WO2021129408A1 - 一种降低轮胎风阻的轮胎外轮廓结构的设计方法 - Google Patents

一种降低轮胎风阻的轮胎外轮廓结构的设计方法 Download PDF

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WO2021129408A1
WO2021129408A1 PCT/CN2020/135519 CN2020135519W WO2021129408A1 WO 2021129408 A1 WO2021129408 A1 WO 2021129408A1 CN 2020135519 W CN2020135519 W CN 2020135519W WO 2021129408 A1 WO2021129408 A1 WO 2021129408A1
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tire
outer contour
model
wind resistance
parameters
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PCT/CN2020/135519
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English (en)
French (fr)
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周海超
李慧云
翟辉辉
夏琦
姜震
陈青云
王国林
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江苏大学
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60C—VEHICLE TYRES; TYRE INFLATION; TYRE CHANGING; CONNECTING VALVES TO INFLATABLE ELASTIC BODIES IN GENERAL; DEVICES OR ARRANGEMENTS RELATED TO TYRES
    • B60C99/00—Subject matter not provided for in other groups of this subclass
    • B60C99/006—Computer aided tyre design or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • 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]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational 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
    • G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • 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

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  • the invention relates to a design method of a tire outer contour structure, in particular to a design method of a tire outer contour structure that can reduce the wind resistance of the tire, and belongs to the technical field of tires.
  • the design of the outer contour of the tire directly affects the movement of the surrounding airflow, which has a decisive influence on the aerodynamic resistance of the tire.
  • the design of the outer contour of the tire is also an important part of the design of a low-drag car. Therefore, it is particularly necessary to study the layout of the outer contour of the tire in depth to guide the structural design of the outer contour of the tire.
  • the present invention provides a tire outer contour structure design method that reduces the wind resistance of the tire, which can effectively avoid the blindness problem in the tire outer contour structure design process, It can effectively reduce the design cycle of the outer contour structure of the tire, thereby improving the efficiency of improvement, and at the same time, it can also improve the wind resistance of the tire and enhance the safety of the driver.
  • a design method of tire outer contour structure to reduce tire wind resistance including the following steps:
  • Step 1 the outer contour parameters of the tire model are divided into five parameters: upper sidewall height, running surface width, shoulder transition radius and tread arc radius. According to the five parameters of the selected tire model The initial values of the outer contour parameters draw the corresponding three-dimensional model of the initial tire;
  • Step 2 Build the initial tire wind resistance calculation model, build the tire wind resistance calculation model according to the above-mentioned three-dimensional model of the initial tire, and perform numerical simulation analysis to obtain the aerodynamic drag coefficient value of the initial tire;
  • Step 3 Design the test plan, take the tire profile parameters as variables, set the value range of the variables, and take the overall aerodynamic drag coefficient of the tire on the tread as the target response value; Proposal design of contour parameters, simulation analysis of tire wind resistance of models under different contour parameters, and obtain the aerodynamic drag coefficient value under each contour parameter;
  • Step 4 Construct the function relationship between the tire profile parameters and its aerodynamic drag coefficient value according to the test data in Step 3, and verify its accuracy;
  • Step 5 Use the optimization algorithm to obtain the tire contour parameters when the aerodynamic drag coefficient value is the smallest.
  • tire outer profile parameters in the first step include upper sidewall height, running surface width, shoulder transition radius and tread arc radius.
  • the method for constructing the tire wind resistance calculation model in the second step is a fluid dynamic calculation method, constructing a three-dimensional model of a virtual wind tunnel of the tire and road surface, and importing the three-dimensional model into the meshing software to generate the fluid domain grid and boundary around the tire Layer grid, using computational fluid dynamics analysis software to set the speed inlet, pressure outlet and tire wall motion mode to realize the simulation analysis of tire aerodynamic drag.
  • the initial tire profile parameters are used as a reference basis, and the value range of the tire profile parameters is 0.47-0.63 of the upper sidewall height of the cross-sectional height, and the driving surface width is 0.73 of the cross-sectional width of the half tire model. -0.9, the shoulder transition radius is 15-45mm, and the tread arc radius is set according to the selected tire model.
  • the statistical sampling test design method is a Latin hypercube test design method; through statistical design and data analysis, the key parameters that have a significant influence on the value of the aerodynamic drag coefficient are screened out through statistical design and data analysis.
  • the functional relationship in the step 4 is to construct a regression function according to the tire profile parameters and the aerodynamic drag coefficient value, and the regression function used is the Kriging approximation model.
