corresponding circumferential angle of the large arc is ⁇ is 15° to 30°, and the lengths of the small arc tangents L 1 and L 2 are equal, 27.12mm to 46.83mm.
  • the statistical sampling test design method is the optimal Latin hypercube test design method; through statistical design and data analysis, the key parameters that have a significant impact on the aerodynamic drag coefficient value are screened out by the wheel spoke opening profile shape.
  • Latin hypercube is a stratified sampling method. For multiple random variable inputs, general stratified sampling needs to convert the input sample space into N regions with equal probability. This It is very difficult to operate. Latin Hypercube uses a multidimensional stratified sampling method, which works as follows:
  • Latin hypercube sampling Compared with simple stratified sampling, the biggest advantage of Latin hypercube sampling is that sampling numbers of any size can be easily generated. But from a spatial distribution perspective, as the number of points decreases, the chance of missing certain areas of the design space increases.
  • the optimal super Latin cubic design makes all test points evenly distributed in the design space as much as possible, and has very good space filling and balance.
  • step four is to construct a regression function based on the wheel spoke opening profile shape and the aerodynamic drag coefficient value, and the regression function used is the RBF approximation model.
  • Radial basis RBF Radial Basis Functions
  • x 1 ,...,x N represent the wheel aerodynamic drag coefficient values under different schemes obtained from the optimal super Latin cubic test design, and the subscripts represent the 1st to Nth values in the optimal super Latin cubic test design.
  • Sample, ⁇ represents the space where the wheel aerodynamic drag coefficient values under different schemes are located.
  • g i ⁇ g( ⁇ xx j ⁇ c ) is the basis function
  • ⁇ xx j ⁇ is the Euclidean distance, also called the Euclidean norm
  • the method for verifying the accuracy in step 4 is to use the coefficient of determination R 2 to test the accuracy of the RBF approximate model after linear regression of the model. The closer the coefficient of determination is to 1, the higher the accuracy of the model, and compare the predicted value with the actual value. , verify its effectiveness.
  • the optimization algorithm in step five is an adaptive simulated annealing optimization method.
  • the principle of this algorithm is to use the similarity between the cooling process of solid substances in physics and general combinatorial optimization problems as the starting point, and use solid annealing simulation to solve the combinatorial optimization problem:
  • the energy function is defined as:
  • x i is the gray value of the original image
  • x' i is the predicted output gray value
  • N is the number of imaging points in the output image.
  • Step2 Randomly generate a new solution x' and calculate the energy increment ⁇ E.
  • ⁇ E E(x')-E(x)
  • Step3 Accept the new solution according to the Metropolis criterion:
  • T is the current temperature, and its value is related to the initial temperature T 0 and the cooling rate ⁇ .
  • Step4 Reduce the temperature according to the temperature attenuation function, and determine whether the iteration termination condition is reached. If so, stop the iteration; otherwise, go to Step 3.
  • Tk is the temperature before cooling
  • Tk +1 is the temperature after cooling
  • ⁇ is a positive number less than 1
  • the simulated annealing algorithm analogizes the combinatorial optimization problem to the heat balance problem in statistical mechanics through the simulated annealing process.
  • the objective function is evaluated every step forward from the initial point. As long as the function value decreases, the new design point is Accept it and iterate until you find the sweet spot.
  • the algorithm includes two inner and outer loops. For the inner loop, it can ensure that the samples in the solution space are fully searched and iterated at each temperature; while the outer loop can ensure that the algorithm is The temperature continues to decrease during the process, and finally reaches an equilibrium and stable state.
  • the present invention can effectively avoid blindness problems in the wheel spoke opening profile design, thereby shortening the design cycle and improving efficiency. It also improves the aerodynamic characteristics of the wheel area and achieves the purpose of reducing vehicle resistance;
  • the RBF network approximate model is selected to verify the accuracy of the model.
  • the RBF network approximate model has a strong ability to approximate complex nonlinear functions; it does not require mathematical assumptions and has black box characteristics; it has fast learning speed and excellent generalization ability; Strong fault tolerance function, even if the sample contains "noise" input, it will not affect the overall performance of the network, etc. It greatly improves the efficiency of model accuracy verification, further reduces blindness in the research and development process, and shortens the design cycle.
  • Figure 1 is a design flow chart of the present invention.
  • Figure 2 is (a) a schematic diagram of the wheel spoke opening variables according to the present invention; (b) a schematic diagram of a single spoke opening.
