第 4 期薛海等 : 铁道车辆天线梁的随机振动疲劳评估 随机振动疲劳分析方法 随机振动疲劳分析首先对结构进行频率响应分 析, 得到输入和输出的传递函数, 然后通过外加激励 的功率谱密度得到响应的功率谱密度, 最后根据材 料的疲劳特性曲线和累计损伤理论估算模型的疲劳 [1-2] 寿命大

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1 第 3 3 卷第 4 期 年 8 月 兰州交通大学学报 Journal of Lanzhou Jiaotong University Vol.3 3 No.4 Aug 文章编号 : (20 1 4) DOI: /j.issn 铁道车辆天线梁的随机振动疲劳评估 薛海 1,2, 赵波 2, 胡伟钢 1 (1. 北京交通大学机电工程学院, 北京 ;2. 兰州交通大学机电工程学院, 甘肃兰州 ) 摘要 : 引发天线梁破坏的主要原因是受到经构架端部传递的随机振动激扰. 为考察天线梁在随机激扰下的疲劳可靠性, 首先将结构动力学 随机振动和材料疲劳理论进行结合, 研究了随机振动疲劳分析方法, 在此基础上, 依据标准 IEC , 采用有限元软件 ANSYS Workbench 对天线梁进行随机振动仿真, 最后采用 Steinberg 法对其应力较严重部位进行疲劳损伤评估. 经分析, 得到天线梁的总体损伤为 0.5 6, 满足 Miner 线性累计损伤准则, 表明天线梁的疲劳设计符合标准的相关要求. 关键词 : 天线梁 ; 随机振动 ; 功率谱 ; 疲劳损伤中图分类号 :U 文献标志码 :A Random Vibration Fatigue Assessment of Railway Vehicle's Antenna Beam XUE Hai 1,2, ZHAO Bo 2, HU Wei-gang 1 (1.School of Mechatronic Engineering,Beijing Jiaotong University,Beijing ,China; 2.School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou ,China) Abstract:The main reason causing the destruction of the antenna beam is subj ected to random vibration excitation transmitted through the frame end.in order to study the fatigue reliability of the antenna beam under Random Excitation,to begin with,the method of random vibration fatigue analysis combined of structural dynamics,random vibration theory and material fatigue is researched.secondly,its random vibration is simulated by using the finite element software Ansys Workbench based on the standard IEC ,and finally fatigue damage assessment for serious parts of its stress is completed by the Steinberg method.the result of the overall damage to the antenna beam is and it meets Miner linear cumulative damage rule,which shows the fatigue design of antenna beam meets the standard requirements. Key words:antenna beam;random vibration;power spectrum;fatigue damage 铁道车辆天线梁安装在转向架构架的端部, 由侧板 吊座和管梁组成, 其吊座下方安装列车运行控制和超速防护的自动防护系统 (ATP). 根据天线梁的结构特点和安装位置, 确定其主要受到构架端部传递的来源于线路不平顺 车轮缺陷 轮轨冲击等外界因素的随机振动激扰, 这些激扰很容易引发天线梁的疲劳破坏. 因此, 保证天线梁的安全可靠性显得至关重要, 直接关系到列车的行车安全. 目前对铁道 车辆附属结构构件在随机振动下的可靠性研究主要有两种方法 : 一是进行实车在线试验研究, 二是依据相关标准进行实物试验或采用相关软件进行虚拟仿真. 由于试验成本和条件的限制, 本文依据 IEC 铁路应用 - 机车车辆设备 - 冲击和振动试验, 采用有限元法对天线梁在随机振动下的疲劳损伤进行评估. 收稿日期 : 学报网址 : tu.edu.cn 作者简介 : 薛 海 ( ), 男, 甘肃张掖人, 讲师, 博士生, 主要研究方向为车辆零部件的现代设计. xuehai3 5 4@1 6 3.com

