Multi-Flexible-Body Dynamic Analysis of
底盘衬套对整车平顺性影响灵敏度分析
收稿日期：2018－09－19基金项目：湖南省科技发展计划（专项）资金（2016WK2042）；长沙市2015科技人才创新创业专项资金（kc1701017）作者简介：王彬（1979—），男，硕士，研究方向为汽车整车性能集成开发。
E-mail ：wang_bingle@ 。
DOI ：10.19466/ki.1674－1986.2019.02.004底盘衬套对整车平顺性影响灵敏度分析王彬（湖南湖大艾盛汽车技术开发有限公司，湖南长沙410205）摘要：应用ADAMS 软件建立包含柔性体车身的刚柔耦合整车多体动力学模型，结合仿真分析和试验测试来研究底盘衬套对平顺性的影响。
选取底盘衬套Z 向刚度作为试验因素，对整车进行随机不平路面下的低频振动测试，并根据试验结果进行极差分析，得出各底盘衬套对整车平顺性的灵敏度结果。
关键词：刚柔耦合；平顺性；灵敏度中图分类号：U463.1文献标志码：B文章编号：1674－1986（2019）02－014－05Sensitivity Analysis of the Effect of Chassis Bushing on Vehicle Ｒide ComfortWANG Bin（Hunan Aisn Auto Ｒ＆D Co．，Ltd．，Changsha Hunan 410205，China ）Abstract ：The Multi-body dynamic model of rigid-flexible coupling vehicle with flexible body was established by using ADAMS software ，and the influence of chassis bushing on ride comfort was studied with test and simulation analysis．By selecting the Z -direction stiffness of the chassis bushing as the test factor ，the low frequency vibration test of the whole vehicle was carried out on the random uneven pavement．The range analysis was carried out according to the test results ，and the sensitivity results of each chassis bushing on the vehicle ride comfort were obtained．Keywords ：Ｒigid-flex coupling ；Ｒide comfort ；Sensitivity0引言平顺性是指汽车在行驶过程中产生的振动和冲击环境对乘员舒适性的影响保持在一定界限之内的能力［1］。
adams知识点总结
adams知识点总结Adams is a multi-body dynamics simulation software used to analyze the motion and behavior of mechanical systems. It is widely used in the automotive, aerospace, and industrial machinery industries to test and validate designs before physical prototypes are built. Adams is known for its ability to accurately predict the performance of complex systems and its user-friendly interface.Key features of Adams include advanced modeling, flexible analysis, and robust post-processing capabilities. The software allows users to create detailed models of mechanical systems, define complex interactions between components, and simulate various operating conditions to predict the system's behavior. In this summary, we will explore the key knowledge points of Adams and how they are used in engineering design and analysis.1. ModelingOne of the key knowledge points in Adams is modeling, which refers to the creation of a digital representation of a mechanical system. Adams offers a wide range of modeling tools to help users build accurate and detailed models of their systems. These tools include parametric modeling, flexible bodies, and contact modeling.Parametric modeling allows users to define their systems using mathematical equations and parameters, making it easy to create complex and customizable models. Flexible bodies enable users to model the deformations and dynamic behavior of components, such as gears, springs, and rubber mounts. Contact modeling allows users to simulate the interactions between bodies in a system, such as collisions, friction, and wear.By using these modeling tools, engineers can create highly realistic digital models of their systems, which can be used to predict the behavior of the physical system under various conditions.2. AnalysisAnother key knowledge point in Adams is analysis, which refers to the process of simulating the behavior of a mechanical system using the digital model. Adams offers a wide range of analysis tools to help users simulate and analyze complex mechanical systems. These tools include dynamic analysis, kinematic analysis, and optimization.Dynamic analysis allows users to simulate the motion and behavior of a mechanical system under various operating conditions, such as acceleration, braking, and cornering. This type of analysis is essential for predicting the performance and safety of systems, such as vehicle suspensions, steering systems, and drivetrains. Kinematic analysis allows users to study the motion and interactions between components in a system, without considering forces and torques. This type of analysis is often used to study mechanisms, such as linkages, cams, and gears.Optimization allows users to find the best design parameters for a given system, such as the shape of a component, the material properties, or the operating conditions. This type of analysis is used to improve the performance, efficiency, and reliability of mechanical systems, such as gears, bearings, and structural components.By using these analysis tools, engineers can gain valuable insights into the behavior of their systems, which can be used to optimize designs and improve the performance and reliability of mechanical systems.3. Post-processingThe final key knowledge point in Adams is post-processing, which refers to the visualization and interpretation of the results from the simulation. Adams offers a wide range of post-processing tools to help users visualize and interpret the behavior of their systems. These tools include animation, plotting, and reporting.Animation allows users to visualize the motion and behavior of their systems in a dynamic and interactive way. This type of post-processing is essential for understanding the kinematics and dynamics of systems, such as vehicle suspensions, engine systems, and gearboxes. Plotting allows users to generate graphs and charts to visualize and interpret the results from the simulation, such as the motion, forces, and torques of components. Reporting allows users to generate detailed reports of the results from the simulation, such as the performance, safety, and reliability of the system. This type of post-processing is essential for communicating the results of the analysis to other stakeholders, such as managers, engineers, and customers.By using these post-processing tools, engineers can gain valuable insights into the behavior of their systems, which can be used to make informed decisions about design changes and improvements.In conclusion, Adams is a powerful multi-body dynamics simulation software used to analyze the motion and behavior of mechanical systems. It offers advanced modeling, flexible analysis, and robust post-processing capabilities to help engineers create detailed models, simulate the behavior, and interpret the results of complex systems. By using these knowledge points, engineers can optimize designs, improve the performance, and ensure the reliability of mechanical systems in various industries.。
基于ADAMSCar的汽车悬架系统_动力学建模与仿真分析毕业设计
毕业设计（论文）题目：基于ADAMS/Car的汽车悬架系统动力学建模与仿真分析毕业设计（论文）原创性声明和使用授权说明原创性声明本人郑重承诺：所呈交的毕业设计（论文），是我个人在指导教师的指导下进行的研究工作及取得的成果。
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作者签名：日期：年月日导师签名：日期：年月日指导教师评价：一、撰写（设计）过程1、学生在论文（设计）过程中的治学态度、工作精神□优□良□中□及格□不及格2、学生掌握专业知识、技能的扎实程度□优□良□中□及格□不及格3、学生综合运用所学知识和专业技能分析和解决问题的能力□优□良□中□及格□不及格4、研究方法的科学性；技术线路的可行性；设计方案的合理性□优□良□中□及格□不及格5、完成毕业论文（设计）期间的出勤情况□优□良□中□及格□不及格二、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格三、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格建议成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）指导教师：（签名）单位：（盖章）年月日评阅教师评价：一、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格二、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格建议成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）评阅教师：（签名）单位：（盖章）年月日教研室（或答辩小组）及教学系意见教研室（或答辩小组）评价：一、答辩过程1、毕业论文（设计）的基本要点和见解的叙述情况□优□良□中□及格□不及格2、对答辩问题的反应、理解、表达情况□优□良□中□及格□不及格3、学生答辩过程中的精神状态□优□良□中□及格□不及格二、论文（设计）质量1、论文（设计）的整体结构是否符合撰写规范？□优□良□中□及格□不及格2、是否完成指定的论文（设计）任务（包括装订及附件）？□优□良□中□及格□不及格三、论文（设计）水平1、论文（设计）的理论意义或对解决实际问题的指导意义□优□良□中□及格□不及格2、论文的观念是否有新意？设计是否有创意？□优□良□中□及格□不及格3、论文（设计说明书）所体现的整体水平□优□良□中□及格□不及格评定成绩：□优□良□中□及格□不及格（在所选等级前的□内画“√”）教研室主任（或答辩小组组长）：（签名）年月日教学系意见：系主任：（签名）年月日********大学毕业设计（论文）任务书姓名：院（系）：专业：班号：任务起至日期：毕业设计（论文）题目：基于ADAMS/Car汽车悬架系统动力学建模与仿真分析立题的目的和意义：汽车悬架是车架（或车身）与车轴（或车轮）之间的弹性联结装置的统称。
多体动力学模型 英文
多体动力学模型英文英文回答：Multi-body dynamics (MBD) modeling is a powerful tool used to analyze the behavior of complex mechanical systems consisting of multiple rigid or flexible bodies connected by joints and constraints. It employs advanced numerical techniques to simulate the dynamic interactions between these bodies, considering factors such as gravity, external forces, and contact forces.MBD models are commonly utilized in various engineering disciplines, including automotive, aerospace, robotics, and biomedical engineering. Engineers leverage MBD software to design, analyze, and optimize systems ranging from vehicles to industrial machinery and human bodies.The primary advantages of MBD modeling include:Accurate representation of complex systems: MBD modelscapture the intricate interactions and behaviors of multi-body systems, which can be challenging to analyze using traditional methods.Insight into system dynamics: MBD simulations provide valuable insights into the dynamic behavior of a system, allowing engineers to assess its stability, performance,and safety.Optimization of system design: By analyzing MBD models, engineers can identify potential design improvements, optimize component interactions, and enhance overall system performance.Virtual prototyping: MBD models enable virtual prototyping, reducing the need for physical prototypes and accelerating the product development process.Collaboration and communication: MBD models facilitate collaboration among engineers from different disciplines, providing a shared platform for design analysis and optimization.The process of creating an MBD model typically involves the following steps:1. Modeling the geometry: The physical geometry of the system is defined using CAD software or other modeling tools.2. Defining joints and constraints: The connections and constraints between bodies are specified, defining the permissible motions and interactions.3. Applying loads and boundary conditions: External forces, gravity, and other boundary conditions are applied to the model.4. Solving the equations of motion: Numerical integration methods are employed to solve the equations of motion, simulating the dynamic behavior of the system.5. Analyzing the results: The simulation outputs are analyzed to extract insights about system dynamics,performance, and potential design improvements.中文回答：多体动力学模型。
汽车盘式制动分析毕业设计论文
3
制动器刚体模型分析........................................................................................................15 3.1 多刚体系统动力学................................................................................................. 15 3.1.1 3.1.2 3.1.3 3.1.4 3.2 多刚体系统的坐标系...................................................................................15 多刚体系统组成成分...................................................................................15 多刚体系统的自由度...................................................................................16 多刚体系统的动力学方程...........................................................................16
关键词：盘式制动器；虚拟样机；振动；多柔体模型
I
沈阳理工大学学士学位论文
Abstract
With the development of the economy,the vehicles have been one of the best means of transportation in modern time.Because the brakes play an important part in the vehicles’Safety and Comfort,how to reduce the cars’brake vibration and noise has become an important research topic. First the paper introduced the history of brakes.the research status of brake vibration,then introduced a multi-body dynamic model of the basic theory and self-excited vibration theoretical of the disc brake vibration.All these theories provide a feasible means for further develop.Next,introduced how to build the flexible multi-body of the brake system using the FEA technology and the multi-body dynamic technology.Including hhow to get the model neutral file(MNF)of the brake disc and brake pad by utilizing the FEA technology.In the process of building the MNF,the free model analysis of the brake disc and pads were studied.Introduced the process of the multi-body dynamics modeling:import flexible bodies and rigid bodies,in order to calculate accurately,should gave the rigid bodies a certain material properties,add the constraints between the disc and brake pads were achieved by the contact command. The brake angular velocity and acceleration curves can be carried out by dynamical simulation and analysis.The flexible multi-body model not only concerned the flexibility deformation of the components of the brake system,but also concerned the influence of moment of inertia of the rotating components of the automobile,so the simulation was more reasonable.The method of building the flexible multi-body model is universal and it can be useful for future disk brake noise analysis and structural optimization design.
