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.

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 amulti-body system vibrating with impacts.We discover that if every motion of the system is bounded,it hasonly 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 chaoticmotions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is differentfrom that obtained by Holmes.

Dynamic Investigation on Composite Flexible Multi-body System Considering Thermal Effect

<Abstract>The dynamic performance of composite flexible multi-body system under the simultaneous action of thermal fields and driving constraint is analyzed.Based on strain-displacement relation of the Mindlin plate the- ory which includes transverse shear deformation,and considering thermal effect,variation equations of laminated plate are derived by the principle of virtual work.The finite element method is used for discretization.According to kinematics constraint relation,dynamic equations for spatial slider-crank system are established.Simulation results show that spatial deformation(torsion deformation)appears in the multi-layered composite slider-crank mechanism which is simulated with planar motions.Furthermore,the influence of coupling between thermal expansion and flexible deformations of non-symmetrical composite plates on the large overall motion under the uniform temperature field is investigated.Finally,significant change in constraint force due to the spatial deformation is shown.

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.

A flexible multi-body model of a surface miner for analyzing the interaction between rock-cutting forces and chassis vibrations

The discontinuous nature of rock cutting can easily cause unwanted vibrations in the structure of a surface miner.If these vibrations are not properly addressed,the related stress cycles can gradually damage the chassis resulting in fatigue failures.These events can seriously undermine the safety of operators and digging operations may be stopped for days,with an obvious economic impact.This work presents an analysis of the dynamics of a surface miner,focusing on the interaction between cutting machine dynamics and cutting forces,which is a new approach for this type of machine.For this purpose,the authors developed a numerical model of the cutting process made up of(1)a multi-body model of the cutting machine,which takes into account the chassis's flexibility;(2)a model of the rotating cutting head;and(3)a model of the interaction between the cutting head and rock,based on Shao's model.The model was compared with experimental results and then used to investigate the effects of cutting speed and cutting depth on the machine dynamics.

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.

An Earth multi-body system elasticity and plasticity dynamics model

Research on the elasticity and plasticity dynamics of the Earth multi-body system, including the Earth multi-body system stratum-block's equivalent inertia force system and generalized inertia force, the Earth multi-body system stratum-block's equivalent inertia force system expressed with partial velocity and partial palstance, and Earth multi-body system generalized inertia force expressed with partial velocity and partial palstance. This research provides a theoretical foundation for further investigation of Earth multi-body dynamics.

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.

Study on movement inertia in the Earth multi-body system

This paper summarizes the first movement and mass centre of stratum-block movement inertia in the Earth multi-body system and introduces its application. It also elaborates the moment of inertia and the products of inertia: the inertia dyadic transformation of reference system and the parallel axis theorem of stratum-block movement inertia of the Earth multi-body system. It provides an academic foundation for research on the dynamic model of Earth multi-body system.

Multi-body Contact Problem of Loose-fitted Tyre of Rotary Kiln

According to the character and the condition for shell deformation and force balance, we have set up the mathematical models of the contact angle and the contact pressure distribution between the tyre and the shell, studied The features of a multi-body contact model between the roller and the tyre, and developed the build-up procedure of the contact finite element model between the roller and the tyre. The stress distribution rule of the roller and the tyre is obtained as follows. The contact center is the center of the contact stress circle, and the contact stress is also reduced gradually from the contact center to the contact boundary. The equivalent stress of the tyre varies 5 times per circle, thus making the trye fracture easily.

NUMERICAL SIMULATION OF A SOLITARY WAVE INTERACTION WITH SUBMERGED MULTI-BODIES

The problems of a solitary wave passing over rectangular cylindershave been analysed.The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method.The free surface is dealt with by the Volume of Fluid method (VOF).Results fora solitary wave passing over a single cylinder are compared with the experimentaldata of Seabra-Santos,Penouard and Temperville and better agreement is obtainedthan those obtained from the long wave equation based on the potential flow theory.Results are also given for two cylinders with different gaps.

