Dynamics Analysis of a Parallel Mill-turn Tool Spindle Head Driven by Dual-linear Motors Using Extended Transfer Matrix Method

The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine tool application,due to the difficulty of solving the hybrid equations or the limitation of current software when dealing with the hybrid dynamics.The extended transfer matrix method（E-TMM）,which extends elements in three-dimensional space with higher matrixes,is proposed to simplify the modeling process of the hybrid dynamics.The E-TMM modeling approaches of 3 basic elements including 3D vibrant rigid body,joint and flexible body are studied in details.A parallel mill-turn tool spindle head unit driven by dual-linear motors is chosen as a plant to demonstrate the E-TMM modeling process.By using E-TMM,the spindle head unit is simplified as a topological network consisting of the three types of element,i.e.,3D vibrant rigid body,joint and flexible body,including 11 rigid bodies,14 joints and 1 3D-Timoshenko beam.Then the dynamic model of the system can be easily obtained by deducing the element-network by means of state vector transformation.The dynamic characteristics of the spindle head,such as natural frequencies,dynamic flexibility,etc.can be predicted by solving the obtained model.Experiment verification indicates that the E-TMM is valid with enough accuracy in the dynamic analysis of the parallel mill-turn tool spindle head.The E-TMM is capable of modeling the dynamics of machine tool structure with no requirements of deducing and solving the sophisticated differential equations.Moreover,the E-TMM provides a simple and elegant tool for hybrid dynamic analysis in future dynamic design of machine tools.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Dynamic characteristics of a WPC-comparison of transfer matrix method and FE method

To find the difference in dynamic characteristics between conventional monohull ship and wave penetrating catamaran (WPC), a WPC was taken as an object; its dynamic characteristics were computed by transfer matrix method and finite element method respectively. According to the comparison of the nature frequency results and mode shape results, the fact that FEM method is more suitable to dynamic characteristics analysis of a WPC was pointed out, special features on dynamic characteristics of WPC were given, and some beneficial suggestions are proposed to optimize the strength of a WPC in design period.

Enabling the transfer matrix method to model serial-parallel compliant mechanisms including curved flexure beams

Compliant mechanisms with curved flexure hinges/beams have potential advantages of small spaces,low stress levels,and flexible design parameters,which have attracted considerable attention in precision engineering,metamaterials,robotics,and so forth.However,serial-parallel configurations with curved flexure hinges/beams often lead to a complicated parametric design.Here,the transfer matrix method is enabled for analysis of both the kinetostatics and dynamics of general serial-parallel compliant mechanisms without deriving laborious formulas or combining other modeling methods.Consequently,serial-parallel compliant mechanisms with curved flexure hinges/beams can be modeled in a straightforward manner based on a single transfer matrix of Timoshenko straight beams using a step-by-step procedure.Theoretical and numerical validations on two customized XY nanopositioners comprised of straight and corrugated flexure units confirm the concise modeling process and high prediction accuracy of the presented approach.In conclusion,the present study provides an enhanced transfer matrix modeling approach to streamline the kinetostatic and dynamic analyses of general serial-parallel compliant mechanisms and beam structures,including curved flexure hinges and irregular-shaped rigid bodies.

基于传递矩阵法的指向式旋转导向工具主轴振动特性

指向式旋转导向工具应用于井眼轨迹控制时,其主轴的动力学特性将直接影响到井眼轨迹控制效果及作业安全,而在钻进工况下,工具钻压传递机构在主轴上的位置对主轴的动力学特性起着重要的作用。因此,为了分析钻压传递机构的位置对主轴动力学特性的影响,利用多体系统传递矩阵法建立了指向式旋转导向工具外壳-轴承-主轴系统的动力学模型。通过推导主轴上任意节点的几何和力学方程,该研究能够评估钻压传递机构的位置对主轴动态性能的影响规律。结合实例运算分析了钻压传递机构的安装位置对主轴固有频率和振型的影响,探讨了工具造斜时,钻压传递机构安装位置对主轴动态位移的影响。结果表明,随着钻压传递机构安装位置距离钻头越远,主轴固有频率和动态位移均增大,因此在满足工作要求下,推荐钻压传递机构安装位置尽可能靠近钻头端。为验证基于传递矩阵法建立的主轴动力学模型的正确性以及钻压传递装置安装位置对主轴动态位移影响规律,在指向式旋转导向工具试验台架上进行了钻进工况下主轴测点偏移量测试试验,结果表明,试验测得的数据与理论计算的数据基本吻合,误差最大仅为6.47%。