2 第 4 期薛海等 : 铁道车辆天线梁的随机振动疲劳评估 随机振动疲劳分析方法 随机振动疲劳分析首先对结构进行频率响应分 析, 得到输入和输出的传递函数, 然后通过外加激励 的功率谱密度得到响应的功率谱密度, 最后根据材 料的疲劳特性曲线和累计损伤理论估算模型的疲劳 [1-2] 寿命大小及分布. 由于实际结构是连续体, 具有 无限多自由度, 为得到其动力响应, 一般采用有限元 法将结构离散化, 变成有限多个自由度问题, 然后利 用中心差分法 Houblit 法 模态叠加法等方法进行 [3] 求解. 方程为 多自由度有阻尼系统, 受到外力激扰时的运动 Mẍ (t)+ċx (t)+kx (t)= P (t). (1 ) 式中 :M C K 分别为系统的质量矩阵 阻尼矩阵和 刚度矩阵 ;x (t) ẋ (t) ẍ (t) 分别为系统的位移向量 速度向量和加速度向量 ;P (t) 为系统受到 C 的外部 激励. 将时域方程 (1 ) 经傅里叶变换得到频域方程 : (-ω 2 M +iωc +K)x (ω)= P (ω). (2) 一个 n 自由度的线性系统, 具有 n 个无阻尼固 有频率 ωr (r = 1,2,,n), 相应的将 n 个模态振型 φr 综合为一个模态矩阵 φ =φ1, φ 2,, φ n. 通过模态 分析, 将物理坐标变换为模态坐标 : x (ω)x (ω)=φζ ( ω). (3) 为得到模态坐标下的运动方程, 将式 (3) 代入 式 (2), 并左乘 φ T, 则有 : (-ω 2 φ T Mφ+ωφ T Cφ+φ T Kφ ) ζ ( ω)=φ T P (ω). (4) 对式 (4) 的广义模态质量矩阵 φ T Mφ 广义模态 刚度矩阵 φ T Kφ 和广义模态阻尼矩阵 ω 2 φ T Cφ 正交 化, 从而可使式 (4) 解耦为 n 个独立的方程 [4] : (-ω 2 Mr +iωc r +Kr ) ζr (ω)=φ T r P r (ω). (5) 则第 r 阶的模态传递函数为 H r (ω)= 从而得系统的传递函数为 1 Kr -Mrω 2 +ic rω. (6) n H φrφ r (ω)= T r r = 1 K r -Mrω 2 +ic rω. (7) 在随机过程中, 若输入变量的 PSD 为 G in (ω), 则输出响应 G out (ω) 为 n G out (ω)= H r (ω) 2 G inr (ω). (8) r = 1 得到结构的响应后, 由 f =ω/2π 从而可以得到 应力较严重部位的响应功率谱 Gσ(f ), 则其响应均 方根值 σ 和平均频率 v + [5 ] 分别为 σ= Gσ(f )df, (9) 0 f 2 Gσ(f )df v + = 0. (1 0) Gσ(f )df 0 如果结构在使用中经历了 m 个不同阶段的随 机振动, 在第 i (i = 1,,m) 个阶段, 应力功率谱为 Gσi (f ), 作用时间为 t i, 利用 Miner 线性累计损伤准 则可以进行结构疲劳损伤 D 的评估. 若 D = 1, 说明 结构开始发生疲劳破坏. m D = i = 1 nσi N σi m = i = 1 v + i t i. (1 1 ) N σi 式中 :σi 为第 i 个阶段应力的均方根 ;v + i 为第 i 个阶 段的平均频率 ;Nσi 为第 i 个阶段应力 σi 对应的疲劳 寿命 ;nσi 为第 i 个阶段应力 σi 的作用次数. 2 基于标准的随机振动疲劳评估 2.1 模型的建立 首先采用 Solidworks 软件建立了天线梁的三 维模型, 如图 1 所示. 为减少后期有限元分析时的网 格数量, 提高计算效率, 对结果影响不大的局部结构 进行了简化, 忽略了管梁与侧板连接处和吊挂 ATP 的螺栓孔 ; 由于天线梁为管梁和钢板的焊接结构, 焊 接区往往是其高应力区和疲劳薄弱位置, 为此在建 模中模拟了焊缝. Fig 模态分析 图 1 天线梁实体模型 Solid model of the antenna beam 模态分析是随机振动分析的基础. 采用有限元 软件 ANSYS Workbench 对天线梁进行模态分析. 根据天线梁与构架端部的连接方式, 在天线梁侧板 的螺栓孔处施加全约束, 与构架端部接触的侧板端 面施加全约束. 由于结构的动力响应主要受前几阶