Lightweight Design of Commercial Vehicle Cab Based on Fatigue Durability

To better improve the lightweight and fatigue durability performance of the tractor cab,a multi-objective lightweight design of the cab was carried out in this study.First,the finite element model of the cab with counterweight loading was established and then confirmed by the physical testing,and use the inertial reliefmethod to obtain stress distribution under unit load.The cab-frame rigid-flexible couplingmulti-body dynamicsmodelwas built by Adams/car software.Taking the cab airbag mount displacement and acceleration signals acquired on the proving ground as the desired signals and obtaining the fatigue analysis load spectrum through Femfat-Lab virtual iteration.The fatigue simulation analysis is performed in nCode based on the Miner linear fatigue cumulative damage theory.Then,with themass and fatigue damage values as the optimization objectives,the bending-torsional stiffness and first-order bending-torsional mode as constraints,the thickness variables are screed based on the sensitivity analysis.The experimental design was carried out using the Optimal Latin hypercube method,and the multi-objective optimal design of the cab was carried out using theKriging approximationmodel fitting and particle swarmalgorithm.The weight of the optimized cab is reduced by 7.8%on the basis of meeting the fatigue durability performance.Finally,a seven-axis road simulation test rig was designed to verify its fatigue durability.The results show the optimized cab can consider both lightweight and durability.

不规则波中多体三浮子波能转换器的优化设计

A multi-body wave energy converter,consisting of three floats and modeled as a two body problem,is optimised to enhance its mean absorbed power using the Response Surface Optimisation Method.The optimisation focuses on two input parameters namely;the floats’diameters and the spacing,in various sea states and at different PTO dampings.A frequency domain analysis is performed for the WEC model scaled at 1∶50 in regular and irregular waves.Obtained results are validated against numerical and experimental data available in the literature.Validations show good agreement against the unmoored model’s added mass,radiation damping,response amplitude operator,mean absorbed power and,capture width ratio.The sea states selected for optimisation are represented by a JONSWAP wave spectrum with,a range of significant wave heights(0.04 to 0.06 m)and a range of peak periods(0.8 to 1.3 s).This corresponds to(2 to 3 m)significant wave heights and(5.6 to 9.2 s)peak periods in full scale.Results show that the optimised WEC model demonstrates good and consistent enhancement of its mean absorbed power and capture width ratio.

A Custom Manipulator for Dental Implantation Through Model-Based Design

This paper presents a Model-Based Design(MBD)approach for the design and control of a customized manipulator intended for drilling and position-ing of dental implants accurately with minimal human intervention.While performing an intra-oral surgery for a prolonged duration within a limited oral cavity,the tremor of dentist's hand is inevitable.As a result,wielding the drilling tool and inserting the dental implants safely in accurate position and orientation is highly challenging even for experienced dentists.Therefore,we introduce a customized manipulator that is designed ergonomically by taking in to account the dental chair specifications and anthropomorphic data such that it can be readily mounted onto the existing dental chair.The manipulator can be used to drill holes for dental inserts and position them with improved accuracy and safety.Further-more,a thorough multi-body motion analysis of the manipulator was carried out by creating a virtual prototype of the manipulator and simulating its controlled movements in various scenarios.The overall design was prepared and validated in simulation using Solid works,MATLAB and Simulink through Model Based Design(MBD)approach.The motion simulation results indicate that the manipulator could be built as a prototype readily.

Multi-Barycenter Mechanics, N-Body Problem and Rotation of Galaxies and Stars

In the present paper, the establishment of a systematic multi-barycenter mechanics is based on the multi-particle mechanics. The new theory perfects the basic theoretical system of classical mechanics, which finds the law of mutual interaction between particle groups, reveals the limitations of Newton’s third law, discovers the principle of the intrinsic relationship between gravity and tidal force, reasonably interprets the origin and change laws for the rotation angular momentum of galaxies and stars and so on. By applying new theory, the multi-body problem can be transformed into a special two-body problem and for which an approximate solution method is proposed, the motion law of each particle can be roughly obtained.