  • the optimization algorithm in the step 5 is a simulated annealing optimization method, and the outer contour parameters of the tire when the aerodynamic drag coefficient value is the smallest are obtained by performing a nonlinear optimization design on the outer contour parameters of the tire.
  • the simulated annealing optimization algorithm first designs the temperature update function:
  • the state acceptance function in the algorithm is designed as:
  • E i is the energy function of the algorithm in the current solution state
  • E j is the energy function of the solution state to be accepted
  • the energy function is the value of the objective function
  • the solution to be accepted is generated in an interval search method.
  • the specific method is to search within the neighborhood of the current solution with a small step size.
  • the method for obtaining a new solution is:
  • X i is the current solution
  • X j is the new solution
  • l is the number of cycles
  • ⁇ is the search step size
  • Step 2 Calculate the energy function E(X i ) of the current solution; generate a new solution X j according to formula (4);
  • Step 3 Calculate the energy function E(X j ) of the new solution; and calculate the energy difference ⁇ E;
  • Step 7 Determine whether the temperature has reached the lowest temperature, if not, go to Step 2; otherwise, go to Step 8;
  • Step 8 End the calculation.
  • the present invention can effectively avoid the blindness problem in the design of the outer contour structure of the tire, thereby shortening the design cycle and improving the efficiency, and at the same time, it also plays a certain guiding role for the improvement of the tire wind resistance performance.
  • Figure 1 is a design flow chart of the present invention
  • Figure 2 is a schematic structural diagram of the outer contour of the tire of the present invention.
  • Fig. 3 is a schematic diagram of a virtual wind tunnel model of a tire of the present invention.
  • Figure 4 is a verification diagram of the Kriging approximation model of the present invention.
  • Figure 5 is a Kriging model of the aerodynamic drag coefficient C d, shoulder transition radius R and tread radius R 2 of the present invention
  • Fig. 6 is a Kriging model of the aerodynamic drag coefficient C d, the driving surface width L 2 and the upper sidewall height H of the present invention
  • Fig. 7 is a Kriging model of the aerodynamic drag coefficient C d, the tread radius R 1 and the upper sidewall height H of the present invention
  • Figure 8 is a Kriging model of the aerodynamic drag coefficient C d, shoulder transition radius R and upper sidewall height H of the present invention
  • Fig. 9 is a comparison diagram of the tire outer contour layout before and after optimization of the present invention.
  • Fig. 10 is a comparison diagram of the vortex scene flow field in the tire area before and after optimization of the present invention.
  • a method for designing a tire outer contour structure that reduces the wind resistance of the tire includes the following steps:
  • Step 1 Establish the initial tire model, and draw the three-dimensional model of the tire according to the initial value of the outer contour parameters of the selected tire model; this embodiment takes the tire of the 185/65R15 tire as an example, and its tread width is 185mm, and its half tire
  • the cross-section width of the model is 97.5mm, and the cross-section height of the tire is 121mm.
  • Step 2 Build the initial tire wind resistance calculation model, build the tire wind resistance calculation model according to the above-mentioned three-dimensional model of the tire, and perform simulation analysis to obtain the initial tire aerodynamic drag coefficient value;
  • a tire-road virtual wind tunnel model is established, as shown in Figure 3.
  • the fluid domain grid and boundary layer grid around the tire are divided, and the virtual wind tunnel model is analyzed and calculated using the computational fluid dynamics analysis software ANSYS Fluent double-precision solver to obtain the tire aerodynamic drag coefficient.
  • the inlet airflow velocity flows in the direction of the tire at a speed of 54km/h (15m/s).
  • the boundary conditions of the CFD calculation model are set as follows: the boundary velocity of the incoming flow at the inlet is set to 15m/s along the positive x direction; the outlet boundary condition is the pressure outlet, and the gauge pressure is 0; in order to reduce the calculation amount, a symmetric model is used and the center plane is set It is a symmetrical surface; the ground is a non-sliding wall surface with the same moving speed as the incoming flow along the positive x direction; the tire surface is a non-sliding wall surface and has a rotation angular velocity corresponding to the translational speed of the road surface (48.27rad /s); All other surfaces are sliding wall surfaces with zero shear force.
  • the steady-state pressure base solver is used to select the SST k-omega turbulence model for steady calculation, and the converged result is used as the initial flow field of the unsteady calculation.
