Dynamic Modeling and Simulation of Multi-body Systems Using the Udwadia-Kalaba Theory

Laboratory experiments were conducted for falling U-chain,but explicit analytic form of the general equations of motion was not presented.Several modeling methods were developed for fish robots,however they just focused on the whole fish’s locomotion which does little favor to understand the detailed swimming behavior of fish.Udwadia-Kalaba theory is used to model these two multi-body systems and obtain explicit analytic equations of motion.For falling U-chain,the mass matrix is non-singular.Second-order constraints are used to get the constraint force and equations of motion and the numerical simulation is conducted.Simulation results show that the chain tip falls faster than the freely falling body.For fish robot,two-joint Carangiform fish robot is focused on.Quasi-steady wing theory is used to approximately calculate fluid lift force acting on the caudal fin.Based on the obtained explicit analytic equations of motion(the mass matrix is singular),propulsive characteristics of each part of the fish robot are obtained.Through these two cases of U chain and fish robot,how to use Udwadia-Kalaba equation to obtain the dynamical model is shown and the modeling methodology for multi-body systems is presented.It is also shown that Udwadia-Kalaba theory is applicable to systems whether or not their mass matrices are singular.In the whole process of applying Udwadia-Kalaba equation,Lagrangian multipliers and quasi-coordinates are not used.Udwadia-Kalaba theory is creatively applied to dynamical modeling of falling U-chain and fish robot problems and explicit analytic equations of motion are obtained.

Analysis for the Deployment of Single-Point Mooring Buoy System Based on Multi-Body Dynamics Method

Deployment of buoy systems is one of the most important procedures for the operation of buoy system. In the present study, a single-point mooring buoy system which contains surface buoy, cable segments with components, anchor and so on is modeled by applying multi-body dynamics method. The motion equations are developed in discrete node description and fully Cartesian coordinates. Then numerical method is used to solve the ordinary differential equations and dynamics simulations are achieved while anchor is casting from board. The trajectories and velocities of different nodes without current and with current in buoy system are obtained. The transient tension force of each part of the cable is analyzed in the process of deployment. Numerical results indicate that the transient payload increases to a peak value when the anchor is touching the seabed and the maximum tension force will vary with different floating configuration. This work is helpful for design and deployment planning of buoy system.

Multi-Body Dynamics Modeling and Simulation Analysis of a Vehicle Suspension Based on Graph Theory

Multi-body dynamics,relative coordinates and graph theory are combined to analyze the structure of a vehicle suspension.The dynamic equations of the left front suspension system are derived for modeling.First,The pure tire theory model is used as the input criteria of the suspension multibody system dynamic model in order to simulate the suspension K&C characteristics test.Then,it is important to verify the accuracy of this model by comparing and analyzing the experimental data and simulation results.The results show that the model has high precision and can predict the performance of the vehicle.It also provides a new solution for the vehicle dynamic modeling.

STUDY ON DYNAMICS, STABILITY AND CONTROL OF MULTI-BODY FLEXIBLE STRUCTURE SYSTEM IN FUNCTIONAL SPACE

The dynamics, stability and control problem of a kind of infinite dimensional system are studied in the functional space with the method of modern Mathematics. First, the dynamical control model of the distributed parameter system with multi-body flexible and multi-topological structure was established which has damping, gyroscopic parts and constrained damping. Secondly, the necessary and sufficient condition of controllability and observability, the stability theory and asymptotic property of the system were obtained. These results expand the theory of the field about the dynamics and control of the system with multi-body flexible structure, and have important engineering significance.

Multi-body dynamic simulation research on the influence of piston engine crankshaft thrust bearings abrasion

Fault diagnosis studying on piston engine,crankshaft and gearbox is focused in this paper. The thrust bearing abrasion caused by axial movement of the crankshaft will affect the force of timing gears and oil pump gears,which will result in the fracture of gears,abnormal ignition,connecting rod cracking and collision of cylinder. Simulation based on CREO software is done to build three-dimensional models of crankshaft and gears of a WP10 diesel engine. The models are imported into ADAMS to complete multi-body dynamics simulations. The force analysis of gears in different kinds of axial movements is finished and variations rules of gear dynamic load is obtained. The presented results show that the crankshaft axial movement can cause overload and vibration on gears. Combined with the realistic case data,the fault feature through simulation research is validated and early warming parameters of gear fault are proposed.