  • Figure 3 is a schematic diagram of the virtual wind tunnel model of the wheel of the present invention.
  • FIG 4 is a schematic structural diagram of the experiment (a) Scheme 7 (b) Scheme 11 (c) Scheme 16 of the Latin hypercube design of the present invention.
  • Figure 5 is a schematic diagram of the prediction accuracy of the RBF approximation model of the present invention.
  • Figure 6 is a schematic diagram of the RBF model of C d and one of the design variables R 1 of the present invention.
  • Figure 7 is a schematic diagram of the RBF model of C d and one of the design variables R 1 of the present invention.
  • Figure 8 is a schematic diagram of the RBF model of C d and one of the design variables R 2 of the present invention.
  • Figure 9 is a schematic diagram of the RBF model of C d and one of the design variables R 2 of the present invention.
  • Figure 10 is a schematic diagram of the iterative steps of the optimization process of the adaptive simulation optimization algorithm of the present invention.
  • Figure 11 is a schematic diagram of the contribution of different design variables of the wheel spoke of the present invention to C d .
  • Figure 12 is a schematic diagram comparing the spoke opening shapes before and after optimization according to the present invention.
  • Figure 13 is a schematic diagram of the longitudinal plane pressure of the front and rear wheels optimized according to the present invention.
  • a method for reducing the wheel spoke opening profile shape that reduces wheel wind resistance includes the following steps:
  • Step 1 Establish an initial wheel model, and draw a three-dimensional model of the wheel based on the selected number of wheel spokes and the initial value of the wheel spoke opening profile shape; the spoke opening ratio of commonly used vehicles on the market is concentrated in the range of 20%-80%.
  • the opening area ratio of the five-spoke wheel in the secondary wheel is 54%, and the five-spoke vehicle is selected as shown in Figure 2(a).
  • the initial values of a single spoke hole of the five-spoke wheel are: the circumferential angle ⁇ is 22.5°, the small arc radius R1 is 8mm, and the large arc radius R 2 is 55mm, and the length of the small arc tangents L 1 and L 2 is 35.69mm.
  • the design variables of the spoke opening are parameterized through the three-dimensional modeling software Solidworks.
  • Step 2 Construct an initial wheel wind resistance calculation model, build a wheel wind resistance calculation model based on the above-mentioned three-dimensional model of the wheel, and conduct simulation analysis to obtain the initial wheel aerodynamic drag coefficient value;
  • This calculation process is divided into two processes: steady calculation and unsteady calculation.
  • the steady calculation uses the SST k- ⁇ model to solve the model steadily, and the convergence residual is 0.0001 after 4000 iterations; then the steady calculation results are used as the initial flow field for the unsteady calculation; the unsteady calculation uses the SIMLEC algorithm to couple the pressure and velocity fields.
  • the turbulence model is adjusted to the DES model, the discrete format is the second-order upwind format, the calculation time step is 1 ⁇ 10 -3 s, the unit time step is iterated 5 times, the unsteady calculation time is 2 s, and the total calculation time step is 10,000 steps.
  • the simulation calculation is based on the commercial fluid calculation software STAR-CCM+.
  • Step 3 Design the test plan, using the wheel spoke opening profile shape as the variable, set the value range of the variable, and use the aerodynamic resistance coefficient of the wheel as the target response value; use the statistical sampling test design method to determine the wheel spoke opening profile shape Carry out scheme design, conduct wheel wind resistance simulation analysis on models with different spoke opening contour shapes, and obtain aerodynamic drag coefficient values under each spoke opening contour shape;
  • the value range of the circumferential angle ⁇ corresponding to the large arc of each spoke opening is: [15 ° ,30 ° ], so the value range of the large arc radius R2 is: R2 ⁇ [41.5824,58.6799]mm.
  • the optimal super Latin cubic test method was used for design, and the corresponding values of L 1 , L 2 and R 1 were solved using the above formulas. A total of 20 groups of test plans were designed, as shown in Table 2. .
  • Step 4 Construct the functional relationship between the wheel spoke opening profile shape and its aerodynamic drag coefficient value based on the test data in step 3, and verify its accuracy.
  • the RBF approximate model is a spatial prediction method based on minimizing the average error of the weighted sum of sampled values. Error analysis is usually used to evaluate the fitting accuracy of the approximate model.
  • the fitting coefficient R 2 is a commonly used error evaluation index in statistics. The closer the value is to 1, the better the fit.