Recurdyn介绍
新一代的系统级多体动力学分析软件—虚拟产品设计开发工具RecurDyn (Recursive Dynamic)是由韩国FunctionBay公司基于其划时代算法——递归算法开发出的新一代多体系统动力学仿真软件。
它采用相对坐标系运动方程理论和完全递归算法，非常适合于求解大规模及复杂接触的多体系统动力学问题。
传统的动力学分析软件对于机构中普遍存在的接触碰撞问题解决得远远不够完善，这其中包括过多的简化、求解效率低下、求解稳定性差等问题，难以满足工程应用的需要。
基于此，韩国FunctionBay 公司充分利用最新的多体动力学理论，基于相对坐标系建模和递归求解，开发出RecurDyn软件。
该软件具有令人震撼的求解速度与稳定性，成功地解决了机构接触碰撞中上述问题，极大地拓展了多体动力学软件的应用范围。
RecurDyn不但可以解决传统的运动学与动力学问题，同时是解决工程中机构接触碰撞问题的专家。
RecurDyn 借助于其特有的MFBD(Multi Flexible Body Dynamics)多柔体动力学分析技术，可以更加真实地分析出机构运动中的部件的变形，应力，应变。
RecurDyn 中的MFBD技术用于分析柔性体的大变形非线性问题，以及柔性体之间的接触，柔性体和刚性体相互之间的接触问题。
传统的多体动力学分析软件只可以考虑柔性体的线型变形，对于大变形，非线性，以及柔性体之间的相互接触就无能为力了。
RecurDyn 中为用户提供了完整的解决方案，包含控制，电子，液压以及CFD，为用户的产品开发提供了完整的产品虚拟仿真、开发平台。
RecurDyn 的专业模块还包括，送纸机构模块，齿轮元件模块，链条分析模块，皮带分析模块，高速运动履带分析模块，低速运动履带分析模块，轮胎模块，发动机开发设计模块。
鉴于RecurDyn的强大功能，软件广泛应用航空、航天、军事车辆、军事装备、工程机械、电器设备、娱乐设备、汽车卡车、铁道、船舶机械及其它通用机械等行业。
英语力学词汇英汉对译
力学词汇英汉对译通类名词力学 mechanics牛顿力学 Newtonian mechanics经典力学 classical mechanics静力学 statics运动学 kinematics动力学 dynamics动理学 kinetics宏观力学 macroscopic mechanics,macromechanics细观力学 mesomechanics微观力学 microscopic mechanics,micromechanics一般力学 general mechanics固体力学 solid mechanics流体力学 fluid mechanics理论力学 theoretical mechanics应用力学 applied mechanics工程力学 engineering mechanics实验力学 experimental mechanics计算力学 computational mechanics理性力学 rational mechanics物理力学 physical mechanics地球动力学 geodynamics力 force作用点 point of action作用线 line of action力系 system of forces力系的简化 reduction of force system等效力系 equivalent force system刚体 rigid body力的可传性 transmissibility of force平行四边形定则 parallelogram rule力三角形 force triangle力多边形 force polygon零力系 null-force system平衡 equilibrium力的平衡 equilibrium of forces平衡条件 equilibrium condition平衡位置 equilibrium position平衡态 equilibrium state分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿--雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables 阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method 并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot参量[激励]振动 parametric vibration 模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu-bov-Mitropol'skii method 马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法 harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态 natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB method, Wentzel-Kramers-Brillouin method 缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱 cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振 surge摆振 shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform.陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法 Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support-foundation system 静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动 half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk楔 wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff-Muskhelishvili method 基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforced Plate 中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳 Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳 Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱 Wrinkle塑性全量理论 Total theory of plasticity 滑动 Sliding微滑 Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的 Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振 Flutter弹性波 Elastic wave简单波 Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波 Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波 Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔 Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透 Perforation层裂 Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem 静力安定定理 Static shake-down theorem率相关理论 rate dependent theorem载荷因子 load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷 step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态 hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment累积塑性应变 accumulated plastic strain永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material 刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material材料稳定性 stability of material应变偏张量 deviatoric tensor of strain应力偏张量 deviatori tensor of stress应变球张量 spherical tensor of strain应力球张量 spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material 极限分析 limit analysis极限设计 limit design极限面 limit surface上限定理 upper bound theorem上屈服点 upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面 initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section沙堆比拟 sand heap analogy屈服 Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissible Field流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory of Plasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间 Haigh-Westergaard stress space 洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程 Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶 Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法 moment distribution method 力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法 matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method 屈曲模态 buckling mode复合材料力学 mechanics of composites复合材料 composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料 foamed composite颗粒复合材料 particulate composite层板 Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片 Ply多胞固体 cellular solid膨胀 Expansion压实 Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变 ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracture mechanics, LEFM 弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM 断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹 Crack裂缝 Flaw缺陷 Defect割缝 Slit微裂纹 Microcrack折裂 Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角 crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle, CTOA裂尖张开位移 crack tip opening displacement, CTOD裂尖奇异场 crack tip singularity Field 裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂 crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factor HRR场 Hutchinson-Rice-Rosengren Field 守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度 strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区 heat affected zone, HAZ延脆转变温度 brittle-ductile transition temperature剪切带 shear band剪切唇 shear lip无损检测 non-destructive inspection双边缺口试件 double edge notched specimen, DEN specimen单边缺口试件 single edge notched specimen, SEN specimen三点弯曲试件 three point bending specimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen 中心裂纹板试件 center cracked panel specimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服 large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic risk assessment, PRA损伤力学 damage mechanics损伤 Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳 Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片 crack gage裂纹扩展 crack growth, crack Propagation 裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stress Analysis 工作[应变]片 active[strain] gage基底材料 backing material应力计 stress gage零[点]飘移 zero shift, zero drift应变测量 strain measurement应变计 strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计 bonded foiled gage粘贴丝式应变计 bonded wire gage桥路平衡 bridge balancing电容应变计 capacitance strain gage补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage 半导体应变计 semiconductor strain Gage集流器 slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equal Displacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe光程差 optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope实时全息干涉法 real-time holographic interferometry 网格法 grid method全息光弹性法 holo-photoelasticity全息图 Hologram全息照相 Holograph全息干涉法 holographic interferometry全息云纹法 holographic moire technique全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑 Speckle错位散斑干涉法 speckle-shearing interferometry, shearography 散斑图 Specklegram白光散斑法 white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation of Coordinates计算结构力学 computational structural mechanics加权残量法 weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle赫林格-赖斯纳原理 Hellinger-Reissner Principle 修正变分原理 modified variational Principle约束变分原理 constrained variational Principle 混合法 mixed method杂交法 hybrid method边界解法 boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition自然边界条件 natural boundary condition离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element 拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffness Matrices 载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数 test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化 minimization of band width 波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法 determinant search method 逐步法 step-by-step method纽马克法 Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法 mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体力学流体动力学 fluid dynamics连续介质力学 mechanics of continuous media 介质 medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid 连续介质假设 continuous medium hypothesis 流体运动学 fluid kinematics水静力学 hydrostatics液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程 Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowski condition 布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid质量守恒 conservation of mass动量守恒 conservation of momentum能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线 stream line流面 stream surface流管 stream tube迹线 path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge 涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street 马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform. flow非均匀流 nonuniform. flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流 unsteady flow, non-steady flow 暂态流 transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow浮体 floating body定倾中心 metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口 exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量 added mass ,associated mass 收缩 contraction镜象法 image method无量纲参数 dimensionless parameter 几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源 source汇 sink速度[水]头 velocity head拐角流 corner flow空泡流 cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流 wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速 stall脱体激波 detached shock wave波阻 wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数 critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex综合类：广义连续统力学 generalized continuum mechanics简单物质 simple material纯力学物质 purely mechanical material微分型物质 material of differential type积分型物质 material of integral type混合物组份 constituents of a mixture非协调理论 incompatibility theory微极理论 micropolar theory决定性原理 principle of determinism等存在原理 principle of equipresence局部作用原理 principle of objectivity客观性原理 principle of objectivity电磁连续统理论 theory of electromagnetic continuum 内时理论 endochronic theory非局部理论 nonlocal theory混合物理论 theory of mixtures里夫林-矣里克森张量 Rivlin-Ericksen tensor声张量 acoustic tensor半向同性张量 hemitropic tensor各向同性张量 isotropic tensor应变张量 strain tensor伸缩张量 stretch tensor连续旋错 continuous dislination连续位错 continuous dislocation动量矩平衡 angular momentum balance余本构关系 complementary constitutive relations共旋导数 co-rotational derivative, Jaumann derivative 非完整分量 anholonomic component爬升效应 climbing effect协调条件 compatibility condition错综度 complexity当时构形 current configuration能量平衡 energy balance变形梯度 deformation gradient有限弹性 finite elasticity熵增 entropy production标架无差异性 frame. indifference弹性势 elastic potential熵不等式 entropy inequality极分解 polar decomposition低弹性 hypoelasticity参考构形 reference configuration响应泛函 response functional动量平衡 momentum balance奇异面 singular surface贮能函数 stored-energy function内部约束 internal constraint物理分量 physical components本原元 primitive element普适变形 universal deformation速度梯度 velocity gradient测粘流动 viscometric flow当地导数 local derivative岩石力学 rock mechanics原始岩体应力 virgin rock stress构造应力 tectonic stress三轴压缩试验 three-axial compression test 三轴拉伸试验 three-axial tensile test三轴试验 triaxial test岩层静态应力 lithostatic stress吕荣 lugeon地压强 geostatic pressure水力劈裂 hydraulic fracture咬合[作用] interlocking内禀抗剪强度 intrinsic shear strength循环抗剪强度 cyclic shear strength残余抗剪强度 residual shear strength土力学 soil mechanics孔隙比 void ratio内磨擦角 angle of internal friction休止角 angle of repose孔隙率 porosity围压 ambient pressure渗透系数 coefficient of permeability [抗]剪切角 angle of shear resistance渗流力 seepage force表观粘聚力 apparent cohesion粘聚力 cohesion稠度 consistency固结 consolidation主固结 primary consolidation次固结 secondary consolidation固结仪 consolidometer浮升力 uplift扩容 dilatancy有效应力 effective stress絮凝[作用] flocculation主动土压力 active earth pressure 被动土压力 passive earth pressure 土动力学 soil dynamics应力解除 stress relief次时间效应 secondary time effect 贯入阻力 penetration resistance 沙土液化 liquefaction of sand泥流 mud flow多相流 multiphase flow马格努斯效应 Magnus effect韦伯数 Weber number环状流 annular flow泡状流 bubble flow层状流 stratified flow平衡流 equilibrium flow二组份流 two-component flow冻结流 frozen flow均质流 homogeneous flow二相流 two-phase flow。
在非惯性系中研究动力刚化问题