基于传递矩阵法的足式机器人四连杆腿部机构正向与逆向动力学分析

为了保证足式机器人腿部机构的控制准确性与实时性,利用向量代数方法,对足式机器人四连杆腿部机构进行几何运动学分析;根据有限元形函数理论,建立足式机器人四连杆腿部机构典型构件的质量离散方法;在几何运动学分析的基础上,基于力矩平衡原理,分别进行正向与逆向动力学分析;利用线性变换原理并结合传递矩阵法,建立足式机器人四连杆腿部机构正-逆向动力学统一模型,并利用Adams软件建立足式机器人四连杆腿部机构虚拟样机模型,进行正向与逆向动力学仿真实例分析。结果表明,所建立的足式机器人四连杆腿部机构正-逆向动力学统一模型与虚拟样机模型3个油缸力与3个方向足底力的误差分别小于1%与3%,验证了所建立的足式机器人四连杆腿部机构正-逆向动力学统一模型能够精确地求解油缸力与足底力。

基于分离源矩阵变换器的PMSM无源动态演化控制策略

为了改进传统的永磁同步电机驱动器系统及其PID控制的不足,提出了一种无源动态演化控制策略,并应用于永磁同步电机(permanent magnet synchronous motor,PMSM)和分离源矩阵变换器(split source matrix con-verter,SSMC)中。为打破传统矩阵变换器电压传输比0.866的限制,采用电感、电容和3个二极管代替了双级矩阵变换器中间的支流链路部件,并且证明了分离源网络的升压能力。另外,在矢量控制中,永磁同步电机的转速外环和电流内环都使用了传统PID控制器,但由于PID控制器的参数调节比较困难、控制精度不高、超调量较大和抗干扰能力不强等问题,为此提出了基于动态演化理论和无源理论的控制策略,设计了分离源矩阵变换器和永磁同步电机系统基于互联和阻尼分配(the interconnection and damping assignment,IDA)的无源控制器(passivity-based control,PBC)和动态演化控制器(dynamic evolution controller,DEC)。仿真与实验的结果表明,基于该控制策略的SSMC-PMSM驱动系统能够使永磁同步电机稳定运行在额定转速,并且具有稳定性强、抗干扰能力强和动态响应好等特点。

特种电机转子系统的临界转速分析

针对我公司开发的压裂泵试验台电机在特殊工况下的运行特点进行了研究。采用传递矩阵法,对压裂泵试验台电机在两台电机串联运行的情况进行了分析计算,为了提高计算效率,应用Matlab平台在传递矩阵法的基础上进行了程序编制,并对电机转子结构进行了等效处理,最终实现对此种特殊工况的临界转速计算。通过对这种等效计算方法的研究,为压裂泵试验台电机以及其他特种电机的研发提供了技术支撑。

An efficient and modular modeling for launch dynamics of tubed rockets on a moving launcher

This paper develops a modular modeling and efficient formulation of launch dynamics with marching fire(LDMF)using a mixed formulation of the transfer matrix method for multibody systems(MSTMM)and Newton-Euler formulation.Taking a ground-borne multiple launch rocket systems(MLRS),the focus is on the launching subsystem comprising the rocket,flexible tube,and tube tail.The launching subsystem is treated as a coupled rigid-flexible multibody system,where the rocket and tube tail are treated as rigid bodies while the flexible tube as a beam with large motion.Firstly,the tube and tube tail can be elegantly handled by the MSTMM,a computationally efficient order-N formulation.Then,the equation of motion of the in-bore rocket with relative kinematics w.r.t.the tube using the Newton-Euler method is derived.Finally,the rocket,tube,and tube tail dynamics are coupled,yielding the equation of motion of the launching subsystem that can be regarded as a building block and further integrated with other subsystems.The deduced dynamics equation of the launching subsystem is not limited to ground-borne MLRS but also fits for tanks,self-propelled artilleries,and other air-borne and naval-borne weapons undergoing large motion.Numerical simulation results of LDMF are given and partially verified by the experiment.

