基于确保疲劳强度和减轻重量的转向架构架设计外文资料翻译

1、Bogie frame design in consideration offatigue strength and weight reductionB H Parkand K Y LeeSchool of Mechanical Engineering,Yonsei University,Seoul,Republic of KoreaThe manuscript was received on 8 April 2005 and was accepted after revision for publication on 25 November 2005.DOI: 10.1243/0954409

2、7F01405Abstract: In the development of a bogie, the fatigue strength of a bogie frame is an important design criterion. In addition, weight reduction is required in order to save energy and material .In this study, the fatigue analysis of a bogie frame by using the finite-element method is performed

3、 for various loading conditions according to the UIC standards and it is attempted to minimize the weight of the bogie frame by artificial neural network and genetic algorithm.Keywords: bogie, strength, fatigue analysis, neural network, optimization.1 INTRODUCTIONA bogie in a train is a very importa

4、nt structural component loaded by various forces in the rail way vehicle motion. The motion of a railway vehicle is affect by the geometry of the track, the interaction between wheels and rails, the suspension, and the inertias of component part s. In the meantime, the weight of a bogie structure sh

5、ould be as light as possible at higher running speed. Therefore, the strength of the bogie should be carefully calculated and analysed by the international standards such as UIC 1 and JIS 2, in order to obtain a reasonable design scheme. In the past design process, the steps of many experiments, fie

6、ld tests, and prototypes to improve and obtain a reasonable design required much time and high costs. In the computer-aided engineering (CAE) product design step, however,the practical use of finite- element (FE) analysis can reduce the costs and time. The FE analysis of the bogie frame was studied

7、several times 3,4.In addition, the bogie has a large proportion of the total weight of a vehicle. Savings of energy and material are currently design drivers towards lightweight vehicle constructions. In CAE productdesign step, optimization for weight reduction and application of the optimal algorit

8、hm can make the light weight and the constraint conditions for the fatigue strength satisfy.It is a typical structural optimization problem to minimize the weight of the bogie under the fatigue constraint, but the problem cannot be solved by simply applying the existing numerical optimization algori

9、thms. In the problem, the fatigue constraint isnot expressed as an analytical function in terms of the design variables.In this article, the FE model of the bogie frame is constructed to simulate the fatigue test. The bogie that is used in this study is composed of welded frame, bolster, self-steeri

10、ng mechanism, primary suspension, secondary suspension, and disc brake system. The fatigue strength of the bogie frame is estimated by the international standard UIC615-4 Motive Power Units Bogies and Running Gear Bogie Frame Structure Strength Test. The optimization problem is composed of an object

11、 function for the weight reduction of the bogie and the constraint conditions for the fatigue design criteria. The artificial neural network (ANN) to approximate a function for the fatigue constraint and the micro genetic algorithm (MGA) are used to solve this optimization problem.2 STRESS ANALYSIS

12、OF THE BOGIE FRAME2.1 FE model of the bogie frameIn this study, the analysed bogie frame is a bolster type bogie (Fig. 1(a). The numerical analysis by the FE method is performed to evaluate the fatigue strength of the bogie frame except the bolster.The bogie is modelled using shell and solid element

13、s and the FE model is shown in Fig.1(b ).The trailer bogie frame is meshed to have 28, 251 nodes, 23,870 rectangular shell elements, and 2710 hexagonal solid elements.Considering the boundary conditions of the trailer bogie frame for the primary suspension, the spring boundary elements are establish

14、ed and the stiffness of the elements is the same as the primary suspension. There are 12 spring elements for the primary suspension in the trailer bogie frame. The software programs used are Altair Hyper Mesh and ABAQUS .The material used in the bogie frame is SWS490A defined in reference 2 and the

15、material properties are shown in Table 1.2.2 Load conditions and the evaluation of fatigue strength of the bogie frameThe fatigue analysis is based on the UIC standard. The main in- service load case is designed to verify the absence of any risk of fatigue cracks occurring under the combined effect

16、of the main forces encountered during service. The load case consists of different load scenarios for the bogie frame involving experiencing straight track, curve negotiation, rolling and bouncing effects, and track twist. Tables 2 and 3 show each load and application area and load scenarios.In Tabl

17、e 2, mv(kg) is the empty mass of vehicles, nb the number of bogie, m(kg) the bogie mass, C1(kg)the passenger mass per seat, and g (m/s) and the acceleration due to gravity. From Table 2 and UIC 615-4 1, the load cases of main in-service are defined in Table 3. Variables Fz1, Fz2, Fy, Ft1, Ft2 of the

18、 loads applied during the fatigue strength analysis are presented in Fig.1(a).At each node, the stress resulted from each load case of Table 3 is determined. From the result, the maximum values max and the minimum values min defined in reference 5 are determined by the steps shown in Fig.2. From max