在非惯性系中研究动力刚化问题梁立孚;王鹏;宋海燕【摘要】Correct understanding of the dynamic stiffening problem is signality for further researching spacecraft dynamics and establishing a rational numerical model of flexible body dynamics. The dynamic stiffening problem was studied using the theory of a mechanical problem in a non-inertial coordinate system. Two kinds of numerical models for the dynamic stiffening problem were established. The physical meaning of the dynamic stiffening problem was clarified. The approach of correct zero-order modeling was explored. There is a substantive difference between the research of this paper and the research of other scholars.%正确认识动力刚化问题,对深入研究航天器动力学和合理建立柔体动力学的数值计算模型意义重大.应用非惯性坐标系中的力学问题的理论来研究动力刚化问题,给出两类研究动力刚化问题的计算模型,明确了动力刚化问题的物理意义,探索了正确处理零次建模的途径.这样处理动力刚化问题,表现出与其他学者的研究有实质性的差异.【期刊名称】《哈尔滨工程大学学报》【年(卷),期】2012(033)008【总页数】5页(P1052-1056)【关键词】动力刚化;非惯性坐标系;柔体;刚体;航天器动力学【作者】梁立孚;王鹏;宋海燕【作者单位】哈尔滨工程大学力学一级学科博士点,黑龙江哈尔滨150001;上海大学应用数学与力学研究所,上海200444;哈尔滨工程大学力学一级学科博士点,黑龙江哈尔滨150001【正文语种】中文【中图分类】O313文献［1］指出，1987 年 Kane［2］对大范围刚体运动槽型弹性梁进行了研究，指出在大范围刚体运动作高速旋转时，零次耦合建模方法得到弹性梁的变形将无限增大的结果，与实际情况相反.为此，Kane对弹性梁的变形作了比较精确的描述(包括了弯曲变形、剪切变形和扭曲变形)，首次提出动力刚化(dynamic stiffening)的概念.这一问题的提出，引起了各国学者的普遍关注.1989年，Banerjee和Kane［3］又对作大范围刚体运动的弹性薄板进行了研究.Haering［4］，Padilla ［5］采用类似方法对弹性梁动力学性质进行了分析.所得到的结果表明，人们在关于柔性多体系统动力学耦合机理的认识上有待深入，对所描述对象数学模型的准确性有待进一步研究.为了适应我国航天事业发展的需要，我国学者也对这一问题进行了广泛的、深入的研究［6-12］.以上研究，多数是数值的、定量的分析方法，少数学者进行解析的分析讨论.正确的进行解析分析对于深刻把握动力刚化的力学实质、建立正确的数值计算模型是有利的.因此，有必要继续研究下去.在文献［1，12］中，通过一个典型的实例进行研究，本文在其基础上，应用非惯性坐标系中的力学问题的理论来研究动力刚化问题，给出两类研究动力刚化问题的计算模型，得到具有明确物理意义的研究结果.从物理和数学方面说明了产生零级耦合建模的不合理现象的原因，并且建议了合理的处理方法，以便避免零级耦合建模中可能发生不合理现象.这样处理动力刚化问题，表现出与其他学者的研究有实质性的差异.1 在非惯性系中典型实例研究设有如图1所示的力学系统，2根无质量杆AB和BC在B点用铰链连接，在铰链处有一个刚度系数为k的扭簧.长度为R的杆AB的另一端固定在铰链A上，并且绕A点以角速度ω(t)在平面中转动.长度为L的杆BC的另一端固定着质量块m.杆AB和BC之间的相对转角为θ(t)，并且在系统的运动过程中，θ(t)可以为有限量，也可以为小量，其初始值为0.图1 非惯性坐标系Fig.1 Non-inertial coordinate system建立固连于杆AB的连体坐标系Bb1b2(如图1)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，如前所述θ(t)可以为有限量，也可以为小量.通过运动分析，可得系统的动能为作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在转角θ(t)为有限量假设的情况下，离心惯性力fcf为引起的力矩为切向惯性力ft为引起的力矩为其外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式［13-15］，因此Lagrange方程可以表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得整理可得这里顺便指出，方程式(13)是以角位移θ为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2RLsin θ为离心惯性力引起的力矩，m(Rcosθ+L)L为切向惯性力引起的力矩.2 进一步典型实例研究建立固连于杆AB的连体坐标系Bb1b2(图1)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，假设θ(t)始终为小角，使得sin θ≈θ，cos θ≈1.通过运动分析，可得系统的动能为作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在θ(t)始终为小角假设的情况下，离心惯性力的计算公式为引起的力矩为切向惯性力的计算公式为引起的力矩为其外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为(R+L)，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式［13-15］，因此Lagrange方程可以表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得进而可得动力刚度项式(26)明确显示，在这个典型实例中，引起动力刚化的原因是离心惯性力的影响.这里顺便指出，方程式(25)是以角位移为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2RLθ为离心惯性力引起的力矩，m(R+L)L为切向惯性力引起的力矩.本节处理问题的过程，与一般文献中所提及的零级耦合建模相似，只是这里是在非惯性坐标系中研究问题的，而一般文献中多数是在惯性坐标系中.以上论述表明，在非惯性系中合理的处理问题，所谓的零次建模也是可行的.这一点也可说明在非惯性坐标系中研究动力刚化问题的优越性.3 典型实例的另一类计算模型研究建立固连于杆AB的连体坐标系Bb1b2(图2)，由于杆的转动，使得该坐标系成为非惯性坐标系.在这个非惯性坐标系中，假设θ(t)始终为小角，使得sin θ≈θ，cos θ≈1 .通过运动分析，可以得系统的动能为图2 θ(t)始终为小角Fig.2 θ(t)always small angle作用在系统上的力矩，除了弹性力矩kθ外，还有惯性力矩.在θ(t)始终为小角假设的情况下，离心惯性力的计算公式为引起的力矩为将离心惯性力作为主动力引起的附加势能为这一结果与文献［12］给出的结果相同.切向惯性力的计算公式为引起的力矩为将切向惯性力作为主动力引起的附加势能为系统的总外力势能为在建立动能和势能的表达式时，应当注意:以角速度ω转动的转动中心是A点，该点与质量m的距离为(R+L)，以角速度转动的转动中心是B点，该点与质量m的距离为L.根据广义协变原理，在非惯性坐标系中，只要合理引入惯性力，就可以将相关力学定律表示为与在惯性系中类似的形式，因此Lagrange方程可表示为将动能的表达式和势能的表达式代入Lagrange方程的各项，并且推导如下:将推导结果代入Lagrange方程，可得进而可得动力刚度项为式(42)明确显示，在这个典型实例中，引起动力刚化的原因是离心惯性力的影响.这里顺便指出，方程式(41)是以角位移为基本变量的动力学方程.mL2为动力学项，kθ为扭簧引起的力矩，mω2(R+L)Lθ为离心惯性力引起的力矩，m(R+L)L为切向惯性力引起的力矩.4 讨论零级建模如果在应用Lagrange方程之前，对势能函数应用泰勒展开并且取一级近似，可得可见，将使得离心惯性力引起的外力势能消失.这从物理方面说明了所谓零级建模不可行的原因.正弦函数和余弦函数的泰勒展开为如果在应用Lagrange方程之前，对势能函数应用泰勒展开.以往的简化是将正弦函数和余弦函数的泰勒展开都取一级近似.考虑到正弦函数的泰勒级数收敛较快，余弦函数的泰勒级数的收敛较慢，因而取正弦函数的泰勒展开的一级近似，取余弦函数的泰勒展开的二次近似，可得势能的表达式:可见，式(46)与式(18)相同，这也可以从一个侧面说明这样处理问题的正确性.将势能的表达式代入Lagrange方程的有关势能的项，并且推导如下:动能的表达式及其相关推导同前.将推导结果代入Lagrange方程，可得整理可得可见，在应用Lagrange方程之前简化，只要合理进行近似计算，也可以得到合理的建模.具体问题具体分析对于科技工作者来说是至关重要的.研究表明，考虑动力刚化的柔体动力学的建模问题，内容丰富，可以分门别类的进行研究.5 结束语本文是在非惯性坐标系中研究动力刚化问题.首先，给出在非惯性坐标系中研究动力刚化典型实例的一类力学模型，应用有限位移理论研究动力刚化问题的典型实例，得到具有明确物理意义的结果.将这类研究退化到小位移理论，表明所谓零次耦合建模方法也是可行的.然后，给出在非惯性坐标系中研究动力刚化典型实例的另一类力学模型.最后，进一步讨论了如何正确地进行所谓零次耦合建模的问题.参考文献:【相关文献】［1］洪嘉振，蒋丽忠.动力刚化与多体系统刚-柔耦合动力学［J］.计算力学学报，1999，16(3):295-301.HONG Jiazhen，JIANG Lizhong.Dynamic stiffening and multibody dynamics with coupled rigid and deformation motions［J］.Chinese Journal of Computational Mechanics，1999，16(3):295-301.［2］KANE T R，RYAN R R，BANER J A K，Dynamics of a cantilever beam attached to a moving base［J］.Journal of Guidance Control and Dynamics，1987，10(2):139-151.［3］BANERJEE A K，KANE T R.Multi-flexible body dynamics capturing movtion-induced stiffnes［J］.Journal of Applied Mechanics，1989，56:887-892.［4］HAERING W J，RYAN R R，SCOTT A.New formulation for flexible beams undergoing large overall plane motion［J］.Journal of Guidance，Control and Dynamics，1994，17(1):76-83.［5］PADILLA C E，VON FLOTOW A H.Nonlinear strain displacement relations and flexible multibody dynamics［J］.Journal of 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Shuxin，etal.Generally flexible multi-body system dynamics in consideration of dynamic stiffening terms［J］.Journal of Harbin Institute of Technology，2005，37(1):101-103.［11］章定国，朱志远.一类刚柔耦合系统的动力刚化分析［J］.南京理工大学学报，2006，30(1):21-25.ZHANG Dingguo，ZHU Zhiyuan.Dynamic stiffening of rigid-flexible coupling system［J］.Journal of Nanjing University of Science and Technology，2006，30(1):21-25. ［12］李东旭.挠性航天器结构动力学［M］.北京:科学出版社，2010:285-286.［13］爱因斯坦.相对论的意义［M］.郝建纲，刘道军译.上海:科技教育出版社，2005:36-51. ［14］邱吉宝，向树红，张正平.计算结构动力学［M］.合肥:中国科学技术大学出版社，2009:455-463.［15］梁立孚，刘石泉，王振清，等.飞行器结构动力学中的几个问题［M］.西安:西北工业大学出版社等五社联合出版，2010:158-172.。
多体动力学和非线性有限元联合仿真
A New Solution For Coupled Simulation Of Multi-Body Systems And Nonlinear Finite Element Models Giancarlo CONTI, Tanguy MERTENS, Tariq SINOKROT(LMS, A Siemens Business)Hiromichi AKAMATSU, Hitoshi KYOGOKU, Koji HATTORI(NISSAN Motor Co., Ltd.)1 IntroductionOne of the most common challenges for flexible multi-body systems is the ability to properly take into account the nonlinear effects that are present in many applications. One particular case where these effects play an important role is the dynamic modeling of twist beam axles in car suspensions: these components, connecting left and right trailing arms and designed in a way that allows for large torsional deformations, cannot be modeled as rigid bodies and represent a critical factor for the correct prediction of the full-vehicle dynamic behavior.The most common methods to represent the flexibility of any part in a multi-body mechanism are based on modal reduction techniques, usually referred to as Component Mode Synthesis (CMS) methods, which predict the deformation of a body starting from a preliminary modal analysis of the corresponding FE mesh. Several different methods have been developed and verified, but most of them can be considered as variations of the same approach based on a limited set of modes of the structure, calculated with the correct boundary conditions at each interface node with the rest of the mechanism, allowing to greatly reduce the size of system’s degrees of freedom from a large number of nodes to a small set of modal participation factors. By properly selecting the number and frequency range of the modes, as well as the boundary conditions at each interface node [1], it is possible to accurately predict the static and dynamic deformation of the flexible body with remarkable improvements in terms of CPU time: this makes these methods the standard approach to reproduce the flexibility of components in a multi-body environment. Still, an important limitation inherently lies in their own foundation: since displacements based on modal representation are by definition linear, any nonlinear phenomena cannot be correctly simulated. For example, large deformations like twist beam torsion during high lateral acceleration cornering maneuvers typically lead to geometric nonlinearities, preventing any linear solution from accurately predicting most of the suspension’s elasto-kinematic characteristics like toe angle variation, wheel center position, vertical stiffness.One possible solution to overcome these limitations while still working with linear modal reduction methods is the sub-structuring technique [2]: the whole flexible body is divided into sub-structures, which are connected by compatibility constraints preventing the relative motion of the nodes that lie between two adjacent sub-structures. Standard component mode synthesis methods are used in formulating the equations of motion, which are written in terms of generalized coordinates and modal participation factors of each sub-structure. The idea behind it is that each sub-portion of the whole flexible structure will undergo smaller deformations, hence remaining in the linear flexibility range. By properly selecting the cutting sections it is usually possible to improve the accuracy of results (at least in terms of nodal displacements: less accuracy can be expected for stress and strain distribution). Another limitation of these methods is the preliminary work needed to re-arrange the FE mesh, although some CAE products already offer automatic processes enabling the user to skip most of the re-meshing tasks and hence reducing the modeling efforts.An alternative approach to simulate the behavior of nonlinear flexible bodies is based on a co-simulation technique that uses a Multi-body System (MBS) solver and an external nonlinear Finite Element Analysis (FEA) solver. Using this technique one can model the flexible body in the external nonlinear FEA code and the rest of the car suspension system in the MBS environment. The loads due to the deformation of the body are calculated externally by the FEA solver and communicated to the MBS solver at designated points where the flexible body connects to the rest of the multi-body system. The MBS solver, on the other hand, calculates displacements and velocities of these points and communicates them to the nonlinear FEA solver to advance the simulation. This approach doesn’t suffer from the limitations that arise from the linear modeling of the flexibility of a body. This leads to more accurate results, albeit at the price of much larger CPU time. In fact, simulation results are strongly affected by the size of the communication time step between the two solvers: a better accuracy (and more stable solver convergence) can be generally obtained by using smaller time steps which require larger calculation times, as shown also in [3].2 Overview of the activityThis paper presents the results of a benchmark activity performed in collaboration with Nissan Auto where a new FE-MBS variable-step co-simulation technique was used: a coupling at the iteration level currently implemented in commercial FEA package LMS SAMCEF Mecano [4] and general purpose multi-body system package LMS b Motion [5]. In this technique each solver uses its own integrator but only one Newton solver is used. In this case one solver is designated as the master and will be responsible for solving the Newton iterations. The coupled iterations continue until both solvers satisfy their own solution tolerances and convergence is achieved. The co-simulation process is organized by means of a supervisor code that manages the data exchange and determines the new time step of integration for both solvers. Further technical details on this “coupled simulation“ method, as well as a comparison with the variable-step co-simulation method, are available in [6].A multi-body model of a rear twist beam suspension has been created, where the flexibility of the twist beam was simulated with three alternative modeling techniques to be compared:- Component Mode Synthesis (Craig-Bampton method)- Linear sub-structuring- Nonlinear FE-MBS coupled simulation.As a further step also the two bushings connecting the twist beam with the car body, originally modeled in b Motion as standard force elements with nonlinear stiffness and damping characteristics for all directions, have been replaced by two SAMCEF Mecano nonlinear flexible bodies.Two different suspension events have been simulated in order to compare the results from the different modeling methods:- Suspension roll (opposite wheel vertical travel applied at wheel centers)- Braking in turn (dynamic loads applied at wheel centers).Figure 1 shows the b Motion suspension model used for this activity, where the FE mesh models of twist beam and bushings are also displayed:3 Modeling and simulations3.1 Model validationAs a first step a multi-body model of rear suspension was created in b Motion with input data provided by Nissan Auto from a pre-existing model developed with another multi-body software package: hardpoints location, bodies mass and inertia data, kinematic and compliant connections characteristics, properties of coil springs, shock absorbers, end stop elements. Since the original model included a flexible twist beam based on a modal reduction method (Craig-Bampton) the same original mode set has been used to obtain a linear flexible representation of the twist beam in b Motion. Then a suspension roll has been simulated in both environments in order to validate Motion results with the data from the source model, obtained by applying a vertical displacement in opposite directions at the two wheel centers. The main elasto-kinematic suspension characteristics have been compared: toe and camber variation, wheel center longitudinal and lateral displacements, vertical stiffness. In fig.2 the vertical force at wheel center and the toe angle variation are plotted versus the wheel vertical displacement: the differences between the two models are negligible.Fig. 1b Motion multi-body model of rear suspension with flexible twist beam and bushings3.2 Flexible twist beam modeling Once validated the b Motion model, the linear flexible twist beam was replaced by the two alternative modeling methods intended to take into account the geometric nonlinearities due to the large deformations of the beam element: sub-structuring and coupled simulation Motion – Mecano.