Discrete time transfer matrix method for dynamics analysis of complex weapon systems

Efficient, precise dynamic modeling and analysis for complex weapon systems have become more and more important in their dynamic design and performance optimizing. As a new method developed in recent years, the discrete time transfer matrix method of multibody system is highly efficient for multibody system dynamics. In this paper, taking a shipboard gun system as an example, by deducing some new transfer equations of elements, the discrete time transfer matrix method of multibody sys- tem is used to solve the dynamics problems of complex rigid-flexible coupling weapon systems successfully. This method does not need the global dynamic equations of system and has the low order of system matrix, high computational efficiency. The proposed method has advantages for dynamic design of complex weapon systems, and can be carried over straightforwardly to other complex mechanical systems.

A novel launch dynamics measurement system for multiple launch rocket system and comparative analysis with numerical simulations

In this paper,a novel launch dynamics measurement system based on the photoelectric sensor pair is built.The actual muzzle time(i.e.a time duration that originates from the initial movement to the rocket’s departure from the muzzle)and the muzzle velocity are measured.Compared with the classical methods,the actual muzzle time is obtained by eliminating the ignition delay.The comparative analysis method is proposed with numerical simulations established by the transfer matrix method for multibody systems.The experiment results indicate that the proposed measurement system can effectively measure the actual muzzle time and reduce the error of classical methods,which match well with the simulation results showing the launch dynamics model is reliable and helpful for further analysis and design of the MLRS.

电磁轨道炮导轨身管系统动力学分析

针对电磁轨道炮等新概念电磁发射系统发射动力学建模复杂、计算成本高等难题,考虑上下导轨非对称性影响,将上下导轨视为横向振动梁,身管视为在特定位置作用两弹性支撑的横向振动梁,导轨与身管间的相互作用视为连续分布弹簧,建立导轨身管系统三梁动力学模型。利用多体系统传递矩阵法推导系统各部分传递矩阵,组装系统总传递方程,求解系统任意位置在对应频率下的状态矢量。通过毕奥-萨伐尔定律解算导轨间及枢轨间的电磁力作用系数,分析导轨所受电磁力分布规律。利用模态叠加法求解系统静位移和在重力及时变电磁力作用下的动态响应,并与商业有限元软件计算结果比较,验证该方法的有效性和快速性。分析发现当电流较小时,系统在静变形位置附近波动,电流达到峰值平台后,上下导轨间距在“扩张-收缩”的过程中反复震荡;上导轨由于弹性支撑参数等非对称性因素的影响变形量更大,为电磁轨道炮耦合系统动力学分析提供理论支撑。

Transfer matrix method for multibody systems(Rui method) and its applications

The transfer matrix method for multibody systems, namely the "Rui method", is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.

Multibody system transfer matrix method:The past, the present, and the future

The multibody system transfer matrix method(MSTMM),a novel dynamics approach developed during the past three decades,has several advantages compared to conventional dynamics methods.Some of these advantages include avoiding global dynamics equations with a system inertia matrix,utilizing low‐order matrices independent of system degree of freedom,high computational speed,and simplicity of computer implementation.MSTMM has been widely used in computer modeling,simulations,and performance evaluation of approximately 150 different complex mechanical systems.In this paper,the following aspects regarding MSTMM are reviewed:basic theory,algorithms,simulation and design software,and applications.Future research directions and generalization to more applications in various fields of science,technology,and engineering are discussed.