Fluid-structure interaction simulation for multi-body flexible morphing structures

The multi-body flexible morphing airfoil can improve the aerodynamic characteristics based on different flight missions continuously.Recently researches have focused on the unsteady aerodynamic characteristics of flexible wings under passive actuation.However,the unsteady aerodynamic characteristics with the fluid-structure interaction effects in the multi-body active actuation process of morphing airfoil deserve further investigation.In this paper,a fluid-structure coupled simulation method for multi-body flexible morphing airfoil with active actuation subsystem was investigated,and the aerodynamic characteristics during deformation were compared with different skin flexibility,flow field environment,actuation mode and actuation time.The numerical results show that for the steady aerodynamic,the skin flexibility can improve the stability efficiency.In the unsteady process,the change trend of the transient lift coefficient and pitching moment are consistent with those of the active drive characteristics,while the instantaneous lift-drag ratio coefficient is greatly affected by the driving mode and can be improved by increasing the driving duration.

风力机组整机多体动力学建模与动态特性研究（英文）

选取某MW级风力发电机组为研究对象,设计了机组运动拓扑结构图,构建了风机整机的刚柔耦合多体动力学分析模型,并与气动力计算软件Aero Dyn和控制求解器通过接口力元实现联合仿真。模态分析计算得到了整机前6阶固有频率和模态振型,分析可知机组与关键转速区间激振频率不发生共振。动态仿真计算得到了3种不同工况下风机塔架迎风方向的位移、加速度动响应以及叶片三坐标方向的叶尖挠度,分析发现阵风期间塔架位移突然增大且瞬时波动剧烈;叶片的x方向叶尖挠度值最大,可能使叶片和塔架发生碰撞。

Modeling and Simulation for Refueling Boom and Receiver inCoupled Mode

In coupled mode,the major problem of boom refueling system is undesirable nozzle loads.An automated load alleviation system(ALAS)is needed to alleviate nozzle loads.In order to simulate dynamic of the system and to validate ALAS,dynamic model is developed.Two models are established,which are the static model and the moving model,named after the two relative states between the fixed boom and the extension boom.Kane method is employed as main method considering system′s multi-body characteristics.D′Alembert′s principle is used to calculate nozzle loads.Simulation is conducted to research the effects of position disturbance and velocity disturbance on nozzle loads.Results indicate that position disturbance plays a more significant role in inducing nozzle loads.A fuzzy control law based ALAS is validated using the formulated model.It is concluded that this model can simulate system dynamic and validate ALAS.

Functional Virtual Prototyping in Vehicle Chassis Reform Analysis and Improvement Design

The contribution of functional virtual prototyping to vehicle chassis development is presented. The different topics that we took into consideration were reform analysis and improvement design during the vehicle chassis development. A frame of coordinates based on the digital-model was established, the main CAE analysis methods, multi-body system dynamics and finite element analysis were applied to the digital-model build by CAD/CAM software. The method was applied in the vehicle chassis reform analysis and improvement design, all the analysis and design projects were implemented in the uniform digital-model, and the development was carried through effectively.

Systematical Development of NVH Engineering for Vehicle Electrical Powertrain Based on an Optimized V-Model

For systematical NVH development of vehicle (especially for mass-production passenger vehicles) electric powertrain, an optimized V-Model is designed and has been implemented in the entire component-vehicle development, which integrates three individual branches: simulation, validation and optimization. Compared to the V-models in the traditional sense, this optimized V-model is not only driven by requirement and task accomplishment but also maximum optimization of NVH system performance. In this case, developing procedures are capable to be efficiently iterated and the NVH engineering can be expanded into 3D with this V-model.