- Sub-structuring: the twist beam was cut in3 sections along the central pipe, resultingin 4 separate linear flexible bodies: the twolongitudinal arms + two symmetric halves ofthe beam. Figure 3 shows the three cuttingsections used.- Coupled simulation Motion – Mecano -starting from the original Nastran FE mesh, the dynamic behavior of the full twist beam is calculated by the SAMCEF Mecano nonlinear solver through a specific Analysis Case added to the VL Motion model.3.3 FE bushings modelingAs a further task of the activity, starting from the CAD representation of the geometry of the bushings connecting the twist beam with the car body a Mecano FE model of each bushing has been created and implemented into the b Motion mechanism to replace the original bushing force elements, modeled as nonlinear stiffness and damping curves in all six directions. Material properties for the rubber and metal parts of the bushings were not known in detail, so tentative values have been used for the rubber whereas the metal parts have been considered as rigid: although these assumptions were expected to have a major impact on results, the main purpose of this task was not to obtain accurate and correlated results, rather to prove the capability of the Motion-Mecano coupled simulation method to successfully solve multiple nonlinear flexible bodies in the same model.3.4 Results comparisonFigure 4 shows the results of the suspension roll analysis for two of the most relevant outputs for the handling performance of a car: toe angle and wheel track variation, plotted vs. left wheel vertical displacement. The main outcome is that sub-structuring and coupled Motion-Mecano simulation (not including FE bushings) give very similar results, both different from the linear case: as expected, the linear approach gives reliable results only in a limited range of displacements, whereas for larger deformations of the twist beam a more accurate prediction of the behavior of the system can be obtained only by considering the nonlinear flexibility of the body.In Fig.5 some of the results from the dynamic braking-in-turn maneuver are displayed, where during a cornering maneuver started at around 0.7s a braking force is applied after 1.5s. In this comparison the additional case with the two nonlinear FE bushings is also displayed: again, a remarkable difference can be detected between the linear case and the nonlinear FE-MBS coupled simulation; furthermore a clear effect from nonlinear FE bushings can be seen, although most likely affected by uncertainties on the material properties applied in the Mecano FE bushing models.Fig. 3 Sub-structuring of the linear flexible twist beam Fig. 2Comparison of results between b Motion model and source MBS model4 ConclusionsIn this paper the usage of a new FE-MBS co-simulation technique for an automotive application is compared with two alternative solutions to represent the nonlinear flexibility of a body in a multi-body mechanism. A b Motion rear suspension model with flexible twist beam has been created with the aim to simulate two typical handling events where the proper prediction of the large deformation of the twist beam strongly affects most of the elasto-kinematic characteristics of the suspension. The compared results show a clear difference between the linear approach, based on a modal representation of the flexibility of the body, and the alternative methods which allow a more correct prediction of the geometric nonlinearity.This new b Motion – SAMCEF Mecano co-simulation technique allows also the simulation of multiple nonlinear flexible bodies in the same mechanisms as shown in this paper. Further studies are currently on-going to extend the usage of this solution to complex applications like flexible contact and friction forces, nonlinear material properties, thermal effects.5 References[1] Yoo W.S., Haug E.J.: “Dynamics of flexible mechanical systems using vibration and static correctionmodes ”, Journal of Mechanisms, Transmissions and Automation in Design, 108, 315-322, 1985[2] Sinokrot T.Z., Nembrini M., Toso A., Prescott W.C.: "A Comparison Of Sub-Structuring Synthesis And TheCosimulation Approach In The Dynamic Simulation Of Flexible Multi-body Systems ", MULTIBODYDYNAMICS 2011, ECCOMAS Thematic Conference, Brussels, Belgium, 4-7 July 2011[3] Sinokrot T.Z., Nembrini M., Toso A., Prescott W.C.: "A Comparison Of Different Multi-body SystemApproaches In The Modeling Of Flexible Twist Beam Axles ", Proceedings of the 8th International Conference on Multi-body Systems, Nonlinear Dynamics, and Control, August 28-31, 2011, Washington D.C., USA[4] LMS International, b Online Help Manual , 2013.[5] LMS Samtech, Samcef Online Help Manual – version 15.1, 2013.[6] Sinokrot T., Jetteur P., Erdelyi H., Cugnon F., Prescott W.: "A New Technique for Stronger Couplingbetween Multi-body System and Nonlinear Finite Element Solvers in Co-simulation Environments ",MULTIBODY DYNAMICS 2013, ECCOMAS Thematic Conference, Zagreb, Croatia, 1-4 July 2013Fig. 4Suspension roll analysis: toe angle and wheel track variationsFig. 5Braking-in-turn analysis: wheel base and toe angle variations。
recurdyn软件简介
RecurDyn概述RecurDyn (Recursive Dynamic)是由韩国FunctionBay公司基于其划时代算法——递归算法开发出的新一代多体系统动力学仿真软件。
它采用相对坐标系运动方程理论和完全递归算法，非常适合于求解大规模及复杂接触的多体系统动力学问题。
传统的动力学分析软件对于机构中普遍存在的接触碰撞问题解决得远远不够完善，这其中包括过多的简化、求解效率低下、求解稳定性差等问题，难以满足工程应用的需要。
基于此，韩国FunctionBay 公司充分利用最新的多体动力学理论，基于相对坐标系建模和递归求解，开发出RecurDyn软件。
该软件具有令人震撼的求解速度与稳定性，成功地解决了机构接触碰撞中上述问题，极大地拓展了多体动力学软件的应用范围。
RecurDyn不但可以解决传统的运动学与动力学问题，同时是解决工程中机构接触碰撞问题的专家。
RecurDyn 借助于其特有的MFBD(Multi Flexible Body Dynamics)多柔体动力学分析技术，可以更加真实地分析出机构运动中的部件的变形，应力，应变。
RecurDyn 中的MFBD 技术用于分析柔性体的大变形非线性问题，以及柔性体之间的接触，柔性体和刚性体相互之间的接触问题。
传统的多体动力学分析软件只可以考虑柔性体的线型变形，对于大变形，非线性，以及柔性体之间的相互接触就无能为力了。
RecurDyn 给用户提供了一套完整的虚拟产品解决方案，可以和控制，流体，液压等集合在一起进行分析。
形成机、电、液一体化分析，为用户的产品开发提供了完整的产品虚拟仿真、开发平台。
RecurDyn 的专业模块还包括，送纸机构模块，齿轮元件模块，链条分析模块，皮带分析模块，高速运动履带分析模块，低速运动履带分析模块，轮胎模块，发动机开发设计模块。
鉴于RecurDyn的强大功能，软件广泛应用航空、航天、军事车辆、军事装备、工程机械、电器设备、娱乐设备、汽车卡车、铁道、船舶机械及其它通用机械等行业。
动力电池包载荷谱虚拟迭代分析
10.16638/ki.1671-7988.2019.14.001动力电池包载荷谱虚拟迭代分析陈玉祥，熊飞，朱林培，刘雄（广州汽车集团股份有限公司汽车工程研究院，广东广州511434）摘要：采用ADAMS建立车身-电池包刚柔耦合多体动力学模型以及电池包系统的六通道虚拟试验台。
基于电池包实测载荷谱，通过虚拟迭代分析，各通道的相对损伤值接近1，验证了迭代计算的收敛性。
研究方法对电池包的结构疲劳分析和振动响应特性研究具有重要的参考价值。
关键词：电池包；载荷谱；虚拟迭代中图分类号：U469.72 文献标识码：A 文章编号：1671-7988(2019)14-03-04Virtual iterative analysisof load spectrum for traction battery packChen Yuxiang, Xiong Fei, Zhu Linpei, Liu Xiong( Guangzhou Automobile Group Co., Ltd. Automotive Engineering Institute, Guangdong Guangzhou 511434 )Abstract: The rigid-flexible coupled multi-body dynamic model of the body-battery pack system used for virtual test bench was established by using ADAMS.Based on the measured load spectrum of the battery pack, the relative damage value of each channel was close to 1 through virtual iterative analysis, which verified the convergence of iterative calculation.The research method has important reference value for the structural fatigue analysis and vibration response research of battery pack.Keywords: Battery pack; Load spectrum; Virtual iterativeCLC NO.: U469.72 Document Code: A Article ID: 1671-7988(2019)14-03-04前言电池包系统是电动汽车核心系统之一，电池包良好的结构力学性能是电动汽车具备安全性和可靠性的基础。
木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真
第39卷第5期2023年9月森㊀林㊀工㊀程FOREST ENGINEERING Vol.39No.5 Sep.,2023doi:10.3969/j.issn.1006-8023.2023.05.016木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真任长清,王涛,丁星尘,丁禹程,杨春梅,宋文龙∗(东北林业大学机电工程学院,哈尔滨150040)摘㊀要:实现木窗的高质量加工,需要研究双端复合精铣加工机床主轴系统的动力学特性,可为其结构优化㊁减轻振动提供理论依据,使用软件Adams建立主轴系统的简化三维模型,计算铣床加工木窗时的切削力和主轴系统支承轴承刚度,并联合软件Ansys与Adams建立柔性主轴的刚柔耦合模型,对主轴系统进行刚性体模型和刚柔耦合模型的仿真,提取主轴质心㊁切削力作用点和带轮连接点处的X向㊁Y向㊁Z向的振动曲线㊂仿真结果表明,切削力作用点的X向和Z向振幅最大,且当主轴为柔性体时质心和切削力作用点的振幅要远远小于主轴为刚性时的情况㊂此研究结果表明,将主轴设为柔性体时的动力学特性更符合实际工作情况,3点的振动曲线为主轴系统的结构优化提供一定的理论依据㊂关键词:主轴系统;刚柔耦合模型;振动;动力学分析;仿真中图分类号:TS642㊀㊀㊀㊀文献标识码:A㊀㊀㊀文章编号:1006-8023(2023)05-0133-11Rigid-Flexible Coupled Dynamics Modeling and Simulation of Spindle System of Double-End Compound Finishing Milling MachineTool for Wooden WindowREN Changqing,WANG Tao,DING Xingchen,DING Yucheng,YANG Chunmei,SONG Wenlong∗(College of Mechanical and Electrical Engineering,Northeast Forestry University,Harbin150040,China) Abstract:To realize the high-quality processing of wooden windows,it is necessary to study the dynamic characteristics of the spindle system of the double-ended composite finishing milling machine tool,which can provide a theoretical basis for its structure op-timization and vibration reduction.A simplified three-dimensional model of the spindle system was established using the software Ad-ams,and the cutting force and the stiffness of the spindle system supporting bearings were calculated when the milling machine pro-cessed wooden windows,and combined the software Ansys and Adams to establish a rigid-flexible coupling model of the flexible spin-dle,and simulated the rigid body model and the rigid-flexible coupling model of the spindle system.The X,Y,and Z vibration curves at the centroid of the spindle,cutting force action point and the pulley connection point were extracted.The simulation results showed that the X and Z direction amplitudes of the cutting force action point were the largest,and the amplitude of the centroid and the cutting force action point when the spindle was a flexible body was much smaller than when the spindle was rigid.The results of this study showed that the dynamic characteristics of the spindle as a flexible body are more in line with the actual working conditions,and the vi-bration curve of the three points provides a certain theoretical basis for the structural optimization of the spindle system. Keywords:Spindle system;rigid-flexible coupling model;vibration;kinetics analysis;simulation收稿日期:2022-12-02基金项目:黑龙江省重点研发项目 智能化欧式木窗双端复合精铣成型加工机床关键技术研究 (GA21A405);中央高校基本科研业务费专项资金项目资助(2572020DR12)㊂第一作者简介:任长清,副教授,硕士生导师㊂研究方向为林业与木工机械设计及制造的研究㊂E-mail:dqrcq@∗通信作者:宋文龙,博士,教授㊂研究方向为模式识别与智能系统㊂E-mail:wlsong139@引文格式:任长清,王涛,丁星尘,等.木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真[J].森林工程, 2023,39(5):133-143.REN C Q,WANG T,DING X C,et al.Rigid-flexible coupled dynamics modeling and simulation of spindle system of double-end compound finishing milling machine tool for wooden window[J].Forest Engineering,2023,39(5):133-143.