基于刚柔耦合的轨道车辆转向架构架疲劳分析*

廖爱华， 黄 旭， 方 宇

(上海工程技术大学城市轨道交通学院 上海，201620)



基于刚柔耦合的轨道车辆转向架构架疲劳分析*

廖爱华， 黄 旭， 方 宇

(上海工程技术大学城市轨道交通学院 上海，201620)

对某型地铁车辆转向架构架在运行使用过程中局部区域出现裂纹的问题，首先，基于固定界面模态综合法，通过构架主自由度缩减得到了该型构架柔性体模型，从而建立该型地铁车辆刚柔耦合多体动力学模型；然后，结合一种基于柔性体计算结构动应力的方法，探讨该型构架的动应力响应，得到该型构架的振动特性；最后，采用准静态应力叠加法对构架电机吊座结构进行了疲劳寿命预测。仿真结果与该型构架实际出现疲劳破坏的位置吻合，从而验证了基于刚柔耦合模型对构架进行疲劳分析方法的正确性。结果表明，利用这种方法可以在构架前期开发阶段为其疲劳寿命预测提供理论依据。

转向架构架； 多体动力学； 刚柔耦合； 疲劳寿命

引 言

转向架构架作为地铁车辆的主要承载部件，其承受着频繁的随机载荷，所受工况比较恶劣。以某型地铁车辆转向架构架为例，该型车辆转向架构架在运行使用过程中构架多次出现裂纹现象，构架的使用寿命远远小于设计寿命[1]，该现象严重影响了地铁车辆的运行安全性。因此，对影响地铁车辆运行安全的关键部件转向架构架进行疲劳分析以及疲劳寿命预测显得尤为重要。

国内外学者在结构的疲劳分析这个领域做了大量的研究，这些方法同样可以应用于转向架构架的分析和研究中。目前国内外对于结构的疲劳分析主要从实验[2]和仿真[3-6]两个角度作为切入点。线路实测动应力实验及疲劳实验比较昂贵，且线路实测动应力实验受线路、气候条件的影响较大。而仿真主要依靠多体动力学仿真联合有限元分析的准静态叠加法来实现结构动应力的计算，该方法适用于结构固有频率运离外部载荷频率的情况。由于地铁车辆转向架构架所承受的是复杂的耦合动载荷场，结构架局部动刚度较小，很可能会出现局部共振现象。此时除了外部载荷激励，还需考虑局部共振造成的自振激励。因此，本研究以构架结构自身振动特性作为出发点，建立构架柔性体模型，并结合地铁车辆刚柔耦合多体动力学仿真得到构架结构的动应力响应，从而得到构架的振动特性，并依据此对该型构架进行疲劳分析，进而得到其疲劳破坏机理，最后基于准静态应力叠加法预测构架电机吊座的疲劳寿命。

1 柔性构架的建立

1.1 柔体动力学理论

柔性体理论主要基于固定界面模态综合法[7]，其基本思想是赋予柔性体一个模态集，采用模态法展开，用模态向量和模态坐标的线性组合表示物体的弹性位移，通过计算每一时刻物体的弹性位移来表示其变形，令柔性部件r的界面固定，并建立模态矩阵，其中模态矩阵可表示为

(1)

其中：φIN为主模态矩阵；φIC为约束模态矩阵。

主模态qN是界面自由度固定时所对应的固有模态，其与内部自由度一一对应；而约束模态qC是指依次释放每一边界自由度，使其产生单位位移而形成的静位移分布所构成的静态模态，则可得

(2)

其中：I和0分别为单位矩阵和零矩阵;s为位移矩阵。

通过转换，得到柔性体的运动方程

(3)

由于模态矩阵中，存在惯性耦合，需对其进行正则化转换，消除刚体模态，重新代入柔性多体系统中，采用拉格朗日建立整个系统的方程，从而得到系统的解。

1.2 建立柔性构架

该型转向架构架主体采用牌号为DIN-ST52结构钢，材料的弹性模量为2.1×105MPa，泊松比为0.29，密度为7.8×103kg/m3，极限强度标准值为510MPa，屈服强度标准值为355MPa。选取SHELL63，SOLID45以及MASS三类单元来建立构架的有限元模型，依据模态综合法，选取若干固定交互点进行主自由度缩减，最终得到柔性构架。

2 柔性体结构应力计算方法

传统的刚体动力学模型忽略了结构内部的相对位移，若结构在运动过程中发生了共振，此时如若按照传统结构静强度计算方法，计算得到的应力会小于实际结构应力。所以，从结构动力学的角度出发，以结构模态位移为基础，通过模态应力恢复计算结构应力。

柔性体中的某一节点的模态位移X可以由若干阶模态振型相互叠加得到

(4)

其中：hj为第j阶模态频率；wj为第j阶频率对应的模态位移。

根据模态综合法，模态矩阵H是由静模态与特征模态组合而成，静模态的数量等于约束特征点的自由度的总和，特征模态是通过求解式(5)得到

(5)

其中：M为质量矩阵；C为刚度矩阵；λ为特征值；y为特征模态。

(6)

(7)

通过求解式(8,9)进行模态矩阵的正则化，得到柔性体的模态信息

(8)

(9)

依据有限元离散理论可得

(10)

(11)

通过代入柔性体某一节点i的模态位移可推出柔性体中某节点i的应力与应变。将式(4)分别带入式(10，11)则可推出式(12，13)

(12)

(13)

由此可知,只要获取柔性体中每个节点的模态位移，则可以得到柔性体中每一个节点的动应力响应。

3 地铁车辆刚柔耦合多体动力学模型的建立与仿真

利用1.2节得到的柔性构架，根据该型地铁车辆真实动力学参数以及结构参数，最终建立该型地铁车辆的刚柔耦合多体动力学模型如图1所示。在建模过程中对柔性构架所受初始载荷进行预平衡，则在动力学仿真过程中柔性构架所承受的随机载荷也就模拟了车辆运行过程中构架的实际受力状态。

图1 地铁车辆刚柔耦合多体动力学模型Fig．1 The rigid-flexible coupling multibody dynamics model of metro vehicle

以该型地铁车辆在满载AW2下时速72 km/h作为仿真的边界条件，并以美国五级谱作为轨道激励进行仿真，仿真时间设为80 s。

3.1 构架整体结构动应力响应分析

构架属于准对称结构形式，在不影响仿真计算的精度并能缩短计算时间的情况下，选取构架的一半区域作为分析对象。结合实际情况，由于安装座结构均为整体铸件结构，运营过程无任何裂纹情况发生，未出现疲劳破坏现象，所以计算结构动应力响应时没有考虑在内，构架结构应力分布云图如图2所示。