  • Figure 5 shows the prediction accuracy of the constructed RBF model. It can be seen from the figure that the simulation value and predicted value of C d have a good fitting effect, which means that the prediction accuracy of the selected approximate model is very high and meets the requirements. .
  • FIG 6-9 shows the RBF model of C d and two of the design variables respectively.
  • ⁇ and R 1 have the greatest impact on the C d value.
  • C d have reached the maximum value
  • Figure 7 when ⁇ is changed to L 1 to study the relationship between different variables, we explore the topological relationship between the three and find that the impact on C d when L 1 changes in the figure is very small, indicating that compared with the R 1 variable, L 1 has a smaller impact on the results; in Figure 8, ⁇ is changed to R 2 , As R 2 increases, the impact on the response is still small; comprehensively considered, the corresponding circumferential angle ⁇ of the large arc of each spoke opening and the small arc radius R 1 are both positively correlated with C d , C d increases with the increase of ⁇ and R 1.
  • the large arc radius R 2 and small arc tangents L 1 and L 2 have little influence on C d .
  • Step 5 Use the optimization algorithm to obtain the wheel spoke opening profile shape when the aerodynamic drag coefficient value is the smallest.
  • the principle of this algorithm is to use the similarity between the cooling process of solid substances in physics and general combinatorial optimization problems as the starting point, and use solid annealing simulation to solve the combinatorial optimization problem:
  • the energy function is defined as:
  • x i is the gray value of the original image
  • x' i is the predicted output gray value
  • N is the number of imaging points in the output image.
  • Step3 Accept the new solution according to the Metropolis criterion:
  • T is the current temperature, and its value is related to the initial temperature T 0 and the cooling rate ⁇ .
  • Step4 Reduce the temperature according to the temperature attenuation function, and determine whether the iteration termination condition is reached. If so, stop the iteration; otherwise, go to Step 3.