  • the SIMPLEC method is used to simulate the coupling of pressure and velocity. All discrete methods are used
  • the second-order upwind style is used to improve the calculation accuracy.
  • the unsteady calculation adopts the separated vortex model (DES): first, a time step of 0.001 is used to calculate 2000 steps, which corresponds to a time of 2 seconds, which is the instantaneous fluctuation of the flow field tends to be stable. Then reduce the time step to 0.0001 and then calculate 10000 steps, monitor the aerodynamic resistance of the tire and take the time average value, and calculate the resistance coefficient based on the resistance.
  • DES separated vortex model
  • Step 3 Design the test plan, take the tire profile parameters as variables, set the value range of the variables, and take the overall aerodynamic drag coefficient of the tire on the tread as the target response value; Proposal design of contour parameters, simulation analysis of tire wind resistance of models under different contour parameters, and obtain the aerodynamic drag coefficient value under each contour parameter;
  • the section height of the tire is 121mm, and H is generally 0.47 ⁇ 0.63 of the section height, where H ⁇ [57.4, 76.5] mm, and the tread arc radius is R 1 ⁇ [400, 1200]mm, R 2 ⁇ [180,350]mm, driving width L 2 is generally 0.73 ⁇ 0.9 of the cross-sectional width of the half tire model, taking L 2 ⁇ [70,90]mm, the shoulder transition radius generally taking R ⁇ [15 ,45]mm, take the aerodynamic drag on the tread as the target response value.
  • H is generally 0.47 ⁇ 0.63 of the section height, where H ⁇ [57.4, 76.5] mm, and the tread arc radius is R 1 ⁇ [400, 1200]mm, R 2 ⁇ [180,350]mm, driving width L 2 is generally 0.73 ⁇ 0.9 of the cross-sectional width of the half tire model, taking L 2 ⁇ [70,90]mm, the shoulder transition radius generally taking R ⁇ [15 ,45]mm, take the aerodynamic drag on the tread as the
  • experimental design is to select a limited number of sample points in the entire design space so that it reflects the information of the entire space to the greatest extent.
  • One of them is the excellent Latin hypercube experimental design method. It is based on the Latin hypercube and uses optimization algorithms to make the sampling points evenly distributed in the entire design space to the greatest extent. It can describe the entire design with fewer test samples. space.
  • 24 sets of test plans were designed, and the models under different test plans were simulated and analyzed, and the aerodynamic resistance under each plan was obtained, as shown in Table 1.
  • Step 4 Construct the function relationship between the tire profile parameters and its aerodynamic drag coefficient value according to the test data in Step 3, and verify its accuracy;
  • the Kriging approximate model is used to construct the functional relationship between the tire outline structure design parameters and the aerodynamic resistance under the 24 sets of plans. Before the Kriging approximate model is used to analyze and calculate the relationship between the independent variables and the target response value, the determination coefficient R 2 is used to test the Kriging approximate model The precision of R 2 is:
  • the calculated coefficient of determination is 1, indicating that the built Kriging approximate model has high accuracy and can be used for subsequent optimization analysis.
  • the comparison between the response value predicted by the Kriging approximation model and the experimental value by the Fluent simulation is shown in Figure 4, which further verifies the accuracy of the Kriging approximation model.
  • Figures 5-8 show the Kriging model of C d and two of the design variables. It can be seen from the figure that H and L2 have the greatest impact on Cd, and the Cd change trend is complex, and the nonlinearity between the response and the variable is obvious, indicating that the interaction is large; the tread radius R1 and R2 are positively correlated with Cd, and Cd increases with As R1 and R2 increase, the transition radius R has almost no effect on Cd.
  • Step 5 Use the optimization algorithm to obtain the tire contour parameters when the aerodynamic drag coefficient value is the smallest.
  • the optimization design problem of tire outer contour structure parameters is described by an optimization mathematical model, which is transformed into a problem of finding the minimum skewness of aerodynamic drag coefficient.
  • the simulated annealing optimization algorithm is used to optimize the objective function nonlinearly.
  • the simulated annealing optimization algorithm first designs the temperature update function as shown in equation (2):
  • E i is the energy function of the algorithm in the current solution state
  • E j is the energy function of the solution state to be accepted.
  • the energy function is the objective function value.
  • the to-be-accepted solution is generated in an interval search method.
  • the specific method is to search in the neighborhood of the current solution with a small step size.
  • the new solution acquisition method is equation (4):
  • X i is the current solution
  • X j is the new solution
  • l is the number of cycles
  • ⁇ is the search step.