构架最大应力节点号为47 292，输出该节点的动应力历程如图3所示。

图2 构架结构应力分布云图Fig.2 The structure stress distribution of frame

图3 节点47 292动应力Fig.3 The dynamic stress of node 47 292

图4 构架应力幅值分布云图Fig．4 The stress amplitude distribution of frame

图5 构架裂纹位置Fig.5 The crack area of frame

节点47 292处的应力最大值为142.3 MPa，小于该型构架母材的许用应力178 MPa，符合构架的强度要求。由于结构的破坏主要是由结构动应力的幅值引起的，应力幅值扰动是引起结构破坏的主要原因。应力幅值过大的区域主要集中在电机吊座区域、齿轮箱吊座区域、横梁和侧梁连接区域。该型构架电机吊座区域的应力幅值分布云图如图4所示，仿真结果与构架实际出现疲劳破坏的位置(图5)大体一致。

由于电机吊座工字型加强板(图4)整体所受应力幅值较大，从而导致该处(图5)加强板底部焊缝区域经常出现裂纹。针对此处焊缝区域，取其中应力幅值最大的一个节点(337 853)进行分析，该节点的动应力如图6所示。

图6 焊缝节点动应力Fig.6 The dynamic stress of node in weld bead

由图6得知，焊缝处节点最大应力值为27.6 MPa，电机吊座加强板采用的是对接焊缝，且焊缝焊接材料为脆性材料。依据BS7608焊接疲劳标准，该处的焊缝区域的疲劳强度极限值要远远小于母材，这也是该处经常出现裂纹的主要原因。

3.2 构架各局部区域疲劳分析

以该型地铁车辆在满载AW2下时速80 km/h作为仿真的边界条件，并以美国五级谱作为轨道激励进行仿真，仿真时间设为80 s。分别对上述易疲劳区域进行疲劳分析，得到各区域的应力幅值分布云图，并输出各个区域的应力幅值最大节点的动应力图。

1) 电机吊座区域疲劳分析结果如图7,8所示。

图7 电机吊座区域应力幅值分布云图Fig.7 The stress amplitude distribution of motor suspension

图8 80 km/h工况下节点动应力Fig.8 The dynamic stress of node under the working condition of 80 km/h

2) 齿轮箱吊座区域疲劳分析结果见图9，10。

图9 齿轮箱吊座应力幅值分布云图Fig.9 The stress amplitude distribution of gear suspension

图10 80 km/h工况下节点动应力Fig.10 The dynamic stress of node under the working condition of 80 km/h

3) 横梁-侧梁连接区域疲劳分析结果如图11,12所示。

图11 横梁-侧梁连接区域应力幅值分布云图Fig.11 The stress amplitude distribution of the connection area between beam and side beam

图12 80 km/h工况下节点动应力Fig.12 The dynamic stress of node under the working condition of 80 km/h

由图7，图9，图11得知，电机吊座区域的最大应力幅值为43 MPa，相对于齿轮箱吊座区域和横梁-侧梁连接区域的最大应力幅值较大。由图8、图10、图12可看出，电机吊座区域的结构动应力比齿轮箱吊座区域以及横梁-侧梁连接区域整体要大，这也解释了该型构架在运行过程中电机吊座出现裂纹频率较高的原因。

4 基于准静态应力叠架法的电机吊座结构疲劳寿命预测

准静态应力叠加法的主要思想是计算任一时刻相同结构位置和相同作用方向的单位静态载荷所引起的弹性应力应变状态，然后将其与之对应的载荷谱叠加得到结构的动应力，结合材料S-N曲线，并修正平均应力，最后依据线性损伤累计原则对结构开展疲劳寿命预测。

4.1 单位载荷作用下的电机吊座结构惯性释放有限元分析

惯性释放的原理[8]是通过构造一个自平衡力系来模拟约束不足时的结构静态响应。在电机吊座质心处施加沿x，y，z正方向单位力以及绕x，y，z3个坐标轴顺时针的单位转矩。限于篇幅，以单位垂向载荷作用下为例，电机吊座应力、应变分布云图如图13所示。

从图13可以看出，应力较大的部位主要集中在电机吊座四块工字型加强板区域，工字型加强版区域整体应力较大。

图13 z方向单位载荷作用下的应力分布云图Fig．13 The stress distribution under unit load along z direction

4.2 电机吊座边界载荷的计算

依据建立的地铁车辆刚柔耦合多体动力学模型，根据该型车辆实际运行线路参数选取一段长为10 km的线路。以该型地铁车辆在满载AW2工况下时速72 km/h速度运行，采用美国五级谱作为激励谱，获取电机吊座的边界载荷Fx，Fy，Fz，Mx，My，Mz，其中电机吊座垂向力如图14所示。

图14 电机吊座垂向力FZFig.14 The vertical force FZ of motor suspension

4.3 电机吊座疲劳寿命预测结果

依据上述得到电机吊座有限元分析结果以及动力学仿真获得的电机吊座边界载荷，利用nCode仿真得到电机吊座结构疲劳寿命分布云图，如图15所示。

图15 电机吊座结构疲劳寿命分布云图Fig.15 The fatigue life distribution of motor suspension

由图15得知，电机吊座安装座整体铸件结构为无限寿命，疲劳寿命最短的位置出现在电机吊座工字型加强板与电机安装座的焊缝连接处，仿真获得的电机吊座疲劳寿命较短位置与实际电机吊座发生疲劳破坏的位置吻合的很好。仿真计算得到的电机吊座结构疲劳寿命为1.53×105次循环，每次循环10km，则可计算得到电机吊座节点最短寿命为153万km。根据地铁检修部门提供的数据，电机吊座处出现裂纹平均里程为139万km，两者误差为10%。

5 结 论

1) 该型构架结构应力最大值为142.3MPa，小于该型构架母材的许用应力178MPa，符合构架的强度要求。应力幅值扰动是引起结构破坏的主要原因，该型构架应力幅值过大的区域主要集中在电机吊座区域、齿轮箱吊座区域、横梁-侧梁连接区域。仿真结果与该型构架实际出现疲劳破坏的位置吻合，从而验证了基于刚柔耦合模型对结构进行疲劳分析方法的正确性。

2) 采用准静态应力叠加法对构架易疲劳区域-电机吊座结构进行疲劳寿命预测，仿真得到电机吊座节点最短寿命为153万km。计算结果符合地铁检修部门提供的数据：电机吊座该处出现裂纹平均里程为139万km。仿真结果与实际数据误差为10%，可知仿真可信性及正确度较高。

[1] 金国龙，谢雄耀，王如路. 上海地铁1号线车辆转向架寿命预测数值分析[J]. 地下空间与工程学报, 2009, 5(5): 860-866.

Jin Guolong, Xie Xiongyao, Wang Rulu. Lifetime prediction of the bogie frame of shanghai metro line 1 by 3D FEM [J]. Chinese Journal of Underground Space and Engineering, 2009, 5(5): 860-866. (in Chinese )

[2] Han S H, An D G, Kwak S J, et al. Vibration fatigue analysis for multi-point spot-welded joints based on frequency response changes due to fatigue damage accumulation [J]. International Journal of Fatigue, 2013,48 (1): 170-177.