  • Tk is the temperature before cooling
  • Tk +1 is the temperature after cooling
  • ⁇ is a positive number less than 1
  • the adaptive simulated annealing optimization method is used to optimize the design of the optimization target, and the wheel spoke opening profile shape when the aerodynamic resistance is minimized is used as the optimal wheel spoke opening profile shape arrangement.
  • Figure 13 shows the pressure distribution in the longitudinal plane of the optimized front and rear wheels. Most of the aerodynamic resistance of the wheel comes from the pressure difference resistance between the front and rear of the wheel. As can be seen in the figure, there is almost no change in the pressure on the front of the wheel before and after optimization, but there is a certain increase in the pressure at the rear of the wheel after optimization, which results in a reduction in the pressure difference across the wheel. Small, thereby reducing the aerodynamic resistance of the wheel to a certain extent.
  • Step 1 is used to perform wind resistance simulation analysis on the optimized wheel.
  • the analysis results before and after optimization are shown in Table 2. It can be seen from Table 3 that the optimized spoke shape significantly improves the aerodynamic performance of the wheel, and its aerodynamic drag coefficient is reduced by 5.7% compared to before optimization, thereby reducing the wind resistance of the wheel.

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Abstract

本发明公开了一种降低车轮风阻的轮辐开口轮廓形状的方法，包括：步骤一、建立初始的车轮轮辐模型；步骤二、构建初始的车轮计算模型；步骤三、设计实验方案；步骤四、根据步骤三中的试验数据构建车轮轮辐开口轮廓形状与其气动阻力系数间的函数关系，并对其精度进行验证；步骤五、采用优化算法获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。有益效果：本发明以轮辐开口轮廓形状为切入点提出了降低车轮风阻的全新方法，有效避免在车轮轮辐开口轮廓形状设计中存在的盲目性问题，进而缩短设计周期，提升效率，同时提高了汽车燃油经济性，改善了车轮附近的压力脉动，对指导车轮轮辐开口轮廓形状设计进而降低汽车风阻提高燃油经济性具有重要的意义。

Description

一种降低车轮风阻的轮辐开口轮廓形状的方法 技术领域
本发明涉及一种降低轮辐开口轮廓形状的优化方法，特别涉及一种降低车轮风阻的轮辐开口轮廓形状的方法，属于车辆工程技术领域。
背景技术
近年来全球能源危机加剧，而汽车保有量仍在持续增加，汽车对能源消耗与日俱增，政府和消费者对汽车油耗日益重视，对汽车燃油经济性的要求比以往更加严格。据报道，汽车气动阻力降低10％，可以减少2％-3％的燃油消耗。由于气动阻力与车速的二次方成正比，改善汽车的气动特性能显著降低油耗，这在高速行驶时尤其重要。当汽车速度达到60km/h时，克服气动阻力所需功率占汽车克服行驶阻力所需功率的一半。