Articulated Lifting System Modeling Based on Dynamics of Flexible Multi-Body Systems

In lifting sub-system of deep-sea mining system, spherical joint is used to connect lifting pipes to replace fixed joint. Based on Dynamics of Flexible Multi-body systems, the mechanics model of articulated lifting system is established. Under the four-grade and six-grade oceanic condition, dynamic responses of lifting system are simulated and experiment verified. The simulation results are consistent with experimental ones. The maximum moment of flexion is 322 kN-m on the first pipe under six-grade sea condition. It is seen that the articulated connection can reduce the moment of flexion. The bending deformation of pipe center is researched, and the maximum is 0. 000479 m on the first pipe. Deformation has a little effect on the motion of system. It is feasible to analyze articulated lifting system by applying the theory of flexible multi-body dynamics. The articulated lifting system is obviously better than the fixed one.

DYNAMIC CHARACTERISTICS ON PRECISION NC LATHE BASED ON MULTI-BODY SYSTEM THEORY

Based on multi-body system theory and the mainshafl system of precision NC lathe as object investigated, it is treated as a coupled rigid-flexible multi-body system which is made up of some rigid and elastic bodies in an especial linking mode. And a dynamic model is established, The problems of computing vibration characteristics are resolved by using multi-body system transfer matrix method, Resutts show that the mainshaft system of NC lathe is in the stable and reliable working area all the time. The method is simple and easy, the idea is clear. In addition, the method can be easily used and popularized in the other multi-body system.

基于功率动态分配与容量短期补偿的用户侧BESS复用策略

用户侧电池储能系统(BESS)在维持新能源高渗透电网电力电量平衡中扮演着重要角色,其面向峰谷套利和调频的复用模式受到了广泛关注。但该模式下,BESS调度面临峰谷套利价格时变性和调频需求随机性的双重挑战。为更好地利用BESS资源,以最大化用户侧BESS日内收益为目标,提出了基于功率动态分配与容量短期补偿的用户侧BESS复用策略,并形成以套利功率、调差系数、容量补偿系数为核心参数的复用结果。仿真分析表明,通过动态功率分配,实现了BESS功率面向峰谷套利和调频的动态调整;通过容量短期补偿,实现了BESS对频率偏差信号的持续跟踪,并有效避免了容量越限的发生,BESS综合收益显著提升。

亚里士多德的Dynamis概念——记陈康先生一篇新发现的论文

本文通过细致的文史考证,首先说明了陈康先生的一篇旧文《亚里士多德的Dynamis概念》被重新发现的前因后果、来龙去脉。在此基础上,通过对陈康先生这篇文章中的多个重要观点的阐述,本文指出了这篇文章所具有的学术价值,表明这篇文章不仅对于我们理解亚里士多德的Dynamis概念的多种意义是重要的,而且对于我们理解与Dynamis概念有关的亚里士多德多个重要文本之间的思想关联也是重要的。本文也从发生学方法的角度对陈康先生在这篇文章中的研究结论提出了一些批评。

基于浮标站观测的磨刀门洪枯季径潮动力作用规律及相关性分析

为揭示磨刀门主要动力因子对潮流运动的作用规律,采用主潮通量算法计算洪枯季半月不同时间尺度下的潮流动力特征值,采用多元线性回归法对特征值的相关性进行拟合分析。结果表明,磨刀门水道内平均落潮流速洪季比枯季总体大约14%,但涨潮平均流速仅为枯季一半;水道内洪季余流流速很大,枯季可忽略不计;口门外东汊和西汊涨潮流态洪季存在相互顶托,枯季均为西南向,洪枯季余流流速西汊均大于东汊,近底层水深范围存在逆时针半环流结构,且枯季尤为明显。潮汐动力和海面风对水道内余流影响较小,径流动力洪季影响显著、枯季影响很小。由于洪季径流动力强劲,东汊和西汊净潮通量变化规律一致;枯季磨刀门水道净通量主要输运至东汊水域,随沿岸流朝西南方向输运进入西汊,然后随离岸流朝南侧外海方向输出,符合口门外逆时针半环流结构的输运特征。