[3] Wannenburg J，Heyns P S，Raath A D. Application of a fatigue equivalent static load methodology for the numerical durability assessment of heavy vehicle structures [J]. International Journal of Fatigue, 2009, 31(10): 1541-1549.

[4] Kagnici F. Vibration induced fatigue assessment in vehicle development process [J]. World Academy of Science Engineering and Technology, 2012(64): 88-93.

[5] 张磊安，黄雪梅，王娜，等. 风电叶片单点疲劳加载过程数值仿真与试验[J]. 振动、测试与诊断，2014,34(4):732-736.

Zhang Leian, Huang Xuemei, Wang Na,et al. Numerical simulation and test on MW wind turbine blade single fatigue loading process [J]. Journal of Vibrati-on, Measurement & Diagnosis, 2014,34(4):732-736. (in Chinese)

[6] 兆文忠,魏鸿亮,方吉,等. 基于主S-N曲线法的焊接结构虚拟疲劳试验理论与应用[J]. 焊接学报, 2014, 35(5): 75-79.

Zhao Wenzhong，Wei Hongliang，Fang Ji，et al. The theory and application of the virtual fatigue test of welded structures based on the master S-N curve method [J]. Transactions of the China Welding Institution, 2014, 35(5): 75-79.(in Chinese)

[7] 李兴泉，邓兆祥，李传兵，等. 模态综合的子结构主模态截断方法[J]. 西南交通大学学报, 2014,49(1):173-178.

Li Xingquan, Deng Zhaoxiang, Li Chuanbing, et al. Substructure Normal Modes Selection Method for Component Mode Synthesis [J]. Journal of Southwest Jiaotong University, 2014,49(1): 173-178. (in Chinese)

[8] 扶原放，金达锋，乔蔚炜. 惯性释放原理在车架结构优化设计中的应用[J]. 机械设计与研究, 2009, 25(1): 65-67.

Fu Yuangfang, Jin Dafeng, Qiao Weiwei. Application of inertia relief in vehicle frame structure optimization [J]. Machine Design and Research, 2009, 25(1): 65-67. (in Chinese)

Control of Hysteresis Nonlinearity for Scanning Stage in Scanning Tunneling Microscope

JIHongli1,SUNHongjun1,QIUJinhao1,CHENYuansheng2,ZHUKongjun1

(1.State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics Nanjing ,210016, China) (2.School of Energy and Power Engineering, Nanjing University of Science and Technology Nanjing, 210094, China)

Abstract Piezoelectric actuators have been widely applied in scanning tunneling microscope (STM). A controller combining inverse hysteresis model and PID control law was designed for the STM to compensate for the hysteresis nonlinearity of piezoelectric actuators and to improve the scanning accuracy. For the purpose of comparing the proposed controller with classical displacement feedback control law, experimental system was built in this investigation. The relative measuring error of grating period and width of grating line were 4.41% and 2.65% using the classic displacement feedback control method respectively. And they were reduced to 1.26% and 0.27% in proposed method. Experimental results indicate that the error caused by hysteresis nonlinearity has been well compensated, and the scanning accuracy is improved with the help of such controller.

Keywords scanning tunneling microscope; piezoelectric actuator; hysteresis control; scanning control

Compressed Sensing and Reconstruction Method Based on Sparsity in Phase Space

WENGuangrui,LUANRiwei,RENYanhui,MAZaichao

(Mechanical Engineering College of Xi′an Jiaotong University Xi′an, 710049, China)

Abstract Aiming at the poor frequency sparsity of the vibration signal from a rotating machinery, which is interfered with strong noise and represented by the conventional FFT, a compressed sensing based on the sparsity in phase space is proposed to realize the signal reconstruction with orthogonal matching pursuit (OMP). First, the frequency sparsity is improved by reconstructing the original signal in a phase space and then principal components analysis (PCA) is implemented to extract the features in the constructed space; second, a random gauss matrix and OMP are adopted respectively to compress and reconstruct the improved signal. Analysis of the simulation signal and the misalignment signal of a rotor system suggest that the proposed method can enhance the frequency sparsity of the investigated signal. Moreover, the efficient compression and the accurate reconstruction of the investigated signal have also been realized.

Keywords compressed sensing; phase space reconstruction; principal component analysis; orthogonal matching pursuit

Research on the Identification in of Waveness Error in Diamond Fly Cutting for KDP Crystals

YANGHong,WANGBaorui,JIfang,LIUYouhai,XIAHuan,CHENDongsheng

(Institute of Machinery Manufacturing Technology, CAEP Mianyang, 621900, China)

Abstract Frequency identification is the prerequisite for eliminating or reducing ripple wave error in ultra-precision diamond fly cutting on KDP crystals. To address this problem, a method for the identification of the ripple waves error of diamond fly cutting trajectory based on spatial frequency transformation was proposed. The method calculated the spatial frequencies of ripple wave error according to the fly cutting profile of the arc-shaped trajectories. Then, the accurate separation of the characteristic frequencies was realized when the frequencies were transformed in time . The contrast between the characteristic frequencies of wave error with the cutting vibration frequencies and the natural frequencies of air spindle showed that the self-excited vibration at the natural frequencies of air spindle under intermittent cutting forces and the forced vibration from the motor was the primary reasons for ripple wave erro. Base on the above conclusion, by optimizing the structure and drive of the air spindle, the RMS value at PSD1 band (2.5～33 mm) of KDP crystal fly cutting surface reduced from 53 nm to 12 nm.

Keywords diamond fly cutting; ripple wave error; spatial frequency; KDP crystal

Analysis on Process of Vortex-induced Vibration of Risers Based on FBG Sensing Technology

LIPeng1,2,WANGLai1,2,GUOHaiyan3,WANGFei1,2,ZHANGYongbo4

(1.College of Architecture and Civil Engineering，Shandong University of Science and Technology Qingdao, 266590，China)(2.Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation,Shandong University of Science and Technology Qingdao, 266590, China)(3.College of Engineering， Ocean University of China Qingdao, 266100， China)(4.National Oceanographic Center of Qingdao Qingdao, 266071， China)

Abstract To further investigate the applicability of fiber Bragg grating (FBG)sensors sensing technology for testing of vortex-induced vibration(VIV) of deep-sea risers, this paper describes laboratory tests of VIV of a model deep-sea riser in a uniform current, which were carried out in a wind-wave-current flume. The riser model, 1.5 m long and with a slenderness ratio of 83.33, was tested in conditions in which the upper 0.75 m was in air, while the lower 0.75 m was exposed to a uniform current. FBG sensors were used for data acquisition and dynamic strain sensors were used for comparison. By changing the external flow velocity, the difference of the VIV process of the riser attained by two different sensors was analyzed and the vibration performance of the riser such as dominant frequency, amplitude and modal response based on frequency analysis and modal theory were researched implemented. The results indicate that requirement of FBG technology for testing of VIV of deep-sea risers can be wonderful satisfied. The vibration performance of the riser is accurately demonstrated. Modal characteristics and VIV process of the riser accompanying external flow velocity process are clearly reflected. The instantaneity and self-excitation of generation of the ‘lock-in’ region is found clearly.