19、 and min, the mean stress m and the stress amplitudes a are defined as followsFrom m and a at each node, the Goodman diagram shown in Fig.3 is obtained. Stress amplitudes have to satisfy the following equationThe permissible stress p is obtained from the Goodman diagram and n is the design factor. T

20、he analysis result of the initial design in Tab le 4 is presented in Fig.3. As shown in Fig.3, the fatiguestrength satisfies mostly the Goodman diagram. At welding and grinding locations, some nodes violate the Goodman diagram. The maximum value of n is 1.04.3 OPTIMAL DESIGN OF THE BOGIE FRAME3.1 AN

21、N for the design factor nThe constraint for the fatigue strength is approximated by a three -layered error back propagation neural BPN network. Neural networks are developed to model the way in which the human brain performsa particular task or processes information 6. The use of ANN to approximate

22、the functions with a high degree of non-linearity is well established.Back propagation is a general-purpose learning algorithm. Considering the fatigue strength of the bogie frame, the design factor n is chosen as the output parameter, whereas the upper cover plate, the lower cover plate, and the in

23、ner vertical cover plate of the side frame are chosen as the input parameters of the network. Table 4 and Fig.4 show each design variable and initial, upper , and lower values with the initial weight.First, the fatigue analysis data have to be obtained when approximated by an ANN. The three-level fu

24、ll-factorial design for three design variables is used in order to generate training data sets. Each variable has initial, lower, and upper values, as shown in Table 4. The reliability of approximate model is verified by the three test data sets.The specific nodes to be used in BPN are selected at t

25、he locations with the severest values through the experiments of 27 times. These nodes are presented in Fig.5.In this study, the neural network model of Fig.6 is applied to approximate the design factor at each node.The approximate results for the design factor at the selected nodes are marked in Ta

26、ble 5. As the maximum percentage error between the test data and the fatigue analysis data is 5.34 percent, it is concluded that the training of the model is successfully accomplished.3.2 Genetic algorithm for optimizationGenetic algorithms (GAs) are the search algorithms based on the mechanics of n

27、atural selection and natural genetics. GA would make the combination convergence solutions that are globally optimal ornearly so, and it has been successfully applied to a variety of some functional optimization problems. As the population size increases, the algorithms find a better solution. Howev

28、er, a bigger population size requires more computational time to find the optimum solution. For this reason, Goldberg 7, 8 proposed serial GA (SGA), which used a small population size when compared with conventional GAs.On the basis of SGAs, Krishnakumar 9 proposed mGAs in 1989.In this study, the mG

29、A with a population size of five individuals is used. The flow chart of mGA used in this study is illustrated in Fig.7.The optimization problem is defined as follows where F(X)(kg) is the weight of the plates, N the number of design variables, A() the area of the ith plate, and Xi(mm) the thickness

30、of the ith plate. The density of SWS490A is 7.8510 kg/Figure 8 shows the optimization process of the object function F(X) using mGA. Three different simulations were performed with errors , 0.5 percent . The optimum value of the best result is 0.504 ton (Table6). The weight of the bogie frame was re

31、duced by 4.7 percent than the initial design. The constraint condition n becomes 1.000 at node 4862 (Table 7). Between the values of the optimising results and the values of the analysed results by the optimal values of design variables, the maximum error is 2.93 percent .Table 7 shows that the opti

32、mal value of the approximated ANN model satisfies the modified Goodman diagram, but in the actual calculation with optimal thickness, the Goodman diagram is violated at node 4862. This is due to the error between the prediction and analysis models.4 CONCLUSIONSIn this study, the fatigue strength of

33、the bogie frame was estimated by the UIC in the developing step of the bogie. In this process, the post-process was developed. Then, the weight reduction problem of the bogie frame was solved .The fatigue strength was not satisfied by the design conditions of the modified Goodman diagram. However, a

34、fter the optimization to reduce the weight of the bogie frame was performed, the weight was reduced by 4.7 percent than the initial design . In the process , the BPN network and the GA were used.The approximated model satisfies the design constraint, but the analysis result of the optimal design vio

35、lates the design constraint because of the error between prediction and analysis models.REFERENCES1. International Union of Railways. Motive power units, bogies and running gear, bogie frame structure strength tests. UIC 615-4, 1994.2. Japanese Industrial Standard. Truck frames for railway rolling s

36、tock general rules for design. JIS E4207, 1992.3. Dietz, S., Netter, H., and Sachau, D. Fatigue life prediction of a railway bogie under dynamic loads though simulation. Veh. Sys. Dyn., 1998, 29, 385-402.4. Oyan, C. Structural strength analysis of the bogie frame in Taipei rapid transit systems. Pro