Reduced multibody system transfer matrix method using decoupled hinge equations

In the multibody system transfer matrix method(MSTMM),the transfer matrix of body elements may be directly obtained from kinematic and kinetic equations.However,regarding the transfer matrices of hinge elements,typically information of their outboard body is involved complicating modeling and even resulting in combinatorial problems w.r.t.various types of outboard body's output links.This problem may be resolved by formulating decoupled hinge equations and introducing the Riccati transformation in the new version of MSTMM called the reduced multibody system transfer matrix method in this paper.Systematic procedures for chain,tree,closed-loop,and arbitrary general systems are defined,respectively,to generate the overall system equations satisfying the boundary conditions of the system during the entire computational process.As a result,accumulation errors are avoided and computational stability is guaranteed even for huge systems with long chains as demonstrated by examples and comparison with commercial software automatic dynamic analysis of the mechanical system.

基于GIS的京杭大运河扬州段沿岸土地利用变化分析

以2002年SPOT5影像和2022年的GF1影像为基准,利用随机森林方法对京杭大运河扬州段沿岸1 km范围进行土地利用分类,基于土地利用转换矩阵、土地利用动态度模型和重心迁移模型进行分类后比较。结果表明:20 a间,研究区耕地、林地、水域面积减少,草地、建设用地、未利用地面积增加。耕地为转出面积最多的土地类型,主要转出为建设用地。研究区的综合土地利用动态度为0.63%,整体土地利用类型数量变化相对平稳,未利用地和建设用地的单一土地利用动态度分别为4.61%和4.10%,数量变化相对剧烈。耕地和林地重心向北迁移,建设用地和水域重心向南迁移,耕地重心迁移距离最大(6.38 km)。

高速高精度电主轴温升预测模型

提出高速高精度电主轴温升预测模型,将有限元模型与试验数据相结合,精确预测不同工况下电主轴的温度场。建立电主轴流场、温度场有限元模型,分析冷却系统及润滑系统参数对电主轴温度场的影响;考虑电主轴运行速度、载荷,设计电主轴损耗测试方法,将测得的电主轴总损耗作为计算电动机、轴承生热依据;考虑冷却系统、润滑系统参数及环境条件对换热系数的影响,采用最小二乘算法,基于电主轴表面温度测试数据,优化电主轴换热系数,并将优化后的换热系数作为有限元模型的边界条件。建立170SD30-SY电主轴温升预测模型,将换热系数优化前后的温度场仿真数据分别与试验数据对比。结果表明,换热系数优化后的温升预测模型预测的精度提高了4.78%,提出的电主轴温升预测模型有较高的预测精度。

高频电主轴临界转速计算及其影响参数分析

基于传递矩阵对高频磨削电主轴进行临界转速特性计算,分析预加负荷及砂轮组件的参数变化对临界转速的影响,为电主轴动态性能的设计提供依据。

基于传递矩阵法的电主轴动力学特性分析

研究了电主轴主要的结构参数对电主轴动力学特性的影响。运用传递矩阵法,考虑了陀螺力矩、剪切、变截面等影响因素,建立了电主轴"转子—轴承"系统的多圆盘转子动力学模型,编程并计算了电主轴的前三阶临界转速、振型等动力学特性参数,分析了电主轴轴承轴向预紧力、支承跨距及前、后端悬伸量的变化对电主轴"转子—轴承"系统临界转速的影响和变化规律。结果表明:支承跨距和悬伸量在一定范围内对临界转速有显著的影响,通过研究为电主轴的结构设计和性能优化提供依据和指导。

基于传递矩阵与有限元法对陶瓷电主轴转子动态特性的分析

目的求解170SD30-SY无内圈陶瓷电主轴转子的固有频率,分析转子动态特性.方法利用Prohl传递矩阵法、有限元法对陶瓷电主轴转子进行了固有频率的计算和仿真分析,并绘制位移与频率、刚度与频率曲线,对陶瓷电主轴转子动态特性进行分析.结果通过Prohl传递矩阵法求解的结果与有限元仿真结果对比,固有频率误差最大为12%,有限元分析得出转子前四阶振型,主轴前端振动范围及刚度与固有频率的变化趋势,从而便于研究预紧与振动之间的关系.结论通过计算与仿真验证,证实两种方法的可行性及有限元法便于求解分析,得出陶瓷电主轴的固有频率高于普通钢轴,增加刚度有利于固有频率的提高,为陶瓷电主轴转子的动态特性分析提供充分依据.