  • Step 2 Calculate the energy function E(X i ) of the current solution; generate a new solution X j according to formula (4);
  • Step 3 Calculate the energy function E(X j ) of the new solution; and calculate the energy difference ⁇ E;
  • Step 7 Determine whether the temperature has reached the lowest temperature, if not, go to Step 2; otherwise, go to Step 8;
  • Step 8 End the calculation.
  • the initial temperature in the simulated annealing optimization algorithm is 800°, and the lowest temperature is 0.05°.
  • the optimal combination of variables is obtained.
  • the simulated annealing optimization method is used to optimize the design of the optimization target.
  • the design parameters of the outer contour structure of the tire when the aerodynamic resistance is the minimum are taken as the optimal outer contour arrangement form.
  • the optimized layout of the outer contour of the tire is shown in FIG. 9.
  • Step 1 is used to perform wind resistance simulation analysis on the optimized tires, and the analysis results before and after optimization are shown in Table 2. It can be seen from Table 2 that the optimized tire can significantly reduce the aerodynamic drag experienced by the tread, and its aerodynamic drag coefficient is reduced by 16.92% compared with that before the optimization, thereby improving the aerodynamic drag performance of the tire.
  • Tire profile structure design parameters Original structure Optimized Upper sidewall height H 57.06 72.01 Driving surface width L 2 67.61 79.78 Shoulder transition radius R 35.87 30.65 Radius of tread arc R 1 817.391 434.783 Radius of tread arc R 2 327.83 298.26 Aerodynamic drag coefficient C d 0.402169833 0.33389854

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Abstract

一种降低轮胎风阻的轮胎外轮廓结构的设计方法，包括以下步骤：步骤一、建立初始轮胎模型，步骤二、构建初始轮胎风阻计算模型，步骤三、设计试验方案，步骤四、根据步骤三中的试验数据构建轮胎外轮廓参数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轮胎外轮廓参数。所述方法能有效避免在轮胎外轮廓结构设计中存在的盲目性问题，进而缩短设计周期，提升效率，与此同时对于轮胎风阻性能的改进也起到了一定的指导作用。

Description

一种降低轮胎风阻的轮胎外轮廓结构的设计方法 技术领域
本发明涉及一种轮胎外轮廓结构的设计方法，特别涉及一种可以降低轮胎风阻的轮胎外轮廓结构的设计方法，属于轮胎技术领域。
背景技术
随着全球气候变暖、能源短缺等问题日益加重，世界对环保的重视度不断提高，汽车作为出行工具必将成为节能减排的重要一环，各大车企急需努力提高车辆的能源效率以解决汽车环保问题。汽车在高速行驶过程中，气动阻力引起的燃油消耗率最高可占50％以上，而车轮引起的气动阻力占整车的25％左右。因此，如何形成高效的低风阻轮胎设计方法，实现轮胎风阻的减小，是摆在轮胎研究工作者和汽车开发者面前的一个重要问题。