37、c. Instn Mech. Engrs,Part F: J. Rail and Rapid Transit, 1998, 212 (F3), 253-262.5. European Rail Research Institute. Programme of tests to be carried out on wagons with steel under frame and body (suitable for being fitted with the automatic buffing and draw coupler) and on their cast steel frame bo

38、gies.ERRI B12/RP 17, 7th edition, 1993.6. Hagan, M. T. Neural network design, 1996 (PWS Publish Company, Boston, MA).7. Goldberg, D. E. Sizing populations for serial and parallel genetic algorithms. Proceeding of the 3rd International Conference on Genetic algorithms, Arlington, VA, 1989, pp. 70 79

39、(Morgan Kaufmann).8. Goldberg, D. E. Genetic algorithms in search, optimization and machine learning , 1989 (Addison-Wesley, Boston, MA).9. Krishnakumar, K. Micro-genetic algorithm for stationary and non-stationary function optimization. SPIE, Intell. Control Adapt. Syst., 1989, 1196, 282-296.基于确保疲劳

40、强度和减轻重量的转向架构架设计B.H.Park and K.Y.Lee机械工程学院，延世大学，首尔，韩国.这份手稿是于2005年4月8日收到后接受修改,出版于2005年11月25日。DOI: 10.1243/09544097F01405摘要：在一个转向架的设计发展过程中，转向架构架疲劳强度的影响是一个重要的设计准则。此外,为了节约能源和材料需要减轻重量。在这项研究中，用有限元方法在各种加载条件下对转向架构架进行疲劳分析是根据UIC的标准形成的，这种方法试图通过人工神经网络和遗传算法来减小转向架构架的重量。关键词：转向架、强度、疲劳强度分析、神经网络、优化。1 简介：转向架是列车上一个非常重要的

41、构件，它承载着铁道车辆在运动中的各种力。铁道车辆的运动受到轨道的几何形状、轮轨相互作用、悬挂装置和零部件的惯性力的影响。同时，一台高速运行列车的转向架结构的重量应该尽可能轻。因此，转向架的强度应该在国际标准如UIC1和JIS 2的基础上仔细地进行计算分析，以获得一个合理的设计方案。在过去的设计过程里，诸如一些试验，现场测试，并对原型改进得到一个合理的设计等步骤需要许多时间和很高的成本。然而，在计算机辅助工程(CAE)产品设计中，应用有限元分析方法(FE)可以减少所需的成本和时间。利用有限元分析方法研究转向架构架曾有几次先例3,4。此外，转向架占车辆总重量的一大部分。目前设计者在节省能源和材料的

42、驱动下对车辆的结构进行轻量化设计。在CAE产品设计步骤，降低重量的优化方案以及最优算法的应用可使重量减轻并满足约束条件的疲劳强度。这是一个典型的疲劳约束下降低转向架重量的结构优化问题,但只是应用现有数控优化算法，问题是无法解决的。在这一问题上，疲劳约束作为一种分析不表达功能方面的设计变量。在这篇文章中，建立转向架构架的有限元模型是为了模拟疲劳试验。这项研究中使用的转向架是由焊接构架、摇枕、自导向机制、一系悬挂、二系悬挂和盘形制动装置组成。转向架构架疲劳强度的评估则根据国际标准UIC615-4 进行“动力单位转向架和运行齿轮转向架构架结构强度试验”。该优化问题是由一个降低转向架重量的对象函数和约

43、束条件下的疲劳设计标准构成。近似疲劳的约束的人工神经网络(ANN)函数和微观遗传算法(GA)被用来解决这一优化问题。图1 转向架构架模型2转向架构架的应力分析2.1转向架构架的有限元模型在这项研究中，分析对象是摇枕转向架（图1(a)）。对转向架构架有限元模型数值分析的目的是进行除摇枕外转向架疲劳强度的评估，拖车转向架构架是由28250个节点、23870个矩形壳单元、2710个六角形固体单元紧密连接而成。考虑到拖车转向架构架一系悬挂的边界条件，弹簧边界元件就可以建立，并且这些元件的刚度与一系悬挂完全相同。拖车转向架构架有12根弹簧为基本悬挂单元。软件程序使用Altair Hyper Mesh和A

44、BAQU。这个转向架构架材料是SWS490A，定义在文献2，该材料的性能见表1。2.2负载条件下评价转向架构架疲劳强度的影响疲劳分析是基于暂行标准。在职载荷主要是为了确保使用时在已考虑到的主要力综合作用过程中没有任何发生疲劳裂纹的风险。载荷产生的情况，包含转向架构架的各种不同负载、直线轨道、曲线通过、轧制和跳跃的影响、和跟踪扭曲。表2和3显示各个负载的负载情况和应用领域。表1 转向架构架材料特性（MPa）材料屈服强度抗拉强度疲劳极限基本材料磨削和焊接焊接SWS490A32349015710878表2 主应力情况载荷类型载荷计算施加区域垂向载荷旋启式连接支架水平载荷0.5制动器安装架扭转载荷5的