Keywords FBG sensors; uniform current; marine riser; vortex-induced vibration(VIV); process analysis

Roller Bearing Fault Diagnosis Method Based on LMD-CM-PCA

FUYunxiao1,2,JIALimin1,3,QINYong1,3,YANGJie1

(1.State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University Beijing, 100044, China)(2.School of Electric Engineering, Beijing Jiaotong University Beijing, 100044, China)(3.Beijing Research Center of Urban Traffic Information Sensing and Service Technologies,Beijing Jiaotong University Beijing, 100044, China)

Abstract It is necessary to improve the visual robust fault identification ability of roller bearing in non-stationary operating condition. To achieve it, LMD-CM-PCA approach was proposed. First, based on roller bearing vibration acceleration signals, local mean decomposition(LMD) was applied to extract product function (PF) sample matrix. Second, the discrete correntropy and Pearson product-moment correlation coefficient (PPCC) of PF and primary signal were calculated. Correntropy was modified by PPCC as the amplitude modulation (AM) of correntropy. Then, the correntropy matrix (CM) of the samples was constructed with AM-correntropy being itselements. Finally, principal component analysis (PCA) was employed to implement the integration of CM with the largest variance accumulated contribution rate as the evaluation index. Integrated CM (ICM) of vibration datum under mixed operating conditions was calculated in slight fault and serious fault situations both. The visual results indicated that ICM could isolate operating condition better and separate faults under different fault severity levels more robustly than traditional characteristics, such as energy moment and spectral kurtosis, do. Above all, application of ICM ,like roller bearing fault features provides more effective technical support for roller bearing fault intuitively diagnosis so that it can support applications in fault diagnosis and safety early warning fields.

Keywords local mean decomposition(LMD); integrated correntropy matrix(ICM); principal component analysis(PCA); roller bearing; fault diagnosis; visualization

Study of Fault Classification for Single Channel Signal Based on SDICA

CHENJianguo1,WANGZhen1,LIHongkun2

(1.Department of Mechanical Engineering, Dalian University Dalian, 116622, China)(2.Institute of Vibration Engineering ,Dalian University of Technology Dalian, 116023, China)

Abstract A fault classification method based on Subband decomposition independent component analysis (SDICA) is presented for an engineering single sensor signal. The intrinsic mode functions obtained by the empirical mode decomposition(EMD) method are used as subband signal, and are processed by independent component analysis (ICA) theory, the residual mutual information is extracted in the process of ICA separation, the approximate entropy is abstracted in the estimated subband signal acquired by the SDICA, the characteristic parameters composed by residual mutual information and approximate entropy are used as input of the generalized regression neural network (GRNN) to realize the fault classification. The SDICA import the ICA theory in the single sensor signal actual fault classification, and the engineering single channel bearing signal achieve completely correct classification of three fault type, this method proves the residual mutual information and estimated subband approximate entropy can be importent classification character.

Keywords fault classification; feature extraction; generalized regression neural network; subband decomposition independent component analysis

Experimental Researches for Broadband Piezoelectric Vibration Energy Harvester

WANGGuangqing，YUEYuqiu，ZHANYongzheng，LIXiaojun，GAOShuaishuai

(School of Information and Electronics Engineering, Zhejiang Gongshang University Hangzhou, 310018, China)

Abstract To improve the output performances of the linear resonant piezoelectric vibration energy harvester (PVEH), a two-degree of freedom broadband piezoelectric vibration energy harvester (BPVEH) is developed. The experimental setup used to test the BPVEH performances is established. The effects of the stiffness ratio and the load resistor on the output performances of the BPVEH are studied by experiments. The results have shown that BPVEH can not only broaden the operational frequency bandwidth, but also improve the output voltage and the output power by adjusting the stiffness ratio. The bandwidth of the BPVEH is 7 times of the PVEH, and the maximum output power is 4.5 times of the PVEH when the base acceleration is 40 m/s2and the load resistor is 471 kΩ.

Keywords broadband; piezoelectric vibration energy harvester; elastic magnifier; prototype model

Mechanical Study on Enveloping Characteristics for New Mechanical Elastic Wheel

WANGQiang,ZHAOYouqun,LINFen,DUXianbin,FUHongxun

(College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract The enveloping mechanical characteristics of new mechanical elastic wheel (MEW) were studied using the finite element analysis and test method in this paper. According to the analysis of vertical mechanical characteristics of MEW under the effect of plane and obstacles, the influence of types of cleats on variation regularity of vertical mechanical response was revealed, moreover, the reliability of the finite element model was verified. The MEW-enveloping characteristics while traversing the three different cross-section obstacles at low speed were investigated by the nonlinear finite element model and the bench testing. The vertical and longitudinal dynamic mechanical response while traversing different obstacles were illustrated, and the influence of load and types of cleats on enveloping characteristics were analyzed. The results showed that the vertical force curves were from a parabola to a camel back shape with the increase of load. The longitudinal force response increased with the increase of the load, and the curves were similar to the sine shape. And the vertical and longitudinal force response increased with the increase of the height of the obstacle. Furthermore, the vertical and longitudinal mechanical response peak was relatively low, changed slowly, and the MEW had the typical enveloping characteristics under the certain load.

Keywords mechanical elastic wheel; enveloping characteristics; vertical stiffness; cleat; mechanical response

Performance Test and Analysis of Piezoelectric Motor Drive System Based on DSP

ZHANGTiemin,LIAOYiyong,XUZhilin,LIShenghua,LIANGLi

(College of Engineering, South China Agricultural University Guangzhou, 510642, China)

Abstract In order to realize the large-stroke and high-resolution movement of advanced manufacturing industry, the new liner piezoelectric motor that composes with the ultrasonic motor and the piezoelectric ceramic drive in the structure is proposed. Therefore, the large-stoke and high-resolution drive system that achieve the integration of the macro and micro drive system is proposed. The system realizes the seamless switching between AC and DC voltage. When working in the macro-drive state, it can output two adjustable phase (-90°～90°) and adjustable frequency (10 kHz～60 kHz) AC voltage. When working in the micro-drive state, it outputs the adjustable DC voltage. The controller based on TMS320F28335 processes and controls the state of the drive system. The chip PA85 is used to form DC amplifier stabilization circuit which can output the adjustable high DC voltage for the system. According to the influences on the controlled object which has non-linear, time-varying and coupling characteristics, the control algorithm of fuzzy adaptive incremental PID is proposed. The experiments results show that the outputs of the drive system have been improved obviously by the modification of the regulator. Moreover, using the rotary ultrasonic motor and the new liner piezoelectric motor to test the drive system, the results show that the control accuracy of phase and frequency is 5°and 0.5 kHz, which can drive two types of piezoelectric motor in a good state, and has good generality.