森㊀林㊀工㊀程第39卷0㊀引言欧式木窗双端复合精铣加工机床是加工木窗的重要设备,其加工精度的高低对木窗的质量好坏具有较大的影响,而机床主轴系统的刚度和能否平稳工作是影响加工精度的重要因素㊂双端复合精铣加工机床的主轴系统是机床直接参与加工的重要部件,而在以往对主轴系统的研究中学者都将主轴部件视为刚性体,但在实际加工过程中,机床主轴系统精度极高,在受力后会有一定程度的变形和弹性振动,因此在对机床的主轴系统进行研究时,要考虑到主轴的柔性变形和振幅大小对整个系统的影响,即应将主轴部件视为柔性体㊂因此,如何对主轴系统进行有效的动力学分析,建立控制模型,提高铣削精度和工作可靠性,引起了许多学者的重视[1]㊂本研究以木窗双端复合精铣加工机床的主轴系统为研究对象,使用Solidworks建立主轴系统的多刚体模型并进行仿真分析,利用Ansys生成主轴部件的柔性体模型并联合Adams进行刚柔耦合模型的仿真分析,对比两者仿真结果,旨在获得主轴为刚性体和柔性体时2种不同的主轴系统的动力学特性,在进行比较后得出结论,为主轴系统的结构优化提供理论依据,以提高加工精度㊂1㊀多刚体虚拟样机的建立与动力学仿真1.1㊀三维模型的建立主轴系统的模型建立是其动态特性分析的重要内容[2],主轴系统主要由主轴㊁带轮㊁皮带和轴承等零件组成㊂本研究使用三维建模软件Solidworks 来进行主轴系统的三维模型建立,为方便仿真,建模时省略螺纹㊁倒角和退刀槽等对仿真影响较小的特征[3-4],主轴系统在机床中为直立固定,主轴总长533mm,主轴从上到下分为锁紧部分㊁刀具安装部分㊁上轴承安装部分㊁转子部分㊁下轴承安装部分和带轮安装部分,除锁紧部分外从上到下各轴段的直径分别为50㊁60㊁78㊁50㊁38mm;长度分别为115㊁34㊁222㊁30㊁87mm,下带轮安装部分连接一带轮,上㊁下轴承安装部分分别安装有一对角接触球轴承,安装方式为背对背组配安装㊂主轴系统各零件三维模型建立完成后,将各零件进行配合后完成主轴系统装配体的三维模型建立,如图1所示㊂图1㊀主轴系统三维模型装配图Fig.1Assembly drawing of3D model of spindle system 1.2㊀多刚体虚拟样机的建立将建立完成的主轴系统三维模型通过Adams 中的导入命令导入到Adams中,为了仿真方便,又不影响仿真结果,将模型中的轴承拆去[5],再在Ad-ams中通过Adams Machinery模块重新创建轴承,创建完成后的轴承需要设置刚度㊁阻尼和预载荷等参数,图2为Adams中默认的轴承参数㊂图2㊀Adams默认轴承参数Fig.2Adams default bearing parameters㊀㊀模型导入Adams后各零件的材料属性为默认设置,需要重新设置主轴和带轮零件材料属性,各零件材料属性见表1㊂表1㊀主轴系统零件材料属性Tab.1Material properties of spindle system part零件Component密度/(kg㊃m-3)Density弹性模量/MPaElastic modulus泊松比Poisson's ratio主轴Spindle7850 2.06ˑ1050.29带轮Pulley7150 1.45ˑ1050.26主轴与带轮之间为键连接,在Adams中使用固定副来表示此连接㊂另外,在带轮与ground(Adams431第5期任长清,等:木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真软件中默认的作为背景或地面)之间添加一旋转副,并在带轮上添加一转速为6000r /min 的逆时针驱动㊂建立完成的多刚体虚拟样机,如图2所示,主轴的后端面中心点与坐标系原点重合,重力沿-Y 轴方向㊂图3㊀主轴系统多刚体虚拟样机Fig.3Spindle system multi -rigid body virtual prototype1.3㊀轴承刚度计算为了仿真结果准确,需要对轴承参数进行正确设置[6-7],Adams 中提供了默认的轴承刚度和阻尼等参数,其中刚度对仿真影响较大,需要进行重新设置,而阻尼对仿真的影响较小,可设为Adams 中的默认值㊂通过Solidworks 建立的主轴系统三维模型中的支承轴承为2个角接触球轴承背对背组配安装,而在Adams 中的多刚体虚拟样机创建的轴承为单个安装,虽然这2个模型不同,但只需要正确设置Adams 中的轴承参数,同样能达到轴承背对背组配安装效果,并不会影响仿真结果㊂采用式(1)来计算组配轴承组的轴向和径向刚度㊂假设其组配的轴承为同型号[8]㊂J a =32K(m 23+n 23)㊃F 13a ㊂(1)式中:J a 为组配轴承组轴向刚度,N /mm;m 为组配轴承组中轴承1的个数;n 为组配轴承组中轴承2的个数;F a 为轴向载荷,N;K 为弹性变形综合系数,对于K ,可用式(2)计算㊂K =0.00436Φ1/3Z 2/3sin 5/3α㊂(2)式中:Φ为滚动体直径,mm;Z 为滚动体数量;α为轴承的接触角,(ʎ)㊂本研究所使用的轴承参数见表2㊂表2㊀支承轴承的结构参数Tab.2Structural parameters of support bearings轴承Bearing 轴承类型Bearing type型号Model 内径(r 1)/mm Internal diameter(r 1)外径(r 2)/mm External diameter(r 2)滚动体数(Z )Number of rolling elements(Z )滚动体直径(Φ)/mm Rolling element diameter(Φ)接触角(α)/ʎContact angle(α)高度(b )/mm Height(b )上轴承Upper bearing角接触球轴承7012AC 60952011.522518下轴承Lower bearing角接触球轴承7010AC50801810.24256㊀㊀根据表2中提供的参数计算出上下轴承的弹性变形综合系数K 分别为K 1=1.10ˑ10-3,K 2=1.23ˑ10-3㊂将K 1和K 2代入式(1)中,m 和n 皆为1,轴向载荷(F a )根据主轴系统的重量给定80N,得到上轴承的轴向刚度J a 1=11751.46N /mm,下轴承的轴向刚度J a 2=10509.44N /mm㊂径向刚度(J r )使用式(3)进行计算㊂J r =J r1+J r2㊂(3)J r1=(2ε-1)㊃m 2/3㊃J r (ε)㊃F 1/3a K m ㊃J a (ε)㊃tan 2α㊂(4)J r2=(2ε-1)㊃n 2/3㊃J r (ε)㊃F 1/3aK n ㊃J a (ε)㊃tan 2α㊂(5)式中:ε为载荷分布系数;J r (ε)为径向载荷分布系数;J a (ε)为轴向载荷分布系数㊂当组配的轴承为同型号,且个数皆为m 和n 皆为1时,式(4)和式(5)可写为J r12=(2ε-1)㊃J r (ε)㊃F 1/3aK ㊃J a (ε)㊃tan 2α㊂(6)于是式(3)可改写为J r =2㊃(2ε-1)㊃J r (ε)㊃F 1/3aK ㊃J a (ε)㊃tan 2α㊂(7)在径向载荷F r ㊁轴向载荷F a 和实际接触角已知的条件下,可根据F r tan α/F a 的计算值从表3中查得ε㊁J r (ε)和J a (ε)㊂当F r tan α/F a 的计算值与531森㊀林㊀工㊀程第39卷表中所列的F r tanα/F a不同时,可采用线性内插法计算[8]㊂表3㊀ε㊁J r(ε)和J a(ε)值[8]Tab.3The value ofε,J r(ε)and J a(ε)εF r tanα/F a J r(ε)J a(ε)0.0 1.00001/Z1/Z0.20.93180.15900.17070.30.89640.18920.21100.40.86010.21170.24620.50.82250.22880.27820.60.78350.24160.30840.70.74270.25050.33740.80.69950.25590.36580.90.65290.25760.39451.00.60000.25460.39451.250.43380.22890.50441.670.30880.18710.60602.50.18500.13390.72405.00.08310.71100.8558ɖ0.00000.0000 1.0000给定径向载荷F r=40N,轴向载荷F a=80N,接触角α=25ʎ,计算得到F r tanα/F a=0.2331,介于0.3088~0.1850,为了得到此时对应的ε㊁J r(ε)和J a(ε),使用拉格朗日线性插值法进行计算,设F r tanα/F a为x㊂㊀ε=0.1850-x-0.1238㊃1.67+x-0.3088-0.1238㊃2.5㊂(8)J r(ε)=0.1850-x-0.1238㊃0.1871+x-0.3088-0.1238㊃0.1339㊂(9)J a(ε)=0.1850-x-0.1238㊃0.6060+x-0.3088-0.1238㊃0.7240㊂(10)将x=0.2331代入式(8) 式(10)中,分别得到F r tanα/F a=0.2331时对应的ε=2.18㊁J r(ε)= 0.1546㊁J a(ε)=0.6782㊂将这3个值及K1和K2代入式(7)得到上轴承径向刚度J rs=27596.02N/mm㊁下轴承径向刚度J rx=24679.37N/mm㊂将得到的上下轴承的轴向和径向刚度输入到Adams中,并设置预载荷㊂1.4㊀切削力的计算切削力是木材切削过程中的主要物理现象之一,是切削木材㊁切屑和被加工工件表面的木材在刀具作用下发生弹性变形和塑性变形的结果,正确地掌握木材切削力的大小是木工机床设计的必要依据[6]㊂切削力的大小对主轴系统造成的影响尤为关键,为正确仿真机床主轴铣削木窗时的状态,需要对切削力进行计算㊂目前实际应用的切削力和切削功率计算方法有2种,一种为基于理论分析的计算方法;另一种为经验公式计算方法㊂因为理论计算方法主要是依据断裂力学的概念和计算方法,比较繁琐,牵涉的系数较多,所以在工程计算上多用经验公式,计算切削力和切削功率[9]㊂本研究使用经验公式(11)完成对切削力的计算,表3中给出切削力的计算条件㊂所加工产品为IV68系列欧式木窗㊂表4㊀切削力计算条件Tab.4Cutting force calculation conditions参数Parameter值Value原材料Raw material松木含水率Moisture rate(10%~13%)ʃ2%主轴转速(n)/(r㊃min-1)Spindle speed(n)6000进给速度(U)/(m㊃min-1)Feed speed(U)6铣削深度(h)/mmMilling Depth(h)18刀具齿数(z)Number of teeth(z)4刀具旋转外径(D)/mmTool rotation outer diameter(D)240木材切削力的经验公式为F x=Pab10㊂(11)式中:P为单位切削力,MPa;a为切屑厚度,mm;b 为切屑宽度,mm㊂单位切削力(P)可按式(12)进行计算[10]P=9.807(a w a q q+a w a h HU z sinθ)㊂(12)式中:a w为木材含水率修正系数;q为松木切削的直线斜率;a q为q的修正系数;H为松木切削的直线截距,mm;a h为H的修正系数;U z为每齿进给量,mm;θ为运动遇角(ʎ)㊂查文献[10]得木材含水率修正系数a w=1.0,松木切削的直线斜率q=3.8,q的修正系数a q=1.1,松木切削的直线截距H=0.4,H的修正系数a h=1.45㊂631第5期任长清,等:木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真每齿进给量(U z )的计算公式为[11]U z =1000Un ㊃z㊂(13)将各已知参数带入计算求得U z =0.25mm㊂sin θ可用式(14)进行计算㊂sin θ=㊀h D㊂(14)式中:h 和D 均为已知,将其带入后求得sin θ=0.7㊂将上述各参数带入式(12)中可求出单位切削力P =125.26MPa㊂切屑厚度a 为两相邻切削轨迹间的垂直距离,是一个变化的值,为仿真主轴振动最大的情况,这里取a 的最大值a max 进行计算㊂a max =U z sin φ0㊂(15)式中:U z 为每齿进给量;φ0为接触角(ʎ)㊂由cos φ0=1-hD得φ0=22.33ʎ㊂将已知量带入式(15)得a max =0.09㊂铣削方式为开式圆柱铣削,切屑宽度b 与铣削宽度相等,即b =68mm㊂最终可求得切削力F x 为F x =125.26ˑ0.09ˑ6810=76.66N ㊂将求得的切削力添加到主轴系统多刚体虚拟样机中,并在带轮上添加60N 皮带预紧力,得到最终模型如图4所示,切削力沿坐标系Z 轴方向,作用点位于主轴刀具安装部位,皮带预紧力沿-Z 轴方向㊂图4㊀主轴系统多刚体仿真模型Fig.4Multi -rigid body simulation model of spindle system1.5㊀主轴系统刚性体动力学仿真设置完成所有仿真条件后,进行主轴系统刚性体的动力学仿真,设定仿真持续时间0.04s,步长0.0004㊂仿真后提取主轴质心㊁切削力作用点和带轮连接点的X ㊁Y ㊁Z 向振动曲线,这3点的位置如图5所示,坐标分别为(0,259,0)㊁(0,439,0)㊁(0,41,0),所提取的振动曲线如图6 图11所示㊂图5㊀所提取的3点振动曲线位置Fig.5The position of the extracted three -point vibration curve731森㊀林㊀工㊀程第39卷振幅/m m A m p l i t u d e1.51.00.50.0-0.5-1.0-1.5-2.0-2.5时间/s Time0.00.010.020.030.04刚性主轴质心X 向振动曲线Badyl.CM_Position.X刚性主轴质心Z 向振动曲线Badyl.CM_Position.Z图6㊀刚性主轴质心X ㊁Z 向振动曲线Fig.6Vibration curve in X and Z directions of rigid spindle centroid振幅/m m A m p l i t u d e259.54259.535259.53259.525时间/s Time0.00.010.020.030.04刚性主轴质心Y 向振动曲线Body1.CM_Position.Y图7㊀刚性主轴质心Y 向振动曲线Fig.7Vibration curve in Y directions of rigid spindle centroid时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e2.51.50.50.0-0.5-1.5-2.5-3.5-4.5刚性主轴切削力作用点X 向振动曲线MARKER_54.Translational_Displacement.X 刚性主轴切削力作用点Z 向振动曲线MARKER_54.Translational_Displacement.Z图8㊀刚性主轴切削力作用点X ㊁Z 向振动曲线Fig.8Vibration curve in X and Z directions of rigid spindle cutting force action point时间/s Time振幅/m m A m p l i t u d e刚性主轴切削力作用点Y 向振动曲线MARKER_54.Translational_Displacement.Y439.54439.535439.53439.525439.520.00.010.020.030.04图9㊀刚性主轴切削力作用点Y 向振动曲线Fig.9Vibration curve in Y directions of rigid spindle cutting force acting point831第5期任长清,等:木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真时间/s Time刚性主轴带轮连接点X 向振动曲线MARKER_1.Translational_Displacement.X 刚性主轴带轮连接点Z 向振动曲线MARKER_1.Translational_Displacement.Z振幅/m m A m p l i t u d e0.0015.0E-040.0-5.0E-04-0.001-0.00150.00.010.020.030.04图10㊀刚性主轴带轮连接点X 、Z 向振动曲线Fig.10Vibration curve in X and Z directions of rigid spindle pulley connection point时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e42.542.041.541.040.540.0刚性主轴带轮连接点Y 向振动曲线MARKER_1.Translational_Displacement.Y图11㊀刚性主轴带轮连接点Y 向振动曲线Fig.11Vibration curve in Y directions of rigid spindle pulley connection point1.6㊀主轴系统刚性体动力学仿真结果分析分析图6 图11中的振动曲线可以发现,主轴质心和切削力作用点皆作简谐振动,X ㊁Y ㊁Z 向振动曲线皆为余弦或正弦曲线,且周期都为0.01s㊂结合图6㊁图8和图10分析发现,3点的X 向振幅分别为1.01㊁1.93㊁6.25ˑ10-4mm;Z 向振幅分别为1.08㊁1.70㊁6.50ˑ10-4mm,3点的X 和Z 向振幅几乎一致,3点振幅切削力作用点最大,质心其次,带轮连接点的振幅最小,而且3点的X 和Z 向的振动曲线并非严格对称于0刻度线,即主轴的回转中心不与Y 轴重合,而是向-X 和+Z 方向偏转一定角度,如图12所示㊂由图7㊁图9和图11可知,切削力作用点的Y 向振幅最大,为0.01mm,其次是质心,振幅为0.006mm,而带轮连接点在Y 向上没有振动㊂2㊀刚柔耦合模型的建立与仿真2.1㊀刚柔耦合模型的建立把模型当作刚性系统来处理,没考虑构件的变YZX图12㊀偏移的主轴回转中心Fig.12Offset spindle center of rotation形,在精度要求较高时,可能出现仿真与实践不符的情况[6]㊂主轴系统对精度要求较高,为能准确研究主轴系统的动力学特性,不能忽略在实际工作过程中的微小振动与变形,将主轴设为柔性体能使仿真结果更加接近实际情况㊂Adams 中柔性体的载体是包含构建模态信息的模态中性文件(Modal Neutral File,MNF),因此柔性931森㊀林㊀工㊀程第39卷体的创建必须借助功能强大的有限元软件来完成[12]㊂借助有限元软件Ansys可以完成对柔性主轴的创建㊂基本步骤[13-18]:1)将主轴三维模型导入Ansys㊂2)设置单元类型为Solid(Brick8node185),设置材料属性㊂3)分别在上下轴承支承部位及带轮连接部位中心创建连接点㊂4)划分单元,划分单元后主轴如图13所示㊂图13㊀划分单元后的主轴Fig.13Main axis after dividing the unit将上下轴承支承部位及带轮连接部位设置为刚性区域,如图14所示㊂使用Adams接口输出模态中性文件㊂将主轴模态中性文件导入Adams的模型中替换原有刚性主轴㊂替换完成后得到的主轴系统的刚柔耦合模型如图15所示,其中主轴为柔性体,带轮为刚性体㊂图14㊀主轴模型刚性区域Fig.14Spindle model rigidarea图15㊀主轴系统刚柔耦合模型Fig.15Rigid-flexible coupling model of spindle system2.2㊀主轴系统刚柔耦合模型仿真设置仿真条件与进行刚性体仿真时一致㊂进行仿真后得到图16 图21所示结果㊂由于带轮连接点的X㊁Z向振动曲线的起点坐标差较大,为方便分析将2条振动曲线的起点与坐标原点重合㊂时间/sTime0.00.010.020.030.04振幅/mmAmplitude柔性主轴质心X向振动曲线Body1_flex.CM_Position.X0.0150.010.0050.0-0.005-0.01柔性主轴质心Z向振动曲线Body1_flex.CM_Position.Z图16㊀柔性主轴质心X、Z向振动曲线Fig.16Vibration curve in X and Z directions of of flexible spindle centroid041第5期任长清,等:木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真时间/s Time0.00.010.020.030.04柔性主轴质心Y 向振动曲线Body1_flex.CM_Position.Y振幅/m m A m p l i t u d e258.776 7258.776 5258.776 5258.776 3258.776 3258.776 1258.776258.775 9258.775 8258.772 8图17㊀柔性主轴质心Y 向振动曲线Fig.17Vibration curve in Y directions of the flexible spindle centroid时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e0.050.0-0.05-0.1柔性主轴切削力作用点X 向振动曲线MARKER_65.Translational_Displacement.X 柔性主轴切削力作用点Z 向振动曲线MARKER_65.Translational_Displacement.Z图18㊀柔性主轴切削力作用点X ㊁Z 向振动曲线Fig.18Vibration curve in X and Z directions of flexible spindle cutting force action point时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e柔性主轴切削力作用点Y 向振动曲线MARKER_65.Translational_Displacement.Y436.902 9436.902 8436.902 7436.902 6436.902 5436.902 4图19㊀柔性主轴切削力作用点Y 向振动曲线Fig.19Vibration curve in Y directions of flexible spindle cutting force action point时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e柔性主轴带轮连接点X 向振动曲线MARKER_64.Translational_Displacement.X 柔性主轴带轮连接点Z 向振动曲线MARKER_64.Translational_Displacement.Z0.0015.0E-040.0-5.0E-04-0.001-0.0015图20㊀柔性主轴带轮连接点X ㊁Z 向振动曲线Fig.20Vibration curve in X and Z directions of flexible spindle pulley connection point141森㊀林㊀工㊀程第39卷时间/s Time0.00.010.020.030.04振幅/m m A m p l i t u d e柔性主轴带轮连接点Y 向振动曲线MARKER_64.Translational_Displacement.Y41.228 541.228 541.228 441.228 441.228 3图21㊀柔性主轴带轮连接点Y 向振动曲线Fig.21Vibration curve in Y directions of flexible spindle pulley connection point2.3㊀主轴系统刚柔耦合模型仿真结果分析由图16 图21可以看出,柔性主轴质心㊁切削力作用点和带轮连接点的X 向和Z 向振动曲线与主轴为刚性时的情况存在较大差异,虽然振动曲线周期同样为0.01s 的正弦或余弦曲线,但是各点的三向振幅发生了较大的变化㊂主轴质心㊁切削力作用点和带轮连接点的X 向振幅分别为:2.9ˑ10-3㊁0.01㊁6.5ˑ10-4mm;3点的Z 向振幅与X 向振幅一致,分别为:2.9ˑ10-3㊁0.01㊁6.5ˑ10-4mm㊂而且可以看到3点的振动起点较主轴为刚性时发生了变动,但并不影响对3点振幅的分析㊂分析图17㊁图19和图21,3点Y 向振动曲线周期同样为0.01s,振幅分别为4.5ˑ10-4㊁2.0ˑ10-4㊁5ˑ10-5mm㊂3㊀仿真结果比较比较主轴为刚性和柔性2种情况时的振动曲线,发现这2种情况下3点的振动曲线周期皆为0.01s㊂表5中列出了主轴为刚性和柔性时,主轴质心㊁切削力作用点和带轮连接点的X ㊁Y ㊁Z 向振幅㊂表5㊀刚、柔主轴3点振幅Tab.5Three -point amplitude of rigid and flexible spindlesmm位置Position 刚性主轴Rigid spindleX Y Z 柔性主轴Flexible spindleX Y Z 质心Centroid1.016.0ˑ10-31.082.9ˑ10-34.5ˑ10-4 2.9ˑ10-3切削力作用点Cutting force point1.930.01 1.700.012.0ˑ10-40.01带轮连接点Pulleyattachme -nt point6.25ˑ10-46.5ˑ10-46.5ˑ10-45ˑ10-56.5ˑ10-4㊀㊀由表5可以发现,当主轴为柔性体时质心和切削力作用点的振幅远远小于主轴为刚性时,从主轴0.01mm 的检验标准来看,刚性主轴的仿真结果是不准确的,而柔性主轴的仿真结果更加符合实际情况㊂无论是刚性主轴还是柔性主轴,切削力作用点的X ㊁Z 向振幅由于受到切削力的作用,所产生的振幅是3点中最大的,其次是质心,带轮连接点的振幅最小㊂而在3点的三向振动中,Y 向振幅是最小的,若以柔性主轴的Y 向振幅为准,则这个振幅很微小,对木窗的加工精度几乎没有影响,因此在主轴结构改进时可不做考虑㊂切削力作用点即铣刀装配位置的振动对木窗加工质量影响最大,应从如何减小切削力作用点的振幅入手来进行主轴结构的优化㊂4㊀结论1)提取了主轴为刚性体和柔性体时的主轴质心㊁切削力作用点和带轮连接点的X ㊁Y ㊁Z 向振幅㊂2)对比主轴为刚性体和柔性体2种情况时的仿真结果,发现主轴为柔性体时振动规律更加符合实际情况㊂3)以刚柔耦合模型的仿真结果为准,切削力作用点㊁质心和带轮连接点的X ㊁Z 向振幅依次从大到小,而Y 向振幅很微小可忽略不计,如何减少切削力作用点的振幅是主轴改进的重点,本研究中的刚柔耦合模型动力学仿真结果为主轴系统结构的改241第5期任长清,等:木窗双端复合精铣加工机床主轴系统的刚柔耦合动力学建模与仿真善提供了参考依据㊂ʌ参㊀考㊀文㊀献ɔ[1]李荣丽,贺利乐.煤炭采样机械臂的刚柔耦合动力学建模与仿真分析[J].机械设计,2013,30(8):33-36.LI R L,HE L L.Dynamic modeling and simulation analysis for rigid-flexible coupling model of coal sample manipulator [J].Journal of Machine Design,2013,30(8):33-36.[2]闻志,沈金淼,孔辉,等.基于ANSYS的H型刚柔耦合机械臂动力学建模与动态特性机理研究[J].丽水学院学报,2022,44(5):18-26.WEN Z,SHEN J M,KONG H,et al.Dynamic modeling and dynamic characteristic mechanism of H-type 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汽车发动机曲轴扭转振动分析及控制(1)
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重庆大学硕士学位论文
ABSTRACT
Due to the more stringent legislations of vehicle noise and emission as well as the increasing expectation by the consumers, researches on the noise, vibration and harshness (NVH) have become more important in recent years. The traditional cranktrain torsional vibration analysis method is time consuming and needs a lot of experiments to validation in order to gain the high accurate results. The new method which combines finite element method (FEM) and multibody system simulation (MSS) appeared as an alternative choice. This new method has changed the engine design process greatly by employing simulation technique instead of costly experiments (TEST CELL). This paper lucubrated the approach of modeling engine cranktrain MSS simulation model, the analysis model with flexible crankshaft ,flexible con rod and engine block is implemented. The dynamic vibration behavior of cranktrain is obtained after vibration characteristic analysis. Furthermore, the complete dynamic behavior is achieved through forced torsional vibration analysis. On the basis of analysis result, this paper designed torsional damper and optimized the basic parameters of cranktrain. The general rules of structure modification’ s influence on system vibration behavior is researched and simula的研究现状
刚柔耦合车辆动力学动态响应分析
刚柔耦合车辆动力学动态响应分析∗张成功【摘要】为了分析弹性车体结构振动特性及对曲线通过能力的影响，用运多体动力学建模仿真软件SIMPACK分别建立某型动车组刚性动力学仿真模型和柔性车体与刚性走行部耦合动力学仿真模型，通过对两种模型的垂向和横向动力学动态响应进行比较和分析。
结果表明，刚柔耦合模型车体振动加速度均方值( RMS)和Sperling指标均较多刚体模型大，曲线通过能力减小。
%In order to analyze the vibration characteristics of the elastic body and the influence of the vibration response and curving performance of the frame and wheels, The dynamic simulation models of a certain type of EMU about the rigid and the coupling of a flexible body and the rigid running gear are established by the multi-body dynamics simulation software SIM-PACK. After comparing and analyzing the vertical and lateral dynamics performance of the two models, the result is showed that rigid-flexible coupling model vehicle acceleration mean square ( RMS) and Sperling indicators are relatively large rigid body model, and also curving performance has been reduced.【期刊名称】《机械研究与应用》【年(卷),期】2016(029)002【总页数】3页(P12-14)【关键词】耦合模型;垂向与横向;曲线性能【作者】张成功【作者单位】兰州交通大学机电工程学院，甘肃兰州 730070【正文语种】中文【中图分类】TH132.41高速车辆车体的轻量化能够有效的降低轮轨之间的作用力，减少制造费用，节约能源，为了实现车体轻量化目标，中空铝合金或轻质不锈钢等材料被广泛的应用到车体的制造中，但是车体的轻量化往往引起了车体振动的变化，旅客乘坐舒适性有所下降[1]；再者，随运行速度的不断提高，车辆运行的平稳性、舒适性和安全性也受到了一定的影响[2-4]；所以，轨道车辆随着高速化和轻量化的快速发展，将车体考虑成刚性模型已经不能满足研究和分析车体动力学的需求，而考虑车体弹性变形的柔性车体模型将对车体振动的仿真研究更加准确和符合实际。