在汽车行驶过程中，车轮区域对汽车气动阻力的贡献高达25-30％。车轮区域的流场受到汽车侧面和车底的前方来流以及发动机舱内流场的共同影响，与车身、车底结构和地面之间产生比较强烈的相互干扰，并且车轮旋转还会对这一区域的流场产生能量输入，使车轮区域的流场结构更为复杂。已有的研究也表明汽车车轮轮辋的开口形状不同会对车轮气动阻力以及汽车气动阻力产生直接的影响。然而，目前对车轮区域的流动现象和流动规律的认知较为局限，从而使得车轮区域的气动阻力降低对整车气动阻力的改善具有很强的潜在优化空间。因此，掌握车轮区域流场特性，提出车轮区域针对性的减阻方法，从而达到降低汽车气动阻力的目的，这对降低燃油消耗具有重要意义。
车轮辐板上开孔的布置方式对气动特性有很大的影响：在总开口面积相同的情况下，将开口数适量增大有利于气动特性的改善；随着总开口面积的增加，车轮本身的阻力系数均在一定程度上呈现不规则变化。因此，以车轮轮辐作为优化对象，在不改变车轮开口面积的前提下，以降低单个车轮的气动阻力为优化目标，选取单个轮辐孔的小圆弧半径R1、大圆弧半径R2、小圆弧切线L1和L2以及对应的圆周角α为设计变量。综合采用最优超拉丁立方设计、RBF近似模型以及自适应模拟退火算法(ASA)对轮辐孔进行优化，获得了最优的轮辐形状。
发明内容
发明目的：针对现有技术中存在的不足，本发明提供了降低车轮风阻的轮辐开口轮廓形状的方法，所述方法以降低单个车轮的气动阻力为优化目标，能够有效避免在车轮轮辐 开口轮廓设计过程中存在的盲目性问题，可有效降低车轮轮辐开口轮廓设计周期，进而提升改进效率，与此同时也能够改善车轮区域的气动特性，达到降低车辆阻力的目的。
技术方案：一种降低车轮风阻的轮辐开口轮廓形状的方法，包括以下步骤：
步骤一、建立初始车轮模型，根据所选车轮轮辐数量与车轮轮辐开口轮廓形状的初始值绘制车轮的三维模型；所述轮辐开口轮廓形状参数包括小圆弧半径R1、大圆弧半径R2、小圆弧切线L1和L2以及大圆弧对应的圆周角α；
步骤二、构建初始车轮风阻计算模型，根据上述车轮的三维模型构建车轮的风阻计算模型，并进行仿真分析，获得初始车轮的气动阻力系数值；
步骤三、设计试验方案，以车轮轮辐开口面积不变为前提，选择车轮开口轮廓形状为变量，设定变量的取值范围，以车轮所受的气动阻力系数作为目标响应值；通过统计学抽样试验设计方法对车轮轮辐开口轮廓形状进行方案设计，对不同轮辐开口轮廓形状下的模型进行车轮风阻仿真分析，获取各轮辐开口轮廓形状下的气动阻力系数值；
步骤四、根据步骤三中的试验数据构建车轮轮辐开口轮廓形状与其气动阻力系数值间的函数关系，并对其精度进行验证。
步骤五、采用优化算法获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。
进一步，所述步骤一中构建初始车轮的三维模型，选取的初始车轮开孔比在20％～80％之间。
进一步，所述步骤二中车轮风阻计算模型构建方法为流体动力学的计算方法，构建车轮与路面虚拟风洞三维模型，将三维模型导入网格划分软件，生成车轮周围的流体域网格和边界层网格，利用计算流体动力学分析软件设置速度入口、压力出口和车轮壁面运动方式，实现车轮气动风阻的仿真分析。
进一步，所述步骤三中车轮轮辐开口轮廓形状的取值范围是小圆弧半径R1为5.41mm～10.46mm，大圆弧半径R2为41.58mm～58.68mm，大圆弧对应的圆周角α为15°～30°，小圆弧切线L1和L2长度相等，均为27.12mm～46.83mm。
进一步，所述统计学抽样试验设计方法为最优拉丁超立方试验设计方法；通过统计学设计和数据分析，筛选出车轮轮辐开口轮廓形状对气动阻力系数值有显著影响的关键参数。所述的最优超拉丁立方设计，拉丁超立方是一种分层抽样方法，对于有多个随机变量输入，一般的分层抽样需要将输入的样本空间等概率地转化为N个区域，这操作起来是很困难的。拉丁超立方用一种多维分层抽样方法，其工作原理如下：
(1)定义参与计算机运行的抽样数目N；
(2)把每一次输入等概率得分成N，且有：
P(xin<x<xi(n+1))＝1/N
(3)对每一列仅抽取一个样本，各列中所抽取样本位置是随机的。
相对于单纯的分层抽样，拉丁超立方抽样的最大优势就在于任何大小的抽样数目都能容易地产生。但是从空间分布的角度来讲，随着点的数量减少，遗漏设计空间的某些区域的机会也会增加。最优超拉丁立方设计使所有的试验点尽量均匀地分布在设计空间，具有非常好的空间填充性和均衡性。
进一步，所述步骤四中的函数关系为根据车轮轮辐开口轮廓形状和气动阻力系数值构建回归函数，所使用的回归函数为RBF近似模型。
选用RBF模型的的优点包括：
1.很强的逼近复杂非线性函数的能力。
2.无须数学假设，具有黑箱特点。
3.学习速度快，具有极好的泛化能力。
4.较强的容错功能，即使样本中含有“噪声”输入，也不影响网络的整体性能。
径向基RBF(Radial Basis Functions)网络：以待测点与样本点之间的欧几里德距离为自变量，即假设代表一组输入向量，
是基函数。其中‖x-xj‖，是欧几里德距离：
(x-xj)T(x-xj)，且0.2≤c≤3
式中，x1,...,xN表示为最优超拉丁立方试验设计得到的不同方案下的车轮气动阻力系数值，下标表示最优超拉丁立方试验设计中的第1～N个样本，Ω表示不同方案下的车轮气动阻力系数值所处的空间。
gi≡g(‖x-xj‖c)是基函数，‖x-xj‖是欧几里德距离，也称欧几里得范数，下标j表示第j个样本，j＝1...N。