Keywords drive system； AC/DC； macro/micro drive system； digital signal processing; PID control

Using Sub-harmonic Resonance to Detect Bolted Joint Looseness

QUWenzhong,ZHANGMengyang,ZHOUJunyu,XIAOLi

(Department of Engineering Mechanics, Wuhan University Wuhan, 430072， China)

Abstract Bolted-joint structures are prone to loosening under vibration, which affects the structural integrity. This paper presents a bolt looseness recognition method based on the sub-harmonic resonance analysis. The bolted-joint structure was simplified to a nonlinear single-degree-of-freedom (SDOF) model, and the multi-scale method was used to explain the sub-harmonic resonance. Experiments were performed on an aluminum beam with a loosened-bolted simulating the damage. Two surface-bonded piezoelectric transducers were used to generate continuous sinusoidal excitation and receive corresponding wave signals. The experimental results demonstrated that the sub-harmonic components appeared when subject to the excitation frequency twice of the natural value, which can be effective on bolt looseness damage detection.

Keywords bolt looseness; damage detection; method of multiple scales; subharmonic

Frequency Reliability Analysis for Transmission System in Engine Valve Train

YANGZhou,LIUYang,ZHANGYimin

(School of Mechanical Engineering and Automation, Northeastern University Shenyang, 110819, China)

Abstract In order to develop the performance of the transmission system of the engine's valve mechanism and to reduce the resonance invalidation，we defined the quasi-failure resonance state of the transmission system based on the rule that absolute value of difference between the natural frequency of the transmission system and the cam vibration frequency cannot go over the specified threshold. According to the perturbation theory and reliability technology，we derived the expression of the probability of the quasi-failure with normal random variables and put forward the analysis method of reliability to decrease the vibration. Finally, we set the simplified model as an example and calculated the reliability of this system with the proposed method and the Monte Carlo method respectively. Numerical results confirmed that practicability of the proposed method which can avoid the resonance invalidation of valve-train by analyzing the effect of vibration.

Keywords valve train; vibration and impact; transmission system; frequency analysis; reliability

Fault Diagnosis of Hydraulic Pump Based on Symbolic Dynamics Entropy and SVM

ZHANGHua，ZENGWentao，YANWei

(School of Machinery & Automation， Wuhan University of Science and Technology Wuhan， 430081， China)

Abstract In the light of the problem that the early fault feature signal of the hydraulic pump is weak and the fault feature is difficult to extract, a fault diagnosis method of hydraulic pump based on symbolic dynamics entropy and support vector machine(SVM) was proposed. Nine kinds of fault states of hydraulic pump were simulated, and the sample values of the vibration signal of the multi measurement points were measured then, the symbolic dynamics entropyHkof each vibration signal were calculated using time series symbolic dynamics entropy to determine the corresponding symbol dynamics entropy feature vector of each state. Finally, the training set of feature vectors in different status was established for SVM to diagnose and identify the fault state of hydraulic pump, the accuracy of the test was 98.71%.The comparison of the diagnostic results with the improved BP neural network showed that the method has a higher recognition rate of 98.71% and cost less time which helps in online diagnosis．

Keywords hydraulic pump; fault diagnosis; symbolic dynamics entropy; support vector machine

Damage Detection for Shear Frame Structure Based on the Substructure ARMAX Model

LUOJun1，LIUGang1,2，HUANGZongming1,2

(1.College of Civil Engineering, Chongqing University Chongqing, 400045, China)(2.The Key Laboratory of New Technology for Construction of Cities in Mountain Area of the Ministry of Education,Chongqing University Chongqing, 400045, China)

Abstract A damage identification method is proposed to identify the damage of a shear frame structure. First, the substructure division method is proposed based on the motion equation of the shear frame and the center difference method. Next, the order determination method of autoregressive moving-average with exogenous inputs(ARMAX) model for the substructure is proposed based on the comparison with ARMAX model and the motion equation of the substructure. Then, the vector is extracted from the elements of the ARMAX coefficient variables as a damage vector, and the Mahalanobis distance of the damage vector is defined as the damage feature. Finally, the area under a receiver operating characteristic curve is used to localize the damage and the Bhattacharyya distance is used to quantify the magnitude of the damage. Results from a simulated model and a frame structure shows that the damage location and severity of a shear frame structure can be successfully identified and a reasonable amount of noise can be eliminated.

Keywords damage detection; substructure approach; ARMAX model; shear frame structure; statistical identification

Optimal Layout of Tuned Mass Damper on Biaxial Eccentric Structure Based on Parameter Identification

HEHaoxiang1,LÜYongwei1,2,HANEnzhen1

(1.Beijing Laboratory of Earthquake Engineering and Structure Retrofit, Beijing University of Technology Beijing, 100124, China)(2.Patent Examination Cooperation Center of the State Intellectual Property Office in Tianjin Tianjin, 300000, China)

Abstract The seismic responses of engineering structure can be dramatically reduced by the energy dissipation from tuned mass damper (TMD). For the actual eccentric structure, the eccentricity values are hard to be determined, however, the control efficiency will decline if the TMD is simply installed not considering the real eccentricities. Hence, the optimal install location of TMD needs to be studied in details. Under the condition that the eccentricity of actual multidimensional structure is difficult to be obtained accurately, a parameter identification method based on extend Kalman filter (EKF) is presented in order to simultaneously identify the structural mass, the horizontal stiffness and the eccentricities in two horizontal vectors, thus the optimal location of TMD can be determined based on the real physical parameter. As an example, an asymmetric reinforced concrete frame structure is analyzed based on free vibration responses and EKF, and the parameters such as the integrated eccentricities are accurately identified, and the seismic responses for different locations of TMD are compared. The results show that the parameters can be identified accurately with EKF, and best control rate can be obtained after choosing the rational locations, this method has superior feasibility in engineering practice.

Keywords seismic control; eccentric structure; tuned mass damper; parameter identification; extend Kalman filter

Analysis of Mode and Vibration Fatigue Life of Beam with Multiple Cracks

MAYijiang,CHENGuoping

(State Key Laboratory of Mechanics and Control for Mechanical Structures,Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract An analytical method is proposed to predict the fatigue life of the beam with multiple cracks based on the Paris equation. In the modal analysis process, the segment of cracks is replaced with bending springs, a new method for solving natural modes of the beam with multiple cracks is proposed based on the transfer matrix method, and the effect of the number, locations and depths of cracks on the natural frequency of the cracked beam is analyzed. In the vibration fatigue analysis, the effect of the number of cracks on the crack-tip stress intensity factor under harmonic excitation is analyzed. Considering the interaction of cracked beam vibration and fatigue crack growth, the effect of the number and the location of the cracks on the cracked beam fatigue life is analyzed based on timing analysis and Paris equation. The results indicate that the number, locations and depths of cracks have important effects on the modal parameters and the fatigue life of the structure.