一种新型两自由度柔性并联机械手的动力学建模和运动控制_胡俊峰
一种新型两自由度柔性并联机械手的动力学建模和运动控制X DYNAMIC MODELING AND KINEMATIC CO NTROL OF A NOVEL 2-DOF FLEXIBLE PARALLEL MANIPULATOR胡俊峰X X1张宪民2(1.江西理工大学机电工程学院,赣州341000)(2.华南理工大学机械与汽车工程学院,广州510640)HU JunF eng1ZHAN G XianM in2(1.School o f Mechanical&Electrical Engineering,Jiangxi University o f Science andTechnolo gy,Ganzhou,341000,China)(2.School o f Mechanical&Automotive Engineering,South China University o f Technology,Guangzhou510640,China)摘要对一种新型两自由度柔性并联机械手的动力学模型和运动控制进行研究。
首先,考虑刚)柔耦合影响,利用假设模态法和Lagrange乘子法,推导出系统的动力学方程,该方程为微分)代数方程组。
为了设计控制器,采用坐标分块法将该微分)代数方程组化为二阶微分方程组。
然后,根据机械手的控制要求,采用滑模变结构方法设计控制器,该控制器能跟踪所期望的运动轨迹,同时柔性构件的弹性振动得到抑制。
仿真结果表明该控制器的可行性和有效性。
关键词并联机械手柔性构件滑模变结构控制假设模态法中图分类号TH112TH113Abstract For a novel2-DOF(degree of freedom)flexible parallel manipulator,i ts dynamic model and kinematic control were studied.Taking into account the effect of rigid-flexible coupling,the dynamic equations of the system were derived by using assu med mode method and Lagrange multiplier method.It is a differential algebraic equations.In order to design a controller,the coordinate-par-titioned method is used to convert the differen tial algebraic equations in to a second-order differential equations.According to the demand of control,the variable structure control method is applied to design the controller in order to acq uire desired trajectory and attenuate the elastic deformation of flexible parts.The si mulation resul ts show the feasi bility and effectivenss of the controller.Key words Parallel manipulator;Flexible part;Variable structure control;Assum ed mode methodCorrespon ding author:H U JunFen g,E-mail:h jf su per@,Tel:+86-20-87110345,Fax:+86-20-87110069The project supported by the National Natural Science Foundation of Chi na for Distinguished Young Scholars(No.50825504).Manuscript received20091009,in revi sed form20100104.引言并联机器人具有高速度、高精度、高承载能力等特点,在许多领域得到应用。
SimWise 4D 3D 动态运动、压力分析和优化说明书
4D SimWise3D Dynamic Motion, Stress Analysis and Optimizationintegrated with SOLIDWORKSSimWise 4D is a software tool that allows the functional performance of mechanical parts and assemblies to be simulated and validated. It combines 3D multi-body dynamic motion simulation with 3D finite element analysis and optimization in a Windows based product intergated with SOLIDWORKS, priced affordably for every engineer. Each of the major components of SimWise 4D, the motion module, and the FEA module,is available as a separate product and are powerful in their own right but the real benefits arise when the two are combined together in the 4D product.Designs that are made up of moving mechanical parts present challenges when it comes time to answer fundamental questions like “Does it work?”, “Will it break?”, “How can it be designed better?”, and “How long will it last?”.Dynamic forces are hard to calculate and the part stresses induced by motion are even more difficult to quantify. Many of these designs are validated in the test lab or in the field using prototypes of pre-production designs. If problems are found the designs must be revised and the process repeated, resulting in a costly and time-consuming approach to product validationSimWise 4D gives you the ability to explore the functional performance of your design before prototypes are built. Options can be explored in a timely and cost effective manner because hardware does not need to be built until you have confidence that your design works as intended. The capabilities of SimWise 4D make “getting it right the first time” more than just a slogan; it makes it an integral part of your design process.SimWise 4DIntegrated Motion Simulation Stress Analysis and OptimizationIntegration withSOLIDWORKSAll of the SimWise products are integrated with SOLIDWORKS. Using a SOLIDWORKS add-in developed specifically to transfer SOLIDWORKS data to SimWise, geometry, mass properties, materials, assembly constraints, design variables and dimensional values can be transferred to SimWise with a single operation.Assembly constraints areautomatically mapped to SimWisejoints. Design variables anddimensional values are available to use with Optimization. The SimWise model contains associative links back to the SOLIDWORKS model. If a change is made to the SOLIDWORKS model a single operation will update the SimWise model to reflect those changes. The change process can be initiated from either SimWise or SOLIDWORKS.SOLIDWORKS part and assembly models can also be opened directly by SimWise. This method only transfers geometry, mass andmaterial properties. This method also supports updates if the part or assembly model has changed.SimWise Motion3D Motion SimulationSimWise Motion is rigid bodykinematics and dynamics simulation software that lets your build and test functional virtual prototypes of your designs on the computer and simulate the full-motion behavior of those designs. It imports geometry, mass properties, and constraints from SOLIDWORKS and allows you to add motion specific entities to the model resulting in a functional operating prototype of your design. It simulates that prototype using advanced physics and mathematical techniques and presents the results of the simulation in various graphic and numeric formats. You can quickly determine how your design operates and determine if it meets your design objectives or if modifications are necessary. All on the computer, all without costly and time-consuming physical prototypes.SimWise Motion has a rich set of functional objects that are added toyour SOLIDWORKS model to build a functional operating prototype. These objects include:▸Rigid, revolute, spherical, curved slot, planar constraints ▸Rods, ropes, springs, gears, belts, pulleys, conveyors ▸Bushings (flexible connections) ▸Motor and actuators ▸Point forces, torques,distributed forces, pressure, friction forcesCollisions between parts are handled easily allowing the simulation of mechanisms like ratchets, clamps, grips, and others that rely on contact between two or more parts to operate. Contact forces and friction forces that occur at the time of contact are calculated and available for plotting, query or use by SimWise FEA.Motors, actuators and forces can be driven by the SimWise formulalanguage, tabular data, values in an Excel spreadsheet, or by a Simulink™ model co-simulating with SimWise Motion. This allows phenomena like motor start up and spin-down characteristics, variable speed actuators, andelectro-mechanical controllers to be incorporated in the simulation model.Assembly constraints from SOLIDWORKS are automaticallyand associatively converted to SimWise Motion constraints. Many times assembly models are over constrained so a “constraint navigator” is available to walk through each motion constraint and modify as necessary to remove redundancies. Limits can be set for constraints to model rotational or translational “stops”. Friction forces can be activated on an individual constraint basis by specifying thePowerful Formula Languageand Function BuilderSimWise contains a powerful formula language that allows simulation entity properties, instantaneous simulation values, and mathematical expressionsto be combined into an expression that is evaluated during the simulation and which can be used to define physical values in the simulation.Formulas can also be used to generate values for display on meters. For example the formula:0.5*Body[49].mass*mag(Body[49].v)*mag(Body[49].v)When added to a meter will display a graph of the kinetic energy of Body[49].The formula language can also be accessed using a function builder that allows equations to be assembled interactively. The function builder contain an integrated graphing capability so as a function is defined, its graph is displayed and updated.ProgrammabilitySimWise contains a very rich automation interface which allows it to be both interfaced with and controlled by other applications. Programming languages such as C++, C#, Visual Basic, Java, and even vbScript can be used to customize SimWise. You can automate the integration of SimWise into your proprietary processes and your proprietary calculations can be used from within the SimWise environment.The function builder allows complex functions to be defined graphicallyPhotorealistic rendering and animationSimWise uses high quality, high performance rendering technology from Lightworks. Multiple light types and sources, texture mapping, shadowing and other effects are available. Combined with the SimWise animation capabilities it can produce very realistic “movies” of a design as it operates. Stress contour results can also be incorporated in the animations. You can watch your design operate and see how the stresses induced by the operation effect individual parts. The rendered animations and images can be exported to formats that allow placement on web sites, in documents, and presentations.Cameras that move in space or which can be attached to parts aresupported. This allows you to produce “fly-through” type animations or view the design operating from a “birds-eye” view as if you were sitting on one of the parts.SimWise also provides an animation technique known as keyframing. With keyframing you can specify motions in ways that are not based on physics. For example, you can script a corporate logo flying through the air, or a parts-exploding automobile engine to show how it is assembled. Even cameras can be keyframed to create “movie-like” scenes that pan, zoom, and highlight product features. You can also combine physics-based, simulated movement with keyframed animation to create complex motion sequences.friction coefficient and a physical dimension based on the constraint type.All SimWise Motion objects can be selectively made active or inactive based on some criteria defined by the SimWise formula language. For example, a rotational constraint can be active as long as its reaction force is below a specified value. Once the reaction force exceeds the value, the constraint will deactivate and no longer constrain its attached parts. This would model the effect of the constraint “breaking” due to the internal forces being too high.The SimWise Motion simulation engine calculates the displacement,velocity, and acceleration of each body in the motion model and reactions forces that act on each body as a result of its dynamicmotion. This includes the motion and forces that result from any collisions between parts.Each of these quantities can be displayed on meters either in graph or digital format. The values can be accessed with the formula language or tabulated on an HTML report. Graphical vectors can be created that visually show the quantities calculated during the simulation. The vectors can change size and direction as the quantities they display change. Motors and actuators can report their force or power requirements to helpyou determine the proper sizing of these elements, and parasitic losses due to friction can be determined.SimWise Motion help you to answer the question “Does it Work?” and provides the data necessary for SimWise FEA to help you answer the question “Will it Break?”