运动汽车周围气流流过轮胎时，会产生气流分离，形成涡流，从而增加了轮胎的气动阻力。轮胎外轮廓设计直接影响着周围气流的运动，从而对轮胎气动阻力具有决定性的影响。相同型号的轮胎，由于其外轮廓设计的不同会导致汽车空气阻力系数超过0.009的变化，因此，轮胎外轮廓的设计也是低风阻汽车设计的重要环节。因此，深入研究轮胎外轮廓的布置形式进而指导轮胎外轮廓的结构设计则显得尤为必要。
而目前，国内外学者对于轮胎外轮廓结构的改进多集中于从众多试验方案中寻找性能最优的方案作为改进方案，或者仅仅是对轮胎外轮廓参数的单一设计参数影响进行分析，这就导致在改进过程中轮胎外轮廓结构参数的选取受限于所设计的试验方案，并存在很大的不确定性和盲目性，也会造成改进效率低等问题，因此当下亟需一种能够有效降低轮胎气动阻力的轮胎外轮廓设计方法。
发明内容
发明目的：针对现有技术中存在的不足，本发明提供了一种降低轮胎风阻的轮胎外轮廓结构的设计方法，所述方法能够有效避免在轮胎外轮廓结构设计过程中存在的盲目性问题，可有效降低轮胎外轮廓结构的设计周期，进而提升改进效率，与此同时也能够改善轮胎的风阻性能，提升驾驶人员的乘车安全。
技术方案：一种降低轮胎风阻的轮胎外轮廓结构的设计方法，包括以下步骤：
步骤一、依据所选轮胎的型号，将该型号轮胎的外轮廓参数划分为上胎侧高、行驶面宽、胎肩过渡半径和胎面弧半径等五个参数，根据所选轮胎型号的五个外轮廓参数的初始值绘制对应的初始轮胎的三维模型；
步骤二、构建初始轮胎风阻计算模型，根据上述初始轮胎的三维模型构建轮胎的风阻计算模型，并进行数值仿真分析，获得初始轮胎的气动阻力系数值；
步骤三、设计试验方案，以轮胎外轮廓参数为变量，设定变量的取值范围，以胎面处轮胎整体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轮胎外轮 廓参数进行方案设计，对不同外轮廓参数下的模型进行轮胎风阻仿真分析，获取各外轮廓参数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轮胎外轮廓参数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轮胎外轮廓参数。
进一步，所述步骤一中轮胎外轮廓参数包括上胎侧高、行驶面宽、胎肩过渡半径和胎面弧半径。
进一步，所述步骤二中轮胎风阻计算模型构建方法为流体动力学的计算方法，构建轮胎与路面虚拟风洞三维模型，将三维模型导入网格划分软件，生成轮胎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、压力出口和轮胎壁面运动方式，实现轮胎气动风阻的仿真分析。
进一步，所述步骤三中以初始轮胎外轮廓参数为参考基础，轮胎外轮廓参数的取值范围是上胎侧高为断面高的0.47-0.63，行驶面宽为半胎模型的断面宽的0.73-0.9，胎肩过渡半径为15-45mm,胎面弧半径根据所选轮胎的型号设置取值范围。
进一步，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，筛选出轮胎外轮廓参数对气动阻力系数值有显著影响的关键参数。
进一步，所述步骤四中的函数关系为根据轮胎外轮廓参数和气动阻力系数值构建回归函数，所使用的回归函数为Kriging近似模型。
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R 2检验Kriging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，所述决定系数R 2的表达式为：
Figure PCTCN2020135519-appb-000001
式中，n为检验模型精度的数据点数量；
Figure PCTCN2020135519-appb-000002
为第i个响应的近似模型预测值；y i为第i个响应的仿真值；
Figure PCTCN2020135519-appb-000003
为平均值。
进一步，所述步骤五中的优化算法为模拟退火优化方法，通过对轮胎外轮廓参数进行非线性优化设计，获得气动阻力系数值最小时的轮胎外轮廓参数。
所述模拟退火优化算法首先设计温度更新函数式：
t k＝t 0/ln(1+k)             (2)
式中为第k步时温度，t 0为初始温度；
算法中状态接受函数设计为：
Figure PCTCN2020135519-appb-000004
式中ΔE＝E i-E j,E i为算法处于当前解状态下的能量函数，E j为待接受解状态的能量函数；能量函数为目标函数值；
待接受解按区间搜索方式产生，具体方法为以小步长在当前解邻域内搜索，新解获得方法为：
X j＝X i+lΔ            (4)
式中X i为当前解，X j为新解，l为循环次数，Δ为搜索步长；
模拟退火优化算法具体步骤如下：
Step 1：设置算法参数，随机产生初始解X 0，将其设置为当前解X i＝X 0；
Step 2：计算当前解的能量函数E(X i)；按式(4)产生新解X j；
Step 3：计算新解的能量函数E(X j)；并计算能量差ΔE；
Step 4：根据ΔE按式(3)判断是否接受新解；若接受，更新当前解，即X i＝X j，转Step 6；否则转Step 5；