Keywords cracked beam; transfer matrix method; natural frequency; vibration fatigue

Study on Vibration Characteristics of Marine Steam Turbine Rotor Shaft Coupling With Disk

SUNYuanli,LIZhaojun

(Naval Academy of Armamant Beijing, 100161, China)

Abstract Base on small aspect ratio modeling theory, the finite element of rotor shaft coupling with disk was established, and the vibration characteristics of marine steam turbine rotor were analyzed with different modeling methods such as oblique cutting way and disk unit. Then, the significant influences of different modeling methods on the vibration characteristics of the rotor system were studied. The additional modes of rotor bearing system generated by disk unit represented as coupling vibration mode between disk and rotor shaft. The calculation method based on disk-unit model accurately described the vibration characteristics of the rotor shaft coupling with disk. For thicker disk, the disk had less effect on the rotor coupling vibration. The oblique cutting model commonly used in engineering generated additional stiffness and caused larger error in the solving process. This kind of error gradually reduced with the decreasing of the disk thickness.

Keywords rotor shaft coupling with disk; finite element model; disk element; vibration characteristics

Dynamic Analysis of a Flexible Nonlinear Synchronous Vibration Pile System

ZHANGNan1,QIUYanchao1,ZHANGXueliang2,WENBangchun2

(1.Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, Beijing University of Civil Engineering and Architecture Beijing, 102616, China)(2.School of Mechanical Engineering and Automation, Northeastern University Shenyang, 110819, China)

Abstract The dynamic characteristics of the flexible nonlinear synchronous vibration pile system were studied. The nonlinear dynamic models of the system were proposed to analyze the nonlinear stiffness of the soil, which were induced by the relationship between the nonlinear stress and the strain in the soil. The periodic solutions of the system were investigated using Lyapunov function of the amplitude-frequency characteristic equation for the nonlinear models. The amplitude-frequency characteristics were analyzed through the selected parameters. The dynamic characteristics of the system were presented for the changes of system parameters (including the vibrating frequency, the stiffness of the soil and the damping of the soil, the radius of the eccentric block), which are induced by the amplitude-frequency characteristics. Finally, the stable solution of multiple periodic solutions can be obtained by the different initial conditions, using Runge-Kutta method. The stability of periodic solutions was theoretically analyzed by theory and verified by simulation, and the influence of different parameters on the periodic solution was presented.

Keywords nonlinear vibration; amplitude frequency; stability; synchronous vibrating pile system

Wind-Induced Responses Analysis for the Typical Transmission Tower with Narrow Base Based on an Aero-Elastic Model Wind Tunnel Test

ZHANGQinghua1，MAWenyong2，ZHAOLong2,3

(1.School of Civil Engineering and Communication, North China University of Water Resources and Electric Power Zhengzhou, 450000, China)(2.Wind Engineering Research Center, Shijiazhuang Tiedao University Shijiazhuang, 050043, China)(3.CRL Group, China Railway Tunnel Survey & Design Institute Co., Ltd Tianjin, 300133, China)

Abstract Based on the discrete stiffness method, aero-elastic model for the typical transmission tower with narrow base (TTNB) was firstly made. Then the displacements and accelerations of the TTNB under various heights and wind directions were investigated through boundary layer wind tunnel tests. Finally, based on the wind tunnel test data, the wind-induced vibration coefficients of TTNB were calculated and compared with Chinese architectural structure load standards. The results showed that the mean displacements on the TTNB were mostly in the along-wind direction; but, the along-wind and across-wind fluctuating displacements and accelerations were in the same order of magnitude and cannot be ignored. Moreover, the fluctuating responses did not change remarkably with the variation of wind directions; however, the heights above ground had different influence on fluctuating displacements and accelerations. In addition, since the high-order modes had influence on the dynamic displacement responses, the wind-induced vibration coefficients which were only deduced from the first-order displacement response would be lower. And the wind-induced vibration coefficients obtained from Chinese architectural structure load standards were bigger than that from the wind tunnel tests.

Keywords transmission tower; aero-elastic model; wind tunnel test; wind-induced responses; wind-induced vibration coefficients

Vibration State of Remanufactured Engine Based on Sensitive IMF

CHENChengfa1,2,BAIYunchuan1,ZHANGYingfeng1,JIAOYufei1,LIShumin1

(1.Department of Automobile Engineering, Military Transportation University Tianjin, 300161, China)(2.State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University Tianjin, 300072, China)

Abstract In order to improve the quality of remanufactured engine, ensemble empirical mode decomposition(EEMD) decomposition and sensitive intrinsic mode function(IMF) selection algorithm is introduced in the study of remanufactured engine performance. Based on the EEMD decomposition, interrelated coefficient is drawn into the study of IMF, the interrelation between the IMF weight and original signal is analyzed, the original signal IMF weight’s sensitive determination is computed, then the sensitive IMF Hilbert commutation is used, and the vibration condition is analyzed. The results show that, using the EEMD decomposition algorithm and sensitive IMF marginal spectrum can reflect the vibration state on different parts of remanufactured engine. Cylinder, cylinder head, crankshaft, the sensitive frequency region of these three parts is different. Through the study of vibration condition of main parts, using manufacture technology, thus providing technology to improve Remanufactured Engine level.

Keywords sensitive IMF; vibration state; remanufactured engine; marginal spectrum

Feature Extraction Method Based on Empirical Mode Decomposition and Bispectrum Analysis

JIANGYonghua,LIRongqiang,JIAOWeidong,TANGChao,CAIJiancheng,SHIJizhong

(Institute of Precision Machinery, Zhejiang Normal University Jinhua, 321004, China)

Abstract In view of the deficiency of traditional bispectrum that has good insensitivity to independent Gaussian noise but is incapable of avoiding the disturbance of non-Gaussian noise, a new feature extraction method based on EMD and bispectrum analysis is proposed. Firstly, decompose the signal by EMD. Then, energy-related method is applied to removal the illusive intrinsic mode functions (IMFs) of EMD. Finally, bispectrum analysis is applied to the real IMFs to extract the fault feature. The results of experiment and practical signals analysis show that the proposed method is feasible and effective for extracting feature of rolling bearing, and it is more effective compared with traditional power spectral analysis and traditional bispectrum analysis.

Keywords empirical mode decomposition(EMD); bispectrum analysis; energy-related; feature extraction; intrinsic mode function(IMF)

Investigation on Longitudinal Vibration of Hollow Shaft Based on Dynamic Vibration Absorber

ZHAOShuai，CHENQian，YAOBing

(State Key Laboratory of Mechanics and Control of Mechanical Structures，Nanjing University of Aeronautics and Astronautics Nanjing, 210016, China)

Abstract With the increasing size of ship, the damage of the longitudinal vibration of shaft is increasingly exposed. This paper adopted a damping vibration absorber to attenuate longitudinal vibration of the hollow shaft system, established the dynamic model of shaft with dynamic vibration absorber combining with the substructure synthetic method and transfer matrix method, and analyzed the frequency response function of shaft under harmonic excitation, which is verified by the traditional finite element method using ANSYS software. The theoretical calculation and simulation results showed that the frequency response function curve near the resonance frequency turned to smooth by adding dynamic vibration absorber. A dynamic vibration absorber is designed and then an experimental verification is conducted. The testing results show that the resonance peak is strongly attenuated when dynamic vibration absorber attached to the shaft, which indicates the attenuation effect of dynamic vibration absorber is obvious. Based on hollow characteristics of a large marine propulsion shafting system, a DVA can be installed into the void location of the hollow shafting, which saves space and has a good absorption performance, can be a new choice in the control of longitudinal vibration of marine propulsion shafting system in future.