进一步，所述步骤四中的精度进行验证方法为对模型线性回归后，采用决定系数R2检验RBF近似模型的精度，决定系数越接近1说明模型精度越高，并将预测值与实际值对比，验证其有效性。
进一步，其特征在于：
所述决定系数R2的表达式为：
式中，n为检验模型精度的数据点数量；为第i个响应的近似模型预测值；yi为第i个响应的仿真值；为平均值。
进一步，其特征在于：所述步骤五中的优化算法为自适应模拟退火优化方法，通过对车轮轮辐开口轮廓形状进行非线性优化设计，获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。
进一步，其特征在于：该算法原理在于将物理中固体物质的降温过程与一般组合优化问题之间的相似性作为出发点，用固体退火模拟解决组合优化问题：
Step1：初始化任选初始解，设定初始温度T0，终止温度Tf，令迭代指标k＝0，计算能量初值E0能量函数定义为:
式中:xi是原始图像灰度值；x'i是预测输出灰度值；N是输出图像成像点的数目。
Step2：随机产生新解x'，计算能量增量ΔE。
ΔE＝E(x')－E(x)
Step3：按Metropolis准则接受新解:
式中:T为当前温度，其值与初始温度T0以及降温速率α有关。
Step4：:按温度衰减函数降低温度，判断是否达到迭代终止条件，若是，停止迭代；否则，转Step3温度衰减函数为:
Tk+1＝αTk
式中:Tk为降温前的温度；Tk+1为降温后的温度，α为小于1的正数
模拟退火算法通过模拟退火过程，将组合优化问题与统计力学中的热平衡问题类比，从初始点开始每前进一步就对目标函数进行一次评估，只要函数值下降，新的设计点就被 接受，反复进行，直到找到最优点。添加自适应后，该算法包括内部和外部两个循环，对于内部循环而言，它能保证在每个温度下对解空间内的样本执行充分的搜索和迭代；而外部循环则可以确保算法在进程中温度不断降低的趋势，最终达到平衡稳定状态。
有益效果：本发明能有效避免在车轮轮辐开口轮廓设计中存在的盲目性问题，进而缩短设计周期，提升效率，对于车轮区域的气动特性的改进也起到了改善作用，达到降低车辆阻力的目的；本发明中选用RBF网络近似模型对模型精度进行验证，RBF网络近似模型具有很强的逼近复杂非线性函数的能力；无须数学假设，具有黑箱特点；学习速度快，具有极好的泛化能力；较强的容错功能，即使样本中含有“噪声”输入，也不影响网络的整体性能等优点，对模型精度验证的效率有很大的提升，进一步减少研发过程中的盲目性，缩短设计周期。
附图说明
图1为本发明的设计流程图。
图2为本发明(a)车轮轮辐开口变量示意图(b)单个轮辐开口示意图。
图3为本发明车轮虚拟风洞模型示意图。
图4为本发明拉丁超立方设计的试验(a)方案7(b)方案11(c)方案16的结构示意图。
图5为本发明RBF近似模型的预测精度示意图。
图6为本发明Cd与其中一个设计变量R1的RBF模型示意图。
图7为本发明Cd与其中一个设计变量R1的RBF模型示意图。
图8为本发明Cd与其中一个设计变量R2的RBF模型示意图。
图9为本发明Cd与其中一个设计变量R2的RBF模型示意图。
图10为本发明自适应模拟优化算法优化过程迭代步示意图。
图11为本发明轮辐不同设计变量对Cd的贡献度的示意图。
图12为本发明优化前后轮辐开口形状对比示意图。
图13为本发明优化前后车轮纵向平面压力示意。
下面结合附图和具体实施例对本发明作进一步说明。
如图1所示，一种降低车轮风阻的轮辐开口轮廓形状的方法，包括以下步骤：
步骤一、建立初始车轮模型，根据所选车轮轮辐数量与车轮轮辐开口轮廓形状的初始值绘制车轮的三维模型；市面上常用车车轮辐开孔比集中在20％-80％的范围内，本次车轮中五轮辐车轮开孔面积比为54％，选定如图2(a)所示的五轮辐车。如图2(b)所示五轮辐车轮的单个轮辐孔初始值分别为：圆周角α为22.5°，小圆弧半径R1为8mm，大圆弧半径 R2为55mm，小圆弧切线L1和L2长度为35.69mm，通过三维建模软件Solidworks对轮辐开口的设计变量进行参数化。
步骤二、构建初始车轮风阻计算模型，根据上述车轮的三维模型构建车轮的风阻计算模型，并进行仿真分析，获得初始车轮的气动阻力系数值；
在车轮模型的基础上，建立如图3所示的车轮-路面虚拟风洞模型。边界条件设置：计算域入口-速度入口，V＝40m/s；计算域出口-压力出口，0Pa；计算域侧面及顶面-对称平面；车身与立柱-固定壁面，无滑移；计算域地面-移动地面，V＝40m/s。由于车轮所处外流场视作三维、定常、等温、恒压，不可压缩的大气环境中，物理场参数为：温度-20℃；压强-101325Pa；粘度-1.7894e-6Pa·s；密度-1.225kg·m-3。边界层网格设置参照如下表1；
表1计算域网格尺寸
本次计算过程分为定常计算和非定常计算两个过程。定常计算采用SST k-ω模型对模型进行定常求解，迭代4000步后满足收敛残差0.0001；之后将定常计算结果作为非定常计算的初始流场；非定常计算采用SIMLEC算法耦合压力与速度场，湍流模型调整为DES模型，离散格式为二阶迎风格式，计算时间步长为1×10-3s，单位时间步内迭代5次，非定常计算时长为2s，总计算时间步为10000步。仿真计算基于商业流体计算软件STAR-CCM+。