Step 5：判断是否达到搜索次数上限，若满足，转Step 8；否则，更新循环次数即l＝l+1，转Step 2；
Step 6：更新温度循环步数k＝k+1，按式(2)更新温度；
Step 7：判断温度是否到达最低温度，若未达到转Step 2；否则转Step 8；
Step 8：结束计算。
有益效果：本发明能有效避免在轮胎外轮廓结构设计中存在的盲目性问题，进而缩短设计周期，提升效率，与此同时对于轮胎风阻性能的改进也起到了一定的指导作用。
附图说明
图1为本发明的设计流程图；
图2为本发明轮胎外轮廓的结构示意图；
图3为本发明轮胎虚拟风洞模型的示意图；
图4为本发明Kriging近似模型的验证图；
图5为本发明气动阻力系数C d与胎肩过渡半径R和胎面半径R 2的Kriging模型；
图6为本发明气动阻力系数C d与行驶面宽L 2和上胎侧高H的Kriging模型；
图7为本发明气动阻力系数C d与胎面半径R 1和上胎侧高H的Kriging模型；
图8为本发明气动阻力系数C d与胎肩过渡半径R和上胎侧高H的Kriging模型；
图9为本发明优化前后的轮胎外轮廓布置形式对比图。
[根据细则91更正 05.02.2021]　
图10为本发明优化前后的轮胎区域涡景流场对比图。
具体实施方式
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，一种降低轮胎风阻的轮胎外轮廓结构的设计方法包括以下步骤：
步骤一、建立初始轮胎模型，根据所选轮胎型号的外轮廓参数的初始值绘制轮胎的三维模型；本实施例以185/65R15型轮胎的轮胎为例，其胎面宽度为185mm，其半胎模型的断面宽为97.5mm，轮胎断面高为121mm。依据初始轮胎模型确定出外轮廓参数为上胎侧高H＝57.06mm，行驶面宽L 2＝67.61mm，胎肩过渡半径R＝35.87mm，胎面弧半径R 1＝817.391mm，R 2＝327.83mm在CATIA中建立如图2所示的轮胎三维模型。
步骤二、构建初始轮胎风阻计算模型，根据上述轮胎的三维模型构建轮胎的风阻计算模型，并进行仿真分析，获得初始轮胎的气动阻力系数值；
在轮胎模型的基础上，建立轮胎-路面虚拟风洞模型，如图3所示。在HYPERMESH中划分轮胎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ANSYS Fluent双精度求解器对虚拟风洞模型进行分析计算，获得轮胎气动阻力系数。
为模拟轮胎54km/h的速度在路面上滚动的工况，入口气流速度迎着轮胎方向以54km/h(15m/s)的速度流过。
CFD计算模型边界条件设置如下：入口处来流的边界速度设为沿x正方向15m/s；出口边界条件为压力出口，表压为0；为减小计算量，采用对称模型，中心平面设置为对称面；地面为无滑动壁面，并带有沿着x正方向的、与来流相同的移动速度；轮胎表面为无滑动壁面，并有与路面平动速度相对应的转动角速度(48.27rad/s)；其余各个面均为零剪切力的滑动壁面。
设置好边界条件后进行CFD仿真计算。首先，采用稳态压力基求解器，选取SST k-omega湍流模型进行定常计算，将其收敛后的结果作为非定常计算的初始流场，采用SIMPLEC方法模拟压力和速度耦合，所有离散方法均采用二阶迎风格式以提高计算精度。非定常计算采用分离涡模型(DES)：首先采用时间步0.001计算2000步，对应时间2秒，是流场的瞬时波动趋于稳定。然后缩小时间步至0.0001再计算10000步，监测轮胎所受到的气动阻力取时间平均值，并根据阻力计算得阻力系数。
步骤三、设计试验方案，以轮胎外轮廓参数为变量，设定变量的取值范围，以胎面处轮胎整体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轮胎外轮廓参数进行方案设计，对不同外轮廓参数下的模型进行轮胎风阻仿真分析，获取各外轮廓参数下的气动阻力系数值；
对轮胎外轮廓各参数的上下限值进行设置，轮胎断面高为121mm，H一般为断面高的0.47～0.63，其中H∈[57.4,76.5]mm、胎面弧半径取R 1∈[400,1200]mm、R 2∈[180,350]mm、行驶宽L 2一般为半胎模型的断面宽的0.73～0.9，取L 2∈[70,90]mm、胎肩过渡半径一般取R∈[15,45]mm，以胎面处所受的气动阻力作为目标响应值。为探寻提升轮胎风阻性能的最优轮廓结构形式，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。优拉丁超立方试验设计方法就是其中一种，其以拉丁超立方为基础，利用优化算法使采样点在最大程度上均匀地分布在整个设计空间中，它能够以较少的试验样本描述整个设计空间。利用最优拉丁超立方试验设计方法设计了24组试验方案，对不同试验方案下的模型进行仿真分析，获取各个方案下的气动阻力，如表1所示。
表1 试验方案及性能分析结果
Figure PCTCN2020135519-appb-000005
Figure PCTCN2020135519-appb-000006
步骤四、根据步骤三中的试验数据构建轮胎外轮廓参数与其气动阻力系数值间的函数关系，并对其精度进行验证；
利用Kriging近似模型构建轮胎外轮廓结构设计参数与24组方案下气动阻力间的函数关系，在利用Kriging近似模型分析分析计算自变量对目标响应值的关系之前，采用决定系数R 2检验Kriging近似模型的精度，R 2的表达式为：