.SimWise Motion3D Motion SimulationAnnotation and Mark-upAnnotations in the form of text, call-outs, and distance and radial dimensions can be added to the simulation model. The distance dimensions are active in that they update if the model is moved or animated. SimWise also provides a distance dimension that shows the points of closest approach and the minimum distance between two bodies. This dimension also updates as the bodies move.Texture mapping, reflections, and shadows can all be used in animationsSimWise Motion supports a conveyor constraint for modeling materials handlingSimWise FEAMechanical Stress and Thermal AnalysisSimWise FEA is a Finite Element Analysis tool that performs stress, normal modes, buckling, and heat transfer analysis on mechanical parts. It is highly automated and handles much of the complexity associated with FEA while offering powerful features for users who are steeped in the intricacies of the Finite Element Method.It imports geometry from SOLIDWORKS and allows you to add structural and thermal specific entities to the model resulting ina functional structural prototypeof your design. It simulates that prototype using advanced physics and mathematical techniques and presents the results of the simulation in various graphic and numeric formats. You can quickly determine whether your design is robust enough to operate as intended or if modifications are necessary. All on the computer, all without costly and time-consuming physical prototypes and before warranty issues arise.SimWise FEA has a rich set of functional objects that are added to your SOLIDWORKS model to build a functional structural prototype. These objects include:▸Concentrated loads, distributedloads, torques, and pressures▸Restraints and enforceddisplacements▸Prescribed temperatures,conductive and convective heatflux, and radiationAll of these values can be driven bythe SimWise formula language. Allof these objects are applied to theunderlying geometry, not to nodesand elements as in a traditional FEAproduct.SimWise uses a fast iterativeFinite Element Analysis solver thattakes advantage of multi-coreprocessors and which is based on aPreconditioned Conjugate Gradientmethod. SimWise FEA exclusivelyuses ten-node tetrahedral elementsand the solver is optimized for thistype of problem.SimWise FEA performs the followingtypes of analyses:▸Linear Static Stress▸Steady State Thermal▸Trasient Thermal▸Normal Modes▸Buckling▸Combined Thermal/StructuralSimWise FEA can displayFEA results as shadedcontours, deformed shapes,or animations. In additionto these engineeringvalues, SimWise FEA alsocalculates factors of safetyand errors in the stress results andboth of these can be displayed asshaded contours.The error results can be used todrive an iterative solution processcalled h-adaptivity where the errorresults are used to refine the FiniteElement mesh in areas with largeerror values and use that new meshto run another solution. The errors inthe new solution are compared to agoal and if error values in the modelstill exceed the goal, the processis repeated with successive meshrefinements and analyses until theerror goal is achieved. Confidencein the results are increased and nospecial knowledge about appropriatemeshing techniques is required.If more control over the mesh isrequired, SimWise FEA providesmesh controls that can be attachedto geometric faces or edges. Thecontrol allows the mesh size to bespecified on that particular featureand the resulting 3D mesh will bethe specified size along or across thegeometric feature.Refinement 2 - Error < 5%Refinement 1 - Error 8%Initial Mesh - Error 13%h-Adaptivity refines the mesh until an error threshold is achievedSimWise 4D OptimizationOptimization allows you to answer the “How can it be made better?” question about your design.Once you know a design will work and is strong enough to operate safely, you can start to consider making trade-offs between product attributes in the areas of weight, cost, manufacturability, and performance. SimWise 4D includes the HEEDS® optimization engine which, using its unique SHERPA algorithm, rapidly iterates through many design alternatives looking for design parameters that meet all targets and criterias.Three things are needed for optimization:▸Parameters – The values thatwill be changed to achievean optimized objective. Thesecan be any type of SimWise value, such as the stiffness of a spring, or the location of a joint.▸Objective – The value(s) tobe optimized. Any SimWisequantity that can be displayedon a meter along with mostSimWise object attributes canbe an objective.▸Constraints – Place bounds onthe optimization. Any SimWisequantity that can be displayedon a meter along with mostSimWise object attributes canbe used as a bound.As the optimization runs, the enginewill choose different values for theparameters and run multiple Motion,FEA, or Motion+FEA simulations.The high performance SHERPAsearch algorithm in the HEEDS®engine guide the choice of parametervalues. The data from each run arepreserved and can be reviewed.Each run is ranked in terms of howit meets the optimization criteria andthe rankings can be used to arrive atthe final values used for your design.If your SimWise model wastransferred from SOLIDWORKSvia the Plug-In, then you can alsochoose to transfer Design Variablesand Dimensions from SOLIDWORKSto SimWise. These Variables andDimensions can also be used as aParameter, Objective, or Constraint inthe optimzation process. Each timethe optimzation engine determinesthat a CAD Variable or Dimensionneeds to be changed, the CADsystem will be passed the newvalue, the model will be updated,and transferred back to SimWisefor the next optimization step. Thecomplex process of updating theSOLIDWORKS model, and runningmutliple Motion and/or FEA analysesis completly managed by SimWise.Some of the benefits of usingSimWise Optimization include:▸Reduced developmentcosts and improved productperformance - With theoptimization methods availablein SimWise coupled with itsintegrated Motion and FEAsolvers and associative linksto SOLIDWORKS, you canuncover new design conceptsthat improve productsand significantly reducedevelopment, manufacturing,warranty and distribution costs▸Sensitivity studies - UseSimWise Optimization to identifythe variables that affect yourdesign the most. You can thenignore variables that are notimportant or set them to valuesthat are most convenient orleast costly. This allows you tocontrol quality more effectivelywhile lowering cost.▸Lets you focus on innovativedesign - There’s no needto experiment with differentoptimization algorithms andconfusing tuning parameters foreach new problem. The HEEDSSHERPA algorithm adapts itselfto your problem automatically,finding better solutions faster,the first time.Best of all there is nothing extrato purchase. All of the capabilitiesneeded to peform sophisticated,analysis driven optimization are partof SimWise 4D.Simulink Interface MATLAB® /Simulink is widely used to design and simulate control systems in a variety of domains. As products grow more sophisticated,many mechanical assembliesare run by controllers andthe ability to simulate the controller together withthe mechanical system is necessary.SimWise can functon as a “plant” model in Simulinkwhich allows a SimWisemodel to be placed in a Simulink model as a blockrepresenting the mechanical model.Any SimWise value displayed on ameter can be defined as an “ouput”signal from the Plant Model andbe connected to another Simulinkblock’s input.A Simulink block’s output may beconnected to an input control inSimWise and the input controlcan be mapped to almost anynumeric attribute of a SimWiseobject. For example the amountof force generated by a linearactuator or the speed of a rotarymotor.Benefits:▸Control engineers can test theircontrol algorithms with dynamicmechanical models includingphenomena like 3D contact andfriction.▸The mechanical engineer andthe controls engineer cancombine their independantmodels.▸Development time and costcan be saved by evaluatingthe controller and mechanicalsystem early in the designprocess without having to buildphysical prototypes.SimWise Plant model integrates with SimulinkSimWise Durability Fatigue Life AnalysisSimWise Durability is an add-on module to SimWise 4D that allows you to answer the “How long willit last?” question about your design before you ever build a prototype.Fatigue damage is one the most common causes of structural failure, and can lead to disastrous outcomes. Therefore, prediction of structural fatigue life is essential in modern product design.SimWise 4D already calculates the dynamics loads that result from the motion of a mechanism, and the stresses and strains that result fromthose dynamic loads.SimWise Durability applies widelyaccepted FEA fatigue calculations tothe stress/strain history to determinethe part fatigue life. It presents thisdata as a shaded contour plot justlike FEA stress or temperatureresults. From this you can quicklydetermine if the part life is within thedesign objectives, and if not, wherechanges need to made to improvefatigue life.SimWise Durability provides about150 different materials containingfatigue properties per SAE J1022.Fatigue life can be calculated usinguni-axial or biaxial methods andSimWise Durability supports both.The following calculation methodsare supported:▸Manson Coffin▸Morrow▸Basquin▸ASME▸BWI Weld▸Smith-Watson-Toper▸Max Shear Strain▸Goodman▸Gerber▸Dang VanBenefits:▸Reduce reliance on physicaltests and avoid costly designand tooling changes.▸Reduce costs and weight byassessing more design options.▸Perform better physical tests bysimulating first.▸Reduce warranty costs byreducing failures.SimWise 4D is a prerequisite forSimWise Durability.An unprecedented Value PropositionThere are many options whenchoosing a set of CAE tools; FEAapplications, 3D Dynamic Motionapplications, CAE tools that are partof CAD systems. SimWise sets itselfapart in this crowded field because itoffers unsurpassed value.Consider that for a fraction of theprice of some single-purpose CAEtools, SimWise delivers:▸3D Dynamic Motion Simulationincluding contact, friction,formulas, and more.▸Linear static, normal modes,buckling, steady state andtrasient thermal and combinedthermal and structural analysis.▸Adaptive FEA meshing providinglocal mesh refinement inareas of hgh stress gradients,producing accurate results withminimal input.▸Combined Dynamic Motionand FEA analysis allowingthe stresses that result fromthe dynamic operation of anassembly to be calculated.▸Optimization using FEA, Motionor combined results.▸Integration with MATLAB/Simulink for co-simulation ofmechanical assemblies andcontrol systems.▸The ability to open andupdate CAD files directly fromSOLIDWORKS.▸The Plug-in for SOLIDWORKS,that allow associated modeltransfers along with assemblyconstraints, parameters anddimensions to be used foroptimization.▸Key-framed animationcoupled with photo-realisticrendering allowing productionof high definition videos andfly-throughs of a design inoperation.▸Optional Durability moduleproviding fatigue calculations inorder to predict product life.Fatigue life plot of a door armSimWise 4D Integrated Motion and Stress AnalysisAnimation CapabilitiesFlexible key framing and animationsof exploded assembliesShadows, surface rendering,and texture mappingClipping planes to “cutaway” sectionsAVI video creation。
和谐型机车车轮多边形激励下构架动态响应分析
和谐型机车车轮多边形激励下构架动态响应分析张勇，吴兴文，罗贇，刘开成（西南交通大学牵引动力国家重点实验室，四川成都610031）摘要：针对某类型电力机车车轮存在严重的非圆形现象，结合有限元方法和多体动力学的思想，建立了机车刚柔耦合的动力学模型。
并分析了在车轮多边形的轨道激励下机车构架的动应力响应以及机车构架疲劳强度的影响。
通过建立扫频模型，确认构架共振弱区在0～200Hz频率范围内节点的疲劳强度，发现考虑构架的柔性能很好地反映出构架在多边形激励下的动态响应，构架在18阶多边形激励下主要体现为70Hz的主频振动。
进一步分析不同车速和波深对构架振动的影响，结果表明构架加速度幅值与波深呈线性关系，与车速不呈线性关系；通过计算多边形激励下刚性构架和柔性构架随车速变化的加速度可知，柔性构架能很好的反映出车多边形对系统振动的响应，此外，发现在55km/h速度下，柔性构架加速度幅值存在突变现象，是由于多边形通过频率引起的构架的垂直弯曲变形。
分析计算了车轮多边形激励下构架动应力的响应，工况设置为车速120km/h，多边形波深0.2mm，提取构架在该工况下的主应力时间历程，依据疲劳极限法评估节点的主应力，结果表明疲劳强度是可靠的。
关键词：HXD1型电力机车；车轮多边形；主应力；疲劳极限中图分类号：U270.1+1文献标志码：A doi：10.3969/j.issn.1006-0316.2021.01.008文章编号：1006－0316(2021)01－0052－09Dynamic Response of Bogie Frame in the Presence of Wheel Polygonal WearZHANG Yong，WU Xingwen，LUO Yun，LIU Kaicheng(Traction Power State Key Laboratory,Southwest Jiaotong University,Chengdu610031,China) Abstract：Aiming at dealing with the serious non-circular phenomenon of a certain type of electric locomotive wheels,a dynamic model of rigid-flexible coupling locomotive is established with the finite element method and the idea of multi-body dynamics.The dynamic stress response of the locomotive frame under the excitation of the wheel polygon track and the influence of the fatigue strength of the locomotive frame are analyzed.By establishing a frequency sweeping model,the fatigue strength of nodes in the weak resonance region of the framework in the frequency range of0to200Hz is confirmed.Taking the flexibility of the framework into consideration,the dynamic response of the framework under polygonal excitation can be well reflected.Main frequency vibration of the framework is70Hz when excited by the polygon of18th order..Further analysis of the effects of different vehicle speeds and wave depths on the vibration of the frame shows that the amplitude of the frame acceleration has a linear relationship with wave depth but no linear relationship with vehicle speed.By calculating the acceleration of the rigid frame and the flexible frame with the change of vehicle speed under the ———————————————收稿日期：2020－05－18基金项目：国家自然科学基金高铁联合基金（U1734201）；大功率交流传动电力机车系统集成国家重点实验室开放课题（2017ZJKF01）作者简介：张勇（1995－），男，湖北孝感人，硕士研究生，主要研究方向为机车车辆动力学和结构疲劳强度，E-mail：**************；罗贇（1967－），女，贵州安顺人，博士，研究员，硕士生导师，主要研究方向为机车车辆动力学。
基于多柔体动力学的地铁单转向架性能研究