Keywords hollow shaft； longitudinal vibration； dynamic vibration absorber； transfer matrix method； substructure synthetic method

Study on Effect of Subsystem on Vibration Isolation Performance of Two-Stage Vibration Isolation System

CHENJun1,YANBing1,SUNMeiyun2,SHIWeizhen1,LUZhiwen1,DONGDawei1

(1.School of Mechanical Engineering, Southwest Jiaotong University Chengdu, 610031, China)(2.Tangshan Railway Vehicle Co., Ltd Tangshan, 063000, China)

Abstract Since there is little study on subsystem parameters design for powerpack two-stage isolation system attached with a subsystem, experimental method was adopted to tackle the situation. Effects of subsystem parameters (isolator general stiffness, isolator damp, isolator stiffness ratio) on vibration isolation performance and dynamic characteristics of a certain diesel multiple unit powerpack two-stage vibration isolation system were studied. The results showed that the powerpack two-stage vibration isolation system had excellent vibration isolation performance in both conventional condition and shutdown condition of engine when the subsystem act as a vibration absorber of the main system. And a better vibration isolation performance can be obtained with proper value of the stiffness of subsystem isolators, damping and stiffness ratio.

Keywords subsystem; diesel multiple unit powerpack; two-stage vibration isolation system; vibration isolation performance

Rapid Precision Diagnosis of Non-uniform Scroll Part Based on Reverse Engineering

WUZaixin，LIUTao，WUJun

(School of Mechanical and Electronical Engineering, Lanzhou University of Technology Lanzhou, 730050, China)

Abstract Non-uniform scroll parts are more difficult to be examed with traditional fixtures and calibration precision is relatively low because of their compicated shape. In response to the above feature, an approach of rapid precision diagnosis of non-uniform scroll part based on reverse engineering is presented. First a 3D solid model of non-uniform scroll part was created in the Pro/E environment and used as the reference model, and then cloud data of the scroll part machined was collected using the ROMER measuring arm and treated as digital model. The two models are compared to abtain machining precision information of the scroll part. Graphics-directed matching principle of mathematical models is proposed to improve alignment precision of the digital model. In this approach, alignment of multi-look cloud data, de-noising of scattered cloud data and data compacting integrated by random and curvature sampling are adopted to decrease the data-processing error. Analysis of 2D, 3D and geometric tolerance evaluation between the reference and digital models show that the machining precision and geometric tolerance of the presented non-uniform scroll part are satisfied. This study provides a rapid, accurate and visual method of precision diagnosis for complex-surfaced mechanical products.

Keywords reverse engineering; non-uniform scroll part; precision diagnosis; cloud data; digital model

The Blade Vibration Measurement Research Based on the Key Phase Interpolation Method

WANGWeimin，RENSanqun，CHENLifang，SHAOHuajin

(Beijing Key Laboratory of Health Monitoring Control and Fault Self-recovery for High-end Machinery,Beijing University of Chemical Technology Beijing, 100029, China)

Abstract This paper studied the effect of speed fluctuation on the accuracy of blade tip timing and corresponding solution. Based on the method of blade tip timing (BTT), key phase interpolation method is introduced to solve the larger error caused by speed rise (deceleration) or speed fluctuation with once per revolution probe, while it can also be adaptive under the constant speed operation. First, the simulation model was established to compare the results of the key phase interpolation method with the result of the single phase under different frequencies and speed fluctuations. Finally, tests were carried out by the simulant test platform and real impeller test bench. The results showed that the accuracy of results were significantly improved by using key phase interpolation method when the fluctuation period was large or the amplitude of rotation speed fluctuation was big. Because the vibration signal may be affected by the rotor axial displacement, test data in real impeller test bench needs further research.

Keywords blade tip timing (BTT); blades vibration; speed fluctuation; once per revolution probe; key phase interpolation method (KPIM)

Model Updating and Validation for Bearing-Rotor System at Working Speed Considering Model-Form Error

ZHANGBaoqiang1,GUOQintao2,YUANXiukai1

(1.School of Aerospace Engineering, Xiamen University Xiamen, 361005, China)(2.College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics Nanjing, 210016, China)

Abstract Structure dynamical model updating and validation for bearing-rotor system at working speed considering model-form error is presented. The theory of model-form error, model updating based on complex eigenvalue sensitivity analysis is successfully accomplished in this piece of work. The updating for simulation example about flexible rotor-bearing system at working speed, considering model-form error, is performed to bearing stiffness, bearing damping and diameter moment of inertia parameters using wheel frequency and damping as objective residues. The updated model is validated through unbalance response prediction. The simulation results show that the maximum residual errors of updated parameter is still -10.1%, but the maximum residual errors for the real part of updated eigenvalue is 0.95% and for the imaginary part is -1.15% even taking into 2% model-form error account in model updating. The unbalance response prediction of the updated model matches the target model unbalance response quite well. The results, in no doubt, proved the effectiveness and robustness of the model updating method considering model-form error using wheel frequency and damping for bearing-rotor system at working speed.

Keywords model updating; model-form error; rotor dynamics; working speed; validation

Displacement Measurement of Free-Piston Stirling Engine Based on Strain Gauge

LIWei1,2,MOUJian1,2,HONGGuotong1

(1.Technical Institute of Physics and Chemistry, Chinese Academy of Sciences Beijing, 100190, China)(2.University of Chinese Academy of Sciences Beijing, 100049, China)

Abstract Combining the structure characteristics of free-piston Stirling engine, a kind of dynamic displacement measurement that the strain gauge are used to measure indirectly the displacement of displacer and piston by responding to shape change of plate spring is put forward. On the basis of strain-resistance effect and bridge principle of strain indicator, a set of dynamic displacement measurement system based on strain gauge is built up, and experimental data are compared with the data gotten from static displacement measurement. The experimental testing results indicate the data from dynamic displacement measurement are not exactly the same as the data from static displacement measurement, and the attaching position of strain gauge directly affected the accuracy of measurement.

Keywords free-piston Stirling engine; dynamic displacement measurement; strain gauge; plate spring

Analysis Method for Discretization Dynamics of TRUM with Stator Teeth Structure

SUNHexu1,2,3,JINGKai1,2,DONGYan1,2,LIGuoqing1,2

(1.School of Control Science and Engineering, Hebei University of Technology Tianjin, 300130, China)(2.Hebei Control Engineering Technology Research Center Tianjin, 300130, China)(3.School of Electrical Engineering, Hebei University of Science and Technology Shijiazhuang, 050018, China)

Abstract This paper puts forward an analysis method for the dynamics of the contact interface of travelling-wave rotary ultrasonic motors (TRUMs) by discreting the stator/rotor interface to avoid the complexity non-linear deduction of the motor in the recent researches. First, the surface-contact of each stator tooth was equivalent to point-contact, for which the concept of equivalent stiffness of different contact states was proposed to analyze the contact states. The discrete axial forces between the stator teeth and rotor were described as the equivalent stiffness, and the equivalent force between the stator and the rotor was obtained. Thus, the relative movement of the stator and the rotor was calculated, and the axial dynamics characteristics of the stator and the rotor were gained. Then, the radial and circumferential friction was given by the three-dimensional motion in the interface to study the mechanical characteristics and the energy consumption. The final simulations and experiments demonstrated the accurate description of the interface dynamics by the proposed method.