Figure PCTCN2020135519-appb-000007
式中，n为检验模型精度的数据点数量；
Figure PCTCN2020135519-appb-000008
为第i个响应的近似模型预测值；y i为第i个响应的仿真值；
Figure PCTCN2020135519-appb-000009
为平均值。
计算得到其决定系数为1，说明所建的Kriging近似模型精度较高，可用于后续优化分析。同时，利用Kriging近似模型预测的响应值与利用Fluent模拟仿真的试验值之间的对比如图4所示，进一步验证了Kriging近似模型的精度。
图5-8分别为C d与其中两个设计变量的Kriging模型。由图可见，H与L2对Cd影响最大，且Cd变化趋势复杂，响应量与变量之间非线性程度明显，说明交互作用大；胎面弧度半径R1和R2均与Cd呈正相关，Cd随着R1和R2的增大而增大，过渡半径R对Cd几乎没有影响。
步骤五、采用优化算法获得气动阻力系数值最小时的轮胎外轮廓参数。
将轮胎外轮廓结构参数优化设计问题采用优化数学模型进行描述，即转化为求气动阻力系数偏度值最小问题。采用模拟退火优化算法对目标函数进行非线性优化。所述模拟退火优化算法首先设计温度更新函数式(2)所示：
t k＝t 0/ln(1+k)            (2)
式中为第k步时温度，t 0为初始温度。算法中状态接受函数设计为式3：
Figure PCTCN2020135519-appb-000010
式中ΔE＝E i-E j,E i为算法处于当前解状态下的能量函数，E j为待接受解状态的能量函数。在本算法中能量函数为目标函数值。
待接受解按区间搜索方式产生，具体方法为以小步长在当前解邻域内搜索，新解获得方法为式(4)：
X j＝X i+lΔ          (4)
式中X i为当前解，X j为新解，l为循环次数，Δ为搜索步长。
模拟退火优化算法具体步骤如下：
Step 1:：设置算法参数，随机产生初始解X 0,将其设置为当前解X i＝X 0；
Step 2：计算当前解的能量函数E(X i)；按式(4)产生新解X j；
Step 3：计算新解的能量函数E(X j)；并计算能量差ΔE；
Step 4：根据ΔE按式(3)判断是否接受新解；若接受，更新当前解，即X i＝X j，转Step 6；否则转Step 5；
Step 5：判断是否达到搜索次数上限，若满足，转Step 8；否则，更新循环次数即l＝l+1，转Step 2。
Step 6：更新温度循环步数k＝k+1,按式(2)更新温度；
Step 7：判断温度是否到达最低温度，若未达到转Step 2；否则转Step 8；
Step 8：结束计算。
模拟退火优化算法中初始温度为800°，最低温度为0.05°。新解搜索步长Δ＝0.01，区间搜索最大循环次数为1000，能量函数为气动阻力系数。对于气动阻力系数的优化，经过1000次的迭代计算，得到最优的变量组合。利用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轮胎外轮廓结构设计参数作为最优的轮胎外轮廓布置形式，优化后的轮胎外轮廓各结构设计参数H＝72.01mm、L 2＝79.78mm、R＝30.65mm、R 1＝434.78mm、R 2＝298.26mm、、R＝74.081mm，优化后的轮胎外轮廓布置形式如图9所示。
采用步骤1对优化后的轮胎进行风阻仿真分析，优化前后的分析结果如表2所示。由表2可知，优化后的轮胎可以显著降低胎面处所受的气动阻力，相比于优化前其气动阻力系数降低了16.92％，从而提升了轮胎的风阻性能。
表2 优化前后的气动阻力系数对比
轮胎外轮廓结构设计参数 原始结构 优化后
上胎侧高H 57.06 72.01
行驶面宽L 2 67.61 79.78
胎肩过渡半径R 35.87 30.65
胎面弧度半径R 1 817.391 434.783
胎面弧度半径R 2 327.83 298.26
气动阻力系数C d 0.402169833 0.33389854
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. 一种降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于，包括以下步骤：
    步骤一、依据所选轮胎的型号，将该型号轮胎的外轮廓参数划分为上胎侧高、行驶面宽、胎肩过渡半径和胎面弧半径等五个参数，根据所选轮胎型号的五个外轮廓参数的初始值绘制对应的初始轮胎的三维模型；
    步骤二、构建初始轮胎风阻计算模型，根据上述初始轮胎的三维模型构建轮胎的风阻计算模型，并进行数值仿真分析，获得初始轮胎的气动阻力系数值；
    步骤三、设计试验方案，以轮胎五个外轮廓参数为变量，设定变量的取值范围，以胎面处轮胎整体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轮胎外轮廓参数进行方案设计，对不同外轮廓参数下的模型进行轮胎风阻仿真分析，获取各外轮廓参数下组合下的轮胎气动阻力系数值；
    步骤四、根据步骤三中的试验方案和轮胎气动阻力系数值，构建轮胎外轮廓参数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、采用智能优化算法对轮胎外轮廓参数与其气动阻力系数值间的函数关系进行优化计算，从而获得气动阻力系数值最小时的轮胎外轮廓参数，进而确定出风阻最小的轮胎外形。