Hydrodynamic Interactions of Three Barges in Close Proximity in A Floatover Installation

The hydrodynamics of side-by-side barges are much more complex than those of a single barge in waves because of wave shielding, viscous effects and water resonance in the gap. In the present study, hydrodynamic coefficients in the frequency domain were calculated for both the system of multiple bodies and the isolated body using both low-order and higher-order boundary-element methods with different element numbers. In these calculations, the damping-lid method was used to modify the free-surface boundary conditions in the gap and to make the hydrodynamic results more reasonable. Then far-field, mid-field and near-field methods were used to calculate wave-drift forces for both the multi-body system and the isolated body. The results show that the higher-order method has faster convergence speed than the low-order method for the multi-body case. Comparison of different methods of computing drift force showed that mid-field and far-field methods have better convergence than the near-field method. In addition, corresponding model tests were performed in the Deepwater Offshore Basin at Shanghai Jiao Tong University. Comparison between numerical and experimental results showed good agreement.

New Method for Predicting the Motion Responses of A Flexible Joint Multi-Body Floating System to Irregular Waves

A new hybrid method of frequency domain and time domain is developed in this paper to predict the motion responses of a flexibly joint multi-body floating system to irregular waves. The main idea of the method is that the three-dimensional frequency method is used to obtain the hydrodynamic coefficients and the response equations are solved in time domain step by step. All the forces can be obtained at the same time. The motions and nonlinear mooring forces of a box type six-body floating system are predicted. A comparison of the theoretical method-based Solutions with experimental results has shown good agreement.

Optimal design method for force in vibration control of multi-body system with quick startup and brake

A kind of active vibration control method was presented through optimal design of driving load of multi-body system with quick startup and brake. Dynamical equation of multi-body system with quick startup and brake was built, and mathematical model of representing vibration control was also set up according to the moving process from startup to brake. Then optimization vibration control model of system driving load was founded by applying theory of optimization control, which takes rigid body moving variable of braking moment as the known condition, and vibration control equation of multi-body system with quick startup and brake was converted into boundary value problem of differential equation. The transient control algorithm of vibration was put forward, which is the analysis basis for the further research. Theoretical analysis and calculation of numerical examples show that the optimal design method for the multi-body system driving load can decrease the vibration of system with duplication.

Optimization of actuator/sensor position of multi-body system with quick startup and brake

A new method was put forward to optimize the position of actuator/sensor of multi-body system with quick startup and brake. Dynamical equation was established for the system with intelligent structure of piezoelectric actuators. According to the property of the modes varying with time, the performance index function was developed based on the optimal configuration principle of energy maximal dissipation, and the relevant optimal model was obtained. According to its characteristic, a float-encoding genetic algorithm, which is efficient, simple and excellent for solving the global-optimal solution of this problem, was adopted. Taking the plane manipulator as an example, the result of numerical calculation shows that, after the actuator/sensor position being optimized, the vibration amplitude of the multi-body system is reduced by 35% compared with that without optimization.

Dynamic Analysis of the Seafloor Pilot Miner Based on Single-Body Vehicle Model and Discretized Track-Terrain Interaction Model

In order to achieve the complex dynamic analysis of the self-propelled seafloor pilot miner moving on the seafloor of extremely cohesive soft soil and further to make it possible to integrate the miner system with some subsystems to form the complete integrated deep ocean mining pilot system and perform dynamic analysis, a new method for the dynamic modeling and analysis of the miner is proposed and developed in this paper, resulting in a simplified 3D single-body vehicle model with three translational and three rotational degrees of freedom, while the track-terrain interaction model is built by partitioning the track-terrain interface into discrete elements with parameterized force dements built on the theory of terramechanics acting on each discrete dement. To evaluate and verify the correctness and effectiveness of this new modeling and analysis method, typical comparative studies with regard to computational efficiency and solution accuracy are carried out between the traditional modeling method of building the tracked vehicle as a multi-body model and the new modeling method. In full consideration of the particMar structure design of the pilot miner, the special characteristics of the seafioor soil and the hydrodynamic force of near-seafloor currnt, the dynamic simulation analysis of the miner is performed and discussed, which can provide useful guidance and reference for the practical miner system in design and operation. This new method can not only realize the rapid dynamic simulation analysis of the miner but also make possible the integration and rapid dynamic analysis of the complete integrated deep ocean mining pilot system in further researches.