3 1 38 兰州交通大学学报第 3 3 卷 低阶模态的主导作用, 并且经虚拟建模得到天线梁的质量为 kg, 根据 IEC [8] 规定所施加载荷的频率在 5 ~ 2 50 Hz, 为此取天线梁的前 9 阶频率 ( 第 9 阶频率为 Hz) 即可. 表 1 为天线梁的前 9 阶频率, 其中第 1 阶频率为 64 Hz. 图 2 为天线梁的第 3 阶频率对应的振型. 由于构架端部的基表 1 [6] 频一般在 50~60 Hz 之间, 表明天线梁在实际运行的外部激励作用下很有可能发生共振, 这进一步说明准静态疲劳方法不适用于获得天线梁在共振下的应力, 需要采用随机疲劳分析方法来准确获得天线梁的疲劳寿命. 模态分析 Tab.1 Modal Analysis 阶数 频率 /Hz D = n 1σ + n 2σ + n 3σ. (1 2) N 1σ N 2σ N 3σ 式中 :N 1σ N 2σ N 3σ 为应力水平 1σ 2σ 和 3σ 下对应的 疲劳寿命 ;n 1σ n 2σ n 3σ 分别为应力水平 1σ 2σ 和 3σ 对 图 2 第 3 阶频率的振型 Fig.2 Mode of the third-order frequency 2.3 基于标准的随机振动分析依据 IEC [8] 规定, 根据文献 [7] 的方法, 在天线梁上施加如图 3 所示的加速度谱 ( 坐标为双对数坐标 ) [8], 其中垂向 X =6.12 (m/s 2 ) 2 /Hz, 横向 X = 4.62 (m/s 2 ) 2 /Hz, 纵向 X = 1.32 (m/s 2 ) 2 / Hz. 在三向加速度激励谱的作用下, 得到天线梁的应力云图, 如图 4 所示, 说明最大应力发生在侧板与管梁焊接处, 表明该处是整个结构的疲劳薄弱位置, 最容易发生破坏. 图 5 为应力严重区的局部应力云图. 应的实际循环次数,n 1σ = 0.683v + T,n 2σ = 0.2 7v + T,n 3σ = 0.043v + T,v + 为平均频率,T 为振动时间, 标准规定为 5 h. Tybe:Equivalent Stress Scale Factor Value:1 Sigma Probability:68.3% Unit:MPa ASD/((m/s 2 ) 2 /Hz) X 9 db/oct -6 db/oct Fig.4 Tybe:Equivalent Stress Scale Factor Value:1 Sigma Probability:68.3% Unit:MPa 图 4 天线梁的应力云图 Stress contour of antenna beam 频率 /Hz 图 3 加速度谱 Fig.3 Acceleration spectrum 图 6 为应力最严重处的应力频谱图, 从 6 中可 以看出, 在 5 ~ 1 0 Hz 78 ~ 94 Hz 这两个区段的频 率是造成天线梁破坏的主要频率. 2.4 疲劳评估 采用 Steinberg 提出的基于高斯分布和 Miner 线性累计损伤定律的三区间法对天线梁进行疲劳评 [9] 估, 其表达式如下 : 图 5 天线梁的局部应力云图 Fig.5 Local stress contour of antenna beam 经有限元分析, 得到不同应力水平下 (1σ 2σ 和 3σ) 天线梁最大应力处的应力值, 如表 2 所示. 天线梁所用材料的 S-N 曲线为 lg N = lgσ, 根据文献 [1 0] 的方法, 可以得到天线梁的 S

4 第4期 薛 -N 曲线为 l g N = = l gσ,从而得到各 应力水平下的疲劳寿命. 应力谱 /((MPa)2/Hz) 撑结构设计中的应用[J].中 国 光 学 与 应 用 光 学,2 00 9, 20 2 (6 ): [2 ] 王荣乾.军 用 电 子 机 柜 随 机 振 动 疲 劳 分 析 [D ].北 京: 250 北京交通大学, [3 ] 任兴民,秦卫 阳,文 立 华.工 程 振 动 基 础 [M].北 京:机 频率 /Hz 图6 Fi g.6 表2 [4 ] Coleman R E,Allemang R J,刚宪约,等.试验结构动力 Spectrum of the maximum stress 不同应力水平下的疲劳损伤 Fati gue damage under different stress levels 应力 疲劳寿命 实际次数 水平 /MPa /次 /次 σ 械工业出版社, 应力最大值处的频谱图 应力 2σ 1 60 > 疲劳 损伤 根据式(1 2 ),得到天线梁的总体损伤为 n 1σ n 2σ n 3σ + + = < 1. N 1σ N 2σ N 3σ 说明天线梁满足疲劳设计的要求. D = MPa,采 用 Steinber g 法 得 到 天 线 梁 的 疲 劳 损 伤为 0.5 3,说明天线梁满足疲劳设计的要求. [1 ] 余飞,吴清文,王宝石,等.振动疲劳寿命分析 在 主 镜 支 50 1σ [] 2 )基于 IEC ,在天线梁上施加振 动加速度进行虚拟 仿 真,得 到 天 线 梁 的 最 大 应 力 为 参考文献: 40 0 Tab 海等:铁道车辆天线梁的随机振动疲劳评估 结论 1 )考虑结构自身特性(质量 刚度和阻尼)和实 际所受载荷(随机载 荷)的 特 点,应 采 取 将 结 构 动 力 学 随机振动和材料 疲 劳 理 论 相 结 合 的 方 法 进 行 天 线梁的疲劳损伤评估. 学[M].北京:清华大学出版社, [5 ] 张积亭,周苏枫.飞机典型构件振动 疲 劳 寿 命 分 析[J ]. 机械科学与技术,2 00 2,2 1 : [6 ] 尹振坤.动车 组 转 向 架 端 部 结 构 疲 劳 强 度 计 算 方 法 的 //第 八 届 中 国 智 能 交 通 年 会 优 秀 论 文 集.北 对比[C] 京:电子工业出版社, :9. [7 ] 卢彩玲,康宁 民,郑 应 强.对 随 机 振 动 试 验 方 法 的 探 讨 [J].环境试验, (6 ): [8 ] International Electrotechnical Commission.IEC Railway applications-rolling stock equipmentshock and vibration tests [S] [9 ] 孟凡涛,胡愉愉.基于频域法的随机振动载荷 下 飞 机 结 构疲劳分析[J].南京航 空 航 天 大 学 学 报, ,44 (1 ): [1 0 ] 赵少汴.有限寿命疲劳设计法的基 础 曲 线[J ].机 械 设 计, ,1 1 (1 ): (责任编辑:赵冬艳)

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