步骤三、设计试验方案，以车轮轮辐开口轮廓形状为变量，设定变量的取值范围，以车轮所受的气动阻力系数作为目标响应值；通过统计学抽样试验设计方法对车轮轮辐开口轮廓形状进行方案设计，对不同轮辐开口轮廓形状下的模型进行车轮风阻仿真分析，获取各轮辐开口轮廓形状下的气动阻力系数值；
在确保单个开孔面积不变的情况下，固定车轮半径R为75mm，以大圆弧半径R2作为变量进行设计，其余参数在Matlab中进行求解，求解公式见式：

R1＝20.91·sin(α)
L1＝L2＝R2-20.91·cos(α)
每个轮辐开孔的大圆弧对应圆周角α取值范围为：[15°,30°]，因此大圆弧半径R2的取值范围为：R2∈[41.5824,58.6799]mm。根据变量的变化范围，采用最优超拉丁立方试验方法进行设计，并采用上述公式将L1、L2以及R1的相应值进行求解，共设计出20组试验方案，具体如表2所示。
表2试验方案和计算结果
以气动阻力作为目标响应值。为探寻提升车轮风阻性能的最优轮辐开口轮廓形状，选择合理的试验设计方法尤其重要。试验设计的目的是在整个设计空间中选取有限个样本点，令其最大程度上反应出整个空间的信息。根据表2中的最优超拉丁立方试验方法设计得到的参数建立三维模型，其中的典型方案如图4所示。从图中可以看到，不同方案之间的轮辐开孔形状差别比较大，这就导致了车轮之间气动阻力系数有一定的差异。
步骤四、根据步骤三中的试验数据构建车轮轮辐开口轮廓形状与其气动阻力系数值间的函数关系，并对其精度进行验证。
RBF近似模型是一种基于最小化采样值加权和的平均误差的空间预测方法，通常用误差分析来评价近似模型的拟合精度，拟合系数R2是统计学上常用的误差评价指标，其值越接近1，拟合效果越好。如图5所示是构建的RBF模型的预测精度，从图中可以看到，Cd的仿真值和预测值的拟合效果很好，这意味着选用的近似模型预测精度很高，符合要求。
图6-9所示分别为Cd与其中两个设计变量的RBF模型；由图6所示α与R1对Cd值的影响最大，两个变量分别增大到最大值时，Cd均达到了最大值；而在图7中，当将α改成L1，来研究不同变量的关系时，探究此三者之间的拓扑关系发现，图中L1变化时对Cd的影响很小，说明相较于R1变量，L1对结果的影响更小；在图8中，是将α改成R2， 随着R2的增大，对响应量的影响变化幅度依旧不大；综合考虑来讲，每个轮辐开孔的大圆弧对应圆周角α和小圆弧半径R1均与Cd呈正相关，Cd随着α和R1的增大而增大，大圆弧半径R2和小圆弧切线L1、L2对Cd的影响很小。
步骤五、采用优化算法获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。
其特征在于：该算法原理在于将物理中固体物质的降温过程与一般组合优化问题之间的相似性作为出发点，用固体退火模拟解决组合优化问题：
Step1：初始化，任选初始解，设定初始温度T0，终止温度Tf，令迭代指标k＝0，计算能量初值E0能量函数定义为:
式中:xi是原始图像灰度值；x'i是预测输出灰度值；N是输出图像成像点的数目。
Step2：随机产生新解x'，计算能量增量ΔE；
ΔE＝E(x')－E(x)
Step3：按Metropolis准则接受新解:
式中:T为当前温度，其值与初始温度T0以及降温速率α有关。
Step4：:按温度衰减函数降低温度，判断是否达到迭代终止条件，若是，停止迭代；否则，转Step3温度衰减函数为:
Tk+1＝αTk
式中:Tk为降温前的温度；Tk+1为降温后的温度，α为小于1的正数
从步骤五中预测到近似模型的精度，结果符合我们的要求。采用自适应的模拟退火优化算法，其适用范围广，对初始条件要求不高，且收敛速度快，能够获得全部最优解。以气动阻力系数为优化目标进行优化，迭代382次获得一组最优解，迭代过程如图10所示。图11显示了不同设计变量对Cd的贡献度，从图中可以看到，圆周角α和小圆弧半径R1对Cd值有明显影响，其余设计变量对气动特性的影响可以忽略不计。
利用自适应模拟退火优化方法对优化目标进行优化设计，将气动阻力最小时的车轮轮辐开口轮廓形状作为最优的车轮轮辐开口轮廓形状布置形式，优化后的车轮轮辐开口轮廓 各结构设计参数L1、L2＝33.9051mm、R1＝8.4729mm、R2＝53.0161mm、优化后的车轮轮辐开口轮廓形状布置形式如图12所示。
接下来对优化前后车轮的气动特性进行分析。图13是优化前后车轮纵向平面内的压力分布。车轮的气动阻力大部分来自于车轮前后的压差阻力，在图中可以看到，优化前后车轮正面的压力几乎没有变化，而优化后车轮尾部的压力有一定提升，这导致车轮的压差减小，从而使车轮的气动阻力有一定的降低。
采用步骤1对优化后的车轮进行风阻仿真分析，优化前后的分析结果如表2所示。由表3可知，优化后的轮辐形状明显提升了车轮的气动性能，相比于优化前其气动阻力系数降低5.7％，从而降低了车轮的风阻。
表3优化前后的气动阻力系数对比
车轮轮辐开口轮廓各结构设计参数原始结构优化后小圆弧切线L1、L2＝33.9051mm小圆弧半径R1＝8mm，大圆弧半径R2＝55mm，圆周角α＝22.5°，气动阻力系数Cd＝0.87。所述实施例为本发明的优选的实施方式，但本发明并不限于上述实施方式，在不背离本发明的实质内容的情况下，本领域技术人员能够做出的任何显而易见的改进、替换或变型均属于本发明的保护范围。