MOTION TYPES AND CHAOS OF MULTI-BODY SYSTEMS VIBRATING WITH IMPACTS

In this paper,the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts.We discover that if every motion of the system is bounded,it has only four different types:periodic motion 7 t,non-periodic recurrent motion γ2,and non-Poisson stable mo- tions γ3 and γ4 approaching γ1 and γ2, respectively.γ2 is the source of chaos.It is very interesting that cha- otic motions seem stochastic but possess the character of recurrence.By way of example,we discuss chaotic motions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is different from that obtained by Holmes.

KEY TECHNIQUES OF MULTI-BODY MODELING OF OCCUPANT RESTRAINT SYSTEM OF VEHICLE SIDE IMPACT

Based on multi-body dynamics, the simulation models of auto-side structures and occupant＇s dynamic responses are set up, using the occupant injury simulation software MADYMO3D. These models include auto-body structure, impact barrier, seat and dummy. Definitions of multi-body and joints and dynamics properties of joints based on FE combination models, of model setup are introduced. Kelvin element of MADYMO is introduced to show the force action between non-adjoining rigid bodies, too. Then all examples of the methods mentioned are given. By the comparison of simulation and real test, the contract curves between simulation and real test for main structures and biology mechanics properties of dummy are obtained. The result shows the accuracy and validity of the models.

An efficient formulation based on the Lagrangian method for contact–impact analysis of flexible multi-body system

In this paper,an efficien formulation based on the Lagrangian method is presented to investigate the contact–impact problems of f exible multi-body systems.Generally,the penalty method and the Hertz contact law are the most commonly used methods in engineering applications.However,these methods are highly dependent on various non-physical parameters,which have great effects on the simulation results.Moreover,a tremendous number of degrees of freedom in the contact–impact problems will influenc thenumericalefficien ysignificantl.Withtheconsideration of these two problems,a formulation combining the component mode synthesis method and the Lagrangian method is presented to investigate the contact–impact problems in fl xible multi-body system numerically.Meanwhile,the finit element meshing laws of the contact bodies will be studied preliminarily.A numerical example with experimental verificatio will certify the reliability of the presented formulationincontact–impactanalysis.Furthermore,aseries of numerical investigations explain how great the influenc of the finit element meshing has on the simulation results.Finally the limitations of the element size in different regions are summarized to satisfy both the accuracy and efficien y.

Contact-impact formulation for multi-body systems using component mode synthesis

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.

Modeling and Analyzing Dynamic Response for An Offshore Bottom-Fixed Wind Turbine with Individual Pitch Control

The asymmetric or periodically varying blade loads resulted by wind shear become more significant as the blade length is increased to capture more wind power.Additionally,compared with the onshore wind turbines,their offshore counterparts are subjected to additional wave loadings in addition to wind loadings within their lifetime.Therefore,vibration control and fatigue load mitigation are crucial for safe operation of large-scale offshore wind turbines.In view of this,a multi-body model of an offshore bottom-fixed wind turbine including a detailed drivetrain is established in this paper.Then,an individual pitch controller(IPC)is designed using disturbance accommodating control.State feedback is used to add damping in flexible modes of concern,and a state estimator is designed to predict unmeasured signals.Continued,a coupled aero-hydro-servo-elastic model is constructed.Based on this coupled model,the load reduction effect of IPC and the dynamic responses of the drivetrain are investigated.The results showed that the designed IPC can effectively reduce the structural loads of the wind turbine while stabilizing the turbine power out-put.Moreover,it is found that the drivetrain dynamic responses are improved under IPC.