基于多柔体动力学的地铁单转向架性能研究许方炜;唐华平;李云召【摘要】To analyze dynamic performance of metro bogie`s course of traveling along curves systematically, a multi flexible simulation model of the whole bogie was built, which takes the mutual contact between wheels and tracks and the motion relationship among different parts of the bogie into account. The curve of the actuating axis`s motion was designed to simulate the real process of electric motor`s actuating process. The vertical and horizontal acceleration, the wheel load of each side and the dynamic stress of some particular parts of the bogie was calculated. The ride stability and running stability was analyzed. The dynamic performance of the bogie was researched and compared to the experiment data. The simulation result is quite consistent to the experiment data. A new method of system simulation modeling which is closer to the real running state was put forward for the research and analysis of bogies based on multi flexible body dynamics.%为系统分析地铁转向架在曲线通过过程中的动力学性能,以单个地铁转向架整体为研究对象,建立包含轮轨接触和各部件真实运动关系的多柔体地铁单转向架仿真模型.根据实际运行情况设计驱动轴运动曲线来模拟真实的列车运行过程,计算其曲线通过过程的垂向、横向加速度、左右轮重以及部分关键部位的动应力.分析转向架的平稳性与稳定性,研究转向架的动力学性能并与实验数据进行对比,结果基本一致.为转向架的研究与分析提出一种更接近实际运行情况的大型多柔体动力学系统仿真建模方法.【期刊名称】《铁道科学与工程学报》【年(卷),期】2018(015)001【总页数】7页(P206-212)【关键词】轨道车辆;有限元仿真;多柔体;转向架;动力学性能【作者】许方炜;唐华平;李云召【作者单位】中南大学机电工程学院,湖南长沙 410000;中南大学机电工程学院,湖南长沙 410000;中车株洲电力机车有限公司,湖南株洲 412000【正文语种】中文【中图分类】U260.331;U231转向架是承载车体自重以及引导车辆行走的关键部位，地铁的评价标准，即其运行稳定性和平稳性决定着转向架动力学性能的好坏。
最新2020年第五代移动通信技术(5G)测试题库288题(含参考答案)
2020年5G考试题库288题一、选择题1．下面关于BWP的描述正确的是（）A) BWP可以支持更低的UE带宽能力B) BWP可以支持不同的numerologyC) BWP的灵活调度可以大大降低功耗D) 在某一个时刻，最多只能有一个激活的DLBWP和UL BWP2．下列哪些双联接的类型属于MR-DC()A) GNEN-DCB) EN-DCC) NE-DCD) NR-NR3．5G的含义包括：无所不在、超宽带、（）的无线接入。
A) 低延时B) 高密度C) 高可靠D) 高可信4．5G核心网网元包括（）A) AMFB) SMFC) UPFD) NEF5． 5G NR中ΔFGlobal 可以是( )A) 5kHzB) 15kHzC) 30kHzD) 60Khz6．下列哪几种可以称作SpCell. ()A) PrimarycellB) MCGSecondary cellC) PSCellD) SCGSecondary cell7． NR下， RNA的组成方式有下面哪几种选择( )A) List ofcells；B) List ofRAN areas；C) List ofTAs；D) List ofPLMN。
8． EN-DC下可以建立哪些SRB ( )A) SRB0B) SRB1C) SRB2D) SRB39．5G需求驱动力（）A) 大视频B) 物联网C) VR/ARD) 自动驾驶10．下面哪些RB可以配置不同的PDCP Version ( )A) SRB1B) SRB2C) MNterminated MCG BearerD) SNterminated MCG Bearer11．关于5GRLM下面描述正确的是（）A) 至少有一个资源比Q_out好，就上报ISB) 至少有一个资源比Q_in好，就上报ISC) 所有资源都比Q_out差，就上报OOSD) 所有资源都比Q_in差，就上报OOS12．MCGfailure 的触发原因有哪几种. ()A) upon T310expiryB) upon T312expiryC) uponrandom access problem indication from MCG MAC while neither T300, T301, T304nor T311 is runningD) uponindication from MCG RLC that the maximum number of retransmissions has beenreached for an SRB or DRB13．MCGfailure 后，下面正确的是 ( )A) 安全模式已建立情况下，启动重建流程；B) 安全模式已建立情况下，回IDLE；C) 安全模式未建立情况下，启动重建流程；D) 安全模式未建立情况下，回IDLE;14．NR测量根据RS接收信号的类型可以分为：（）A) 基于SSB的测量B) 基于CSI的测量C) 基于CSI-RS的测量D) 基于PSS的测量15．NR测量中测量上报的quantity可以为：（）A) RSRPB) RSRQC) RSSID) SINR16．基于SSB的NR测量，小区的信号质量除了由最好的beam合成这种情况外,其余情况取决于以下哪些因素：（）A) nrofSS-BlocksToAverageB) absThreshSS-BlocksConsolidationC) maxNrofRSIndexesToReportD) reportQuantityRsIndexes17．关于dualConnectivityPHR以下说法正确的是 ( )A) LTE DC下两个CG都会配置B) LTE DC下只配置MCG的相关参数C) EN-DC下两个CG都会配置PHR相关参数D) EN-DC下只配置MCG的相关参数18．划分SUL频段的意义是（）A) 增大上行数据传输速率B) 增大下行数据传输速率C) 与3.5GHz搭配使用，补充上行覆盖范围D) 与5GHz搭配使用，补充下行覆盖范围参考答案：C19． EN-DC下哪些SRB支持被配置成Split SRB ()A) SRB0B) SRB1C) SRB2D) SRB320．5G无线接入的关键技术主要包含（）A) 大规模天线阵列B) 超密集组网（UDN）C) 全频谱接入D) 新型多址21．以下哪种SSB必须在SS raster 上（）A) 用于NR Pcell接入的SSBB) 用于NR Scell接入的SSBC) 用于PScell接入的SSBD) 用于测量的SSB参考答案：A22．题干选项A选项B选项C选项D选项G23．下面属于5G NR下行链路reference signal的是（）A) Demodulation reference signals for PDSCHB) Phase-tracking reference signals for PDSCHC) Demodulation reference signals for PDCCHD) Demodulation reference signals for PBCH24．5G中PDSCH调制方式是（）A) QPSKB) 16QAMC) 64QAMD) 256QAM25．5G中PUCCH中UCI携带的信息（）A) CSI（Channel State Information）B) ACK/NACKC) 调度请求（Scheduling Request）D) 以上都不是26．下面哪些RB可以配置不同的PDCP Version ( )A) SRB1B) SRB2C) MNterminated MCG BearerD) SNterminated MCG Bearer27．下面属于5G频段的是 ( )A) 3300-3400MHzB) 3400-3600MHzC) 4800-5000MHzD) 1880-1900MHz28．5G正在研发中，理论速度可达到（D）参考答案：A、50Mbps参考答案：B、100Mbps参考答案：C、500Mbps参考答案：D、1Gbps29．NR测量中测量上报的quantity可以为（）A) RSRPB) RSRQC) RSSID) SINR30．下面属于长PUCCH的是（）A) PUCCHformat 0B) PUCCHformat 1C) PUCCHformat2D) PUCCHformat331．在NR下，满足如下哪几个条件之后，UE才会验证接收到的PDCCH是否用于SPS的激活和释放（）A) PDCCH的CRC校验位使用SPS C-RNTI进行加扰B) PDCCH的CRC校验位使用CS-RNTI进行加扰C) NDI域为0D) NDI域为132．下列对于SUL描述正确的是（）A) 为补充上行覆盖划分的低频band，仅用与上行传输；B) 当DL RSRP高于设定阈值时，在SUL上发起随机接入；C) 支持PUCCH和PUSCH分别在SUL和NUL上发送；D) R15支持PUSCH同时在normalUL和SUL上传输；33．BWP Generic parameter包括（）A) locationAndBandwidthB) subcarrierSpacingC) cyclicPrefixD) bwp-Id34．NR中上行HARQ采用下列哪种方式（）A) 异步B) 同步C) 自适应D) 非自适应35．5G支持在（）上的RLMA) SpcellB) PscellC) PcellD) Scell36．5G RLM使用的参考信号是 ()A) SSB RSB) CSI-RSC) C-RSD) DM-RS37．5G中PUSCH支持的波形包括（）A) DFT-S-OFDMB) CP-OFDMC) DFT-OFDMD) D.S-OFDM38．NR测量根据RS接收信号的类型可以分为：（）A) 基于SSB的测量B) 基于CSI的测量C) 基于CSI-RS的测量D) 基于PSS的测量39．下列关于5GNR slot format说法正确的是（）A) 对DL/UL分配的修改以slot为单位B) SCS=60KHz时，支持配置Periodic=0.625msC) Cell-specific的单周期配置中，单个配置周期内只支持一个转换点D) 在R15，UE-specific配置的周期和cell-specific配置的周期可以不一致参考答案：C40．当没有配置监听DCIformat 2_0的PDCCH时，以下哪种overwriting的方式是符合规则的（）A) DCI format1_0/1_1 将UE-specific配置为U的符号改写为接收PDSCHor CSI-RS；B) DCI format0_0/0_1/2_3将UE-specific配置为D的符号改写为发送PUSCH, PUCCH, PRACH, or SRS；C) DCI format1_0/1_1 将UE-specific配置为flexible的符号改写为接收PDSCHor CSI-RS；D) DCI formatDCI format 0_0/0_1/1_0/1_1/2_3 将UE-specific配置为flexible的符号改写为发送PUSCH，PUCCH，PRACH或SRS；41．SCG的主小区被称作 ( )A) Primary cellB) MCG Secondary cellC) SCG Secondary cellD) PSCell参考答案：D42．TRS的频域密度（density）为（）A) 0.5B) 1C) 3D) 以上都对参考答案：C43．UE在每个NR serving小区下最多监听几个通过C-RNTI加扰的DCI Format（）。
漂浮式海上风电机组动力学仿真分析-2012-6页
(1) 其方差为：
∫ σ 2 =
∞ −∞
Sζ
1−sided
(ω
)dω
(2)
其中：H 为波高；ω 为频率；λ 为波长；Tp 为波周期； l 为结构特征尺度；γ 为谱峰升高因子；d 为水深。
由此可得波高程为：
∫ ζ (t) = 1
2π
+∞W (ω)
−∞
2πSζ2−Sided (ω)e jωt dω
(3)
为：
F Hydrostatic = −ρ gV0δ13 + CiHj ydrostaticq j
(6)
其中：−ρgV0δ13 为阿基米德浮力，即该力是垂直向上， 其值与平台的重力相等；V0 为当支撑平台不动时排开
第4期
王磊，等：漂浮式海上风电机组动力学仿真分析
1311
的流体体积；CiHj ydrostaticq j 为受水平面和漂浮中心影响 的水静力和力矩部分；j 为水平面内、与 i 为方向垂直 方向的自由度；qj 为 j 方向的坐标。
将式(5)，式(6)与式(8)相加，由此可得浮式平台的 水动力 FiHydro 为：
FiHydro = FiWaves + F Hydrostatic + F rad
3. Department of Ship Engineering, HarBin Engineering University, Harbin 150001, China)
Abstract: Dynamics of deep-sea floating wind turbine was analyzed by the computer simulation technology. Firstly the wave dynamics model of floating platform and aerodynamics model of wind turbine based on the generalized dynamic wake (GDW) theory were established. Secondly, the force was loaded on the multi-flexible body dynamics model of wind turbine including “wind rotor -nacelle- tower- mooring system” which was established in FORTRAN. And then the whole model and results were turned into ADAMS model. Taking a 5 MW wind turbine for example, floating wind turbine system was analyzed by multi-field coupling dynamic model. The results show that during operation of the floating wind turbine, its floating platform must withstand great hydrodynamic force, and the dynamic response of the whole structure and fluctuation of power are greatly impacted by the coupling of aerodynamic and hydrodynamic loads. Key words: floating platform; GDW theory; multi-flexible body dynamics; wind turbine; mooring system
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Presented at the ASME Wind Energy Symp., Reno, January and Stol11 considers coupling of flapping motion of blades, teetering motion of hub, and yawing motion of tower, based on rigid body dynamic analysis using Symdyn, a symbolic dynamic rigid-body dynamic analysis code similar to YawDyn. The result of this study identifies instability may occur in the teetering mode of hub. This significant result indicates that more accurate and meaningful dynamic analysis of HAWT’s demands new methodology to consider both the coupling of the subsystems including teeter degree of freedom of hub and the flexibility of tower and blades. The goal of the present work is to develop a tool for aeroelastic modeling of horizontal-axis wind turbines that, when applied to simplified analytical models, can be used in control design. As a first step, a consistent structural analysis is presented which models the dynamic characteristics of the wind turbine consisting of connected flexible bodies in a vacuum. An aerodynamic model will be added later to construct a complete analysis tool.
∗ Post Doctoral Fellow, School of Aerospace Engineering. Member, AIAA. Presently, Assistant Professor (Research), Duke University, Durham, North Carolina. † Graduate Research Assistant, School of Aerospace Engineering. Student Member, AIAA. ‡ Professor, School of Aerospace Engineering. Fellow, AIAA.
INTRODUCTION
Accurate modeling and analysis of wind turbines is quite useful and has the potential of increasing the economic efficiency of wind-energy generation. Firstly, it helps in understanding the dynamic response of the wind turbine to disturbances at various levels of wind loading. Such insight into the behavior helps in better design of the wind turbines not only to improve efficiency of energy conversion, but also to improve the life of the structure. Secondly, an accurate model will help in designing efficient controllers leading to better performance and extended working life. There are various research efforts throughout the world aimed at
Copyright c 2001 by Mayuresh J. Patil, Donghoon Lee, and Dewey H. Hodges. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.
AIAA 2001–0064
Multi-Flexible-Body Dynamic Analysis of Horizontal-Axis Wind Turbines
Mayuresh J. Patil,∗ Donghoon Lee,† and Dewey H. Hodges‡ Georgia Institute of Technology, Atlanta, Georgia 30332-0150 ABSTRACT
A dynamic stability analysis is presented for a horizontal-axis wind turbine modeled as a multi-body system with both rigid- and flexible-body subsystems. The rigid-body subsystems are modeled as an interconnected set of rigid bodies using Kane’s method, which can lead to equations of motion that are more compact than they would be using other methods. The flexible-body subsystems are modeled using nonlinear beam finite elements, derived from a mixed variational formulation for the dynamics of moving beams. The equations for the rigid and flexible subsystems are coupled to obtain a unified framework that models the dynamic behavior of the complete system. Linearization of the dynamic equations about the steady-state solution yields system equations with periodic coefficients that must be solved by Floquet theory to extract the dynamic characteristics. Numerical studies are presented to investigate the natural frequencies and mode shapes for a wind turbine with flexible blades. The presented results demonstrate the performance of the present methodology to aid in understanding of the dynamic characteristics of the wind turbine. better understanding of the wind-turbine. These research efforts encompass various technical disciplines, including, atmospheric modeling, wind-turbine structural and aerodynamic modeling, energy conversion system, power distribution technology. The present effort is directed towards better understanding of the structural dynamic characteristics of the wind turbines. The previous research on the structural dynamics of HAWT’s can be generally classified into three groups. The first group of studies analyzed isolated blades and were mainly conducted in 1970’s. Ormiston1 considered the basic flapping response of a wind turbine blade using elementary analytical techniques and a simple rigid, centrally hinged, spring restrained blade model. Kaza and Hammond2 considered the flap-lag stability of wind turbine rotors in the presence of velocity gradients, using a single centrally-hinged model for the blade. Kottapalli3 included flap, lead-lag, torsion degrees of freedom along with gravity loads. The coupled flap-lag-torsion dynamics of an isolated wind turbine blade was also treated by Chopra and Dugundji4 with an emphasis on nonlinear effects associated with moderate blade deflection. The studies on rotor/tower or rotor/yaw coupling problem form the second group. Mathematical modeling of coupled rotor/tower dynamical system was first presented by Warmbrodt and Friedmann.5 The coupled rotor/tower dynamics of wind turbine was treated by Garrad and Quarton6 using symbolic computing. Experimental study by Olorunsola7 indicated that the torque associated with rotor stall is an important factor in the yaw motion of HAWT. A concentrated study on the yaw motion of the rotor of HAWT’s was done by Hansen8 along with the development of the YawDyn code. Bir and Butterfield9 studied the effect of tower flexibility on the system modes using ADAMS. The third group of studies consider the complete system dynamics of HAWT’s. Molenaarx and Dijkstra10 presented the development of the complete system dynamics model of a wind turbine using “superelement” modeling method used to divide the structure into a number of superelements consisting of four rigid bodies connected by torsional springs and dampers. A recent study of the structural modeling of HAWT’s