Claims (10)

  1. 一种降低车轮风阻的轮辐开口轮廓形状的方法，其特征在于，包括以下步骤：
    步骤一、建立初始车轮模型，根据所选车轮轮辐数量与车轮轮辐开口轮廓形状的初始值绘制车轮的三维模型；所述轮辐开口轮廓形状参数包括小圆弧半径R1、大圆弧半径R2、小圆弧切线L1和L2以及大圆弧对应的圆周角α；
    步骤二、构建初始车轮风阻计算模型，根据上述车轮的三维模型构建车轮的风阻计算模型，并进行仿真分析，获得初始车轮的气动阻力系数值；
    步骤三、设计试验方案，以车轮轮辐开口面积不变为前提，选择车轮开口轮廓形状为变量，设定变量的取值范围，以车轮所受的气动阻力系数作为目标响应值；通过统计学抽样试验设计方法对车轮轮辐开口轮廓形状进行方案设计，对不同轮辐开口轮廓形状下的模型进行车轮风阻仿真分析，获取各轮辐开口轮廓形状下的气动阻力系数值；
    步骤四、根据步骤三中的试验数据构建车轮轮辐开口轮廓形状与其气动阻力系数值间的函数关系，并对其精度进行验证；
    步骤五、采用优化算法获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。
  2. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤一中构建初始车轮的三维模型，选取的初始车轮开孔比在20％～80％之间。
  3. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤二中车轮风阻计算模型构建方法为流体动力学的计算方法，构建车轮与路面虚拟风洞三维模型，将三维模型导入网格划分软件，生成车轮周围的流体域网格和边界层网格，利用计算流体动力学分析软件设置速度入口、压力出口和车轮壁面运动方式，实现车轮气动风阻的仿真分析。
  4. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤三中车轮轮辐开口轮廓形状的取值范围是小圆弧半径R1为5.41mm～10.46mm，大圆弧半径R2为41.58mm～58.68mm，大圆弧对应的圆周角α为15°～30°，小圆弧切线L1和L2长度相等，均为27.12mm～46.83mm。
  5. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述统计学抽样试验设计方法为拉丁超立方试验设计方法；通过统计学设计和数据分析，筛选出车轮轮辐开口轮廓形状对气动阻力系数值有显著影响的关键参数。
  6. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤四中的函数关系为根据车轮轮辐开口轮廓形状和气动阻力系数值构建回归函数，所使用的回归函数为RBF(Radial Basis Functions)的网络近似模型。
  7. 根据权利要求6所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤四中的精度验证方法为对模型线性回归后，采用决定系数R2检验RBF近似模型的精度，决定系数越接近1说明模型精度越高，并将预测值与实际值对比，验证其有效性。
  8. 根据权利要求7所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：
    所述决定系数R2的表达式为：
    式中，n为检验模型精度的数据点数量；为第i个响应的近似模型预测值；yi为第i个响应的仿真值；为平均值。
  9. 根据权利要求1所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：所述步骤五中的优化算法为自适应模拟退火优化方法，通过对车轮轮辐开口轮廓形状进行非线性优化设计，获得气动阻力系数值最小时的车轮轮辐开口轮廓形状。
  10. 根据权利要求9所述的降低车轮风阻的车轮轮辐开口轮廓形状的设计方法，其特征在于：该算法原理在于将物理中固体物质的降温过程与一般组合优化问题之间的相似性作为出发点，用固体退火模拟解决组合优化问题：
    Step1：初始化,任选初始解，设定初始温度T0，终止温度Tf，令迭代指标k＝0，计算能量初值E0能量函数定义为:
    式中:xi是原始图像灰度值；x'i是预测输出灰度值；N是输出图像成像点的数目；
    Step2：随机产生新解x'，计算能量增量ΔE；
    ΔE＝E(x')－E(x)
    Step3：按Metropolis准则接受新解:
    式中:T为当前温度，其值与初始温度T0以及降温速率α有关；
    Step4：:按温度衰减函数降低温度，判断是否达到迭代终止条件，若是，停止迭代；否则，转Step3温度衰减函数为:
    Tk+1＝αTk
    式中:Tk为降温前的温度；Tk+1为降温后的温度，α为小于1的正数。
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