Keywords travelling-wave rotary ultrasonic motor; stator teeth; contact interface; discretization; dynamics

ANFIS Method to Remove Background Vibration from Traffic Environment Vibration Measured Data

GENGChuanfei1,2,LUWenliang1,YUXing3

(1.School of Civil Engineering, Beijing Jiaotong University Beijing, 100044, China)(2.China Railway Siyuan Survey and Design Group Co.,Ltd Wuhan, 430063, China)(3.Jin Liwen Railway Limited Liability Company Wenzhou, 325003, China)

Abstract In the field of data test, environment vibration signals induced by rail transit and background vibration signals are inseparable. A new adaptive neuro-fuzzy inference system (ANFIS) method is put forward. Basic principle to banish background vibration is discussed, and the implementation steps of ANFIS are determined. A background vibration acceleration time history is superimposed on a ground vibration induced by a train to synthesize a testing field vibration record, which is used to remove background vibration by the proposed ANFIS method and other existing methods. The comparative analysis of results is carried out. The root mean square errors of time history curves calculated by these methods are 0.414 mm/s2with the Fourier amplitude revising method, 0.363 mm/s2with the auto power spectral density (PSD) method, 0.261 mm/s2with auto-cross PSD method and 0.074 mm/s2with the proposed ANFIS method, respectively. The error of ANFIS method is minimal. Also the weighted vibration levelVLzvalues are 63.842 dB with vibration level revising method, 62.894 dB with Fourier amplitude revising method, 63.859 dB with auto PSD method, 63.802 dB with auto-cross PSD method and 63.805 dB with ANFIS method, respectively. The calculation value of ANFIS method is the closest to real value 63.815 dB. The results show that the time history, Fourier spectrum, power spectral density and vibration level obtained with the new ANFIS method are extremely close to true ones of traffic vibration, and the errors are relatively smaller than those of other existing approaches.

Keywords rail transit; environment vibration; measured data; background vibration; adaptive neuro-fuzzy inference system (ANFIS) method; auto power spectral density (PSD) method; auto-cross power spectral density (PSD) method

Fatigue Analysis for Bogie Frame Based on Rigid-Flexible Coupling Simulation

LIAOAihua,HUANGXu,FANGYu

(College of Urban Railway Transportation, Shanghai University of Engineering Science Shanghai, 201620, China)

Abstract Bogie frame is one of the important parts of an urban subway vehicle, but it usually occurs to fatigue crack. Traditional dynamic characteristic analysis for bogie frame is generally based on multi-body dynamics simulation and finite element analysis, this method is suitable for the structural natural frequency away from the external loading frequency, consequently its result has certain limitations. In order to study dynamic response characteristics and fatigue strength of a bogie frame，a rigid-flexible coupled multi-body dynamic model of the bogie frame is established based on the finite element analysis method and the rigid-flexible multi-body dynamics theory. The dynamic stress response of bogie frame is carried out based on rigid-flexible coupling multibody dynamic model of the metro vehicle, from which vibration characteristics of this type of the bogie frame can be obtained. Then, failure mechanism of the bogie frame can be obtained based on fatigue analysis of local fatigue areas of the bogie frame. The stress time histories of its bogie frame necessary for fatigue analysis are calculated with the results of the multi-body dynamic simulation taken as the dynamic load by using the finite element analysis method. The fatigue life of the bogie frame is predicted by using the quasi-static stress superposition method. The calculation results show regions of the bogie frame with excessively large stress amplitude are concentrated on the motor hanger region, gear box hanger region and the connected region between the beam and side beams. The simulation result conforms to the location of actual fatigue bogie damage on this frame, thus verifying the correctness of the method on structure fatigue analysis based on the rigid-flexible coupled model. The shortest lifetime of the motor hanger obtained from the simulation is 1 530 000 km. The error of the result of simulation and the actual data is 10%, which illustrates high credibility and accuracy of the simulation.

Keywords bogie frame； multi-body dynamics； rigid-flexible coupling； fatigue life

(End of the Volume 36)

《振动、测试与诊断》征稿简则

一、征稿范围

《振动、测试与诊断》主要刊登有关振动利用、动态测试和故障诊断的标准、测试理论和测试手段的论文，包括试验测试技术、测试仪器的研制方法和系统组成、信号分析、数据处理、参数识别、故障诊断以及有关装置的设计、使用、控制、标定和校准等。不拘泥于行业(如机械、交通、农业、生物、能源、航空、航天、航海、建筑、地震等)和测试项目(如振动、冲击、力位移、噪声等)。

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三、编辑部地址: 南京市御道街29号《振动、测试与诊断》编辑部(210016)

网址：http:∥zdcs.nuaa.edu.cn 电话、传真: 025-84893332 E-mail:qchen@nuaa.edu.cn

The high firing precision has been continuously required by modern war for weapon systems such as multiple launch rocket system, artillery, tank and armored vehicle. However, bad firing precision, huge consumption of rockets in test and launch unsafety are hard technical problems restricting the development of these modern weapon systems. The firing precision and the launch safety depend on dynamics of the corresponding weapon system. As an engineering subject studying the motion and force for weapon system during launch process, launch dynamics has been a novel sally port to improve the firing precision and to ensure launch safety of weapon systems. In this paper, the theory and technology of launch dynamics of multibody system as well as its applications in the design and test of firing precision and safety for weapon systems are studied. It can provide new theory and technology for the design and test of firing precision and safety of weapons．

firing precision; consumption of rockets in test; launch safety; launch dynamics of multibody system; transfer matrix method for multibody systems

*上海市研究生教育创新计划学位点引导布局与建设培育资助项目(13SC002)；上海市自然科学基金资助项目(15ZR1419200)

2015-04-01；

2015-05-21

10.16450/j.cnki.issn.1004-6801.2017.02.030

TH113

廖爱华，女，1978年1月生，博士、副教授。主要研究方向为车辆结构动力学、有限元分析及车辆故障诊断等。曾发表《A numerical simulation of elastoplastic contact analysis of compressor by overspeeding》(《Advances in Mechanical Engineering》2014，No.4)等论文。 E-mail:aiwa7816@126.com

New Developments in Launch Dynamics of Multibody System and Its Applications

RUIXiaoting

(Institute of Launch Dynamics, Nanjing University of Science and Technology Nanjing, 210094, China)