  2. 根据权利要求1所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述步骤一中轮胎外轮廓参数主要是针对在轮胎宽度方向上一半的半胎进行参数描述的。
  3. 根据权利要求1所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述步骤二中轮胎风阻计算模型构建方法为流体动力学的计算方法，构建轮胎与路面虚拟风洞三维模型，将三维模型导入网格划分软件，生成轮胎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、压力出口和轮胎壁面运动方式，实现轮胎气动风阻的仿真分析。
  4. 根据权利要求1所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述步骤三中，以初始轮胎外轮廓参数为参考基础，轮胎外轮廓参数的取值范围是上胎侧高为断面高的0.47-0.63，行驶面宽为半胎模型的断面宽的0.73-0.9，胎肩过渡半径为15-45mm,胎面弧半径根据所选轮胎的型号设置取值范围。
  5. 根据权利要求1所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，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，筛选出轮胎外轮廓参数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所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述步骤四中的函数关系为根据轮胎外轮廓参数和气动阻力系数值构建回归函数，所使用的回归函数为Kriging近似模型。
  7. 根据权利要求6所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：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R 2检验Kriging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所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述决定系数R 2的表达式为：
    Figure PCTCN2020135519-appb-100001
    式中，n为检验模型精度的数据点数量；
    Figure PCTCN2020135519-appb-100002
    为第i个响应的近似模型预测值；y i为第i个响应的仿真值；
    Figure PCTCN2020135519-appb-100003
    为平均值。
  9. 根据权利要求1所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述步骤五中的优化算法为模拟退火优化方法，通过对轮胎外轮廓参数进行非线性优化设计，获得气动阻力系数值最小时的轮胎外轮廓参数。
  10. 根据权利要求9所述的降低轮胎风阻的轮胎外轮廓结构的设计方法，其特征在于：所述模拟退火优化算法首先设计温度更新函数式：
    t k＝t 0/ln(1+k)       (2)
    式中为第k步时温度，t 0为初始温度；
    算法中状态接受函数设计为：
    Figure PCTCN2020135519-appb-100004
    式中ΔE＝E i-E j,E i为算法处于当前解状态下的能量函数，E j为待接受解状态的能量函数；能量函数为目标函数值；
    待接受解按区间搜索方式产生，具体方法为以小步长在当前解邻域内搜索，新解获得方法为：
    X j＝X i+lΔ     (4)
    式中X i为当前解，X j为新解，l为循环次数，Δ为搜索步长；
    模拟退火优化算法具体步骤如下：
    Step 1：设置算法参数，随机产生初始解X 0，将其设置为当前解X i＝X 0；
    Step 2：计算当前解的能量函数E(X i)；按式(4)产生新解X j；
    Step 3：计算新解的能量函数E(X j)；并计算能量差ΔE；
    Step 4：根据ΔE按式(3)判断是否接受新解；若接受，更新当前解，即X i＝X j，转Step 6；否则转Step 5；
    Step 5：判断是否达到搜索次数上限，若满足，转Step 8；否则，更新循环次数即l＝l+1，转Step 2；
    Step 6：更新温度循环步数k＝k+1，按式(2)更新温度；
    Step 7：判断温度是否到达最低温度，若未达到转Step 2；否则转Step 8；
    Step 8：结束计算。
PCT/CN2020/135519 2019-12-25 2020-12-11 一种降低轮胎风阻的轮胎外轮廓结构的设计方法 WO2021129408A1 (zh)

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