45、跟踪扭矩初级悬挂支架在表2中， 是空车质量， 是转向架数量， 是单个转向架质量， 是乘客的平均质量，g (m/)为重力加速度。根据表2和标准UIC 615-4 1 ，主要载荷的情况可由表3进行规定。疲劳强度分析时使用的变量如 的施加情况列在图.1(a)中。 在每个节点， 每种载荷下的应力由表3确定。可以从结果看出，表5中定义的最大应力和最小应力的大小由图2中步骤确定， 根据 ，平均应力 和 应力幅值 由下式定义：表3主应力载荷（KN）载荷垂向载荷水平载荷扭转载荷1120.82120.8202108.7484.5703108.7484.57+16.674157.06132.9005157.061

46、32.90+16.67684.57108.740784.57108.74-16.678132.90157.0609132.90157.06-16.6710108.7484.57+16.674.5211108.7484.57+16.674.5212157.06132.90+16.674.5213157.06132.90+16.674.521484.57108.74-16.674.521584.57108.74-16.674.5216132.90157.06-16.674.5217132.90157.06-16.674.52根据每一节点上的，可以得到如图.3所示的古德曼图。应力幅值需满足下式要求：

47、 图2 最大和最小应力的确定应力分析根据表2载荷推算应力结果计算主应力和方向选定最大应力和方向其它载荷下该方向的应力确定最小应力图3 修改后的古德曼图许用应力 从古德曼图中获得，n是设计因数。表4中的初始设计的分析结果如图3中所示。如图3所示，疲劳强度大多满足古德曼应力图的要求。在焊接和磨削处，一些节点违反古德曼图。最高值的n是1.04。3转向架构架的优化设计中3.1 人工神经网络的设计因数n疲劳强度约束为一个三层逼近误差反向传播神经BPN网络。神经网络塑造了人脑执行某一特定任务或处理信息的方式6。人工神经网络的高度非线性逼近函数得到了很好的利用。反向传播是一种多用途的学习算法。考虑转向架构架

48、的疲劳强度，设计因子n被选择作为输出参数，然而其上盖板、下盖板和里面的侧架垂直盖板是被选择作为输入参数网络。表4和图4显示各个设计变量的初始值，上、下限值和最初的重量。首先，疲劳分析数据应该在逼近人工神经网络时获得。这三个水平的设计变量的全因子设计被用来产生训练数据集。每一个变量如表4所示有初始值和上下限值。三项测试验证了近似模型的可靠性。用于BPN的特定的节点通过27次最严格的试验选择。这些结点呈现在图5中。在这项研究中，图6所示的神经网络模型被应用于在每个节点上逼近设计因子。表5标记了选定节点设计因子近似结果。测试数据及疲劳分析数据之间的最高百分比误差为5.34%，结果表明，该模型的测试成

49、功完成。表4设计变量和限值设计变量位置厚度（mm）下限值初始值上限值初始重量：0.529tX(1)侧架上盖板121620X(2)侧架下盖板121620X(3)侧架垂直盖板812163.2遗传算法优化遗传算法(GAs)是一种基于自然选择力学和自然遗传学的搜索算法。遗传算法会结合收敛性解决方案得到全局最优或近似解，已经被成功运用到各种各样的一些功能优化问题。数量增加时，算法找到一个更好的解决办法。然而，一个更大的数量规模需要更多的计算时间才能找到最合适的解决方案。因此，戈德堡7,8提出了串行遗传算法(SGA)，它通过与常规遗传算法相比一个更小的规模。在SGA的基础上，Krishnakumar9在1

50、989年提出了GA。图4转向架构架的设计变量X 图5节点约束条件在这项研究中，五个个体规模的GA得到使用。GA流程图如图7。该优化问题是定义如下F( X ) (kg) 是盖板的重量，N是设计变量的个数， A () 是第i个的盖板的面积，(mm)是第i个盖板的厚度。SWS490A的密度7.8510 kg/图6 3-3-1神经网络模型表5各项测试中人工神经网络设计因子和疲劳分析的误差图8遗传算法结果图8显示目标函数F(X)的优化过程使用GA。三种不同仿真研究在小于误差0.5%的范围进行了。最优值的最好结果是0.504吨(表6)。转向架构架的重量比最初的设计降低了4.7%。约束条件变成节点4862处的1.000了(见表7)。优化结果的值和设计变量最优值的分析结果之间最大误差为2.93%。表6 优化结果最优值（ton）设计变量（mm）X(1)X(2)X(3)0.50418.15139812.01953711.875135表7设计因子预测值与比较值节点号1126848621088412075预测值（a）0.8811.0000.9610.995分析值（b）0.8841.0