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.

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.

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.

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.

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.

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.

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.

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.

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.

Investigation on the choice of boundary conditions and shape functions for flexible multi-body system

The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference （FFR） formulation. The deformations obtained by the absolute nodal coordinate （ANC） formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Nu- merical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free- free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.

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.

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.

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.

Engine Multi-Body with Flexible Crankshaft Modeling and Numerical Simulation

A multi-body model of engine system with flexible crankshaft was presented in this paper to analyze the dynamic behavior of an internal combustion engine. The flexible crankshaft structural dynamics was coupled with the main beating hydrodynamic lubrication in this model by a system approach. An application of an 14 engine was given to show this sophisticated simulation model and to predict the loads and the orbit plots in the journal beatings by the dynamic response of the multi-body engine system with flexible crankshaft. The numerical results show the capabilities and significance of the flexible crankshaft in this system. The objective of the research is to provide the scientific guidance for design and maintenance of the internal combustion engine.

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.

Surrounding rock deformation analysis of underground caverns with multi-body finite element method

Discontinuous deformation problems are common in rock engineering. Numerical analysis methods based on system models of the discrete body can better solve these problems. One of the most effective solutions is discontinuous deformation analysis （DDA） method, but the DDA method brings about rock embedding problems when it uses the strain assumption in elastic deformation and adopts virtual springs to simulate the contact problems. The multi-body finite element method （FEM） proposed in this paper can solve the problems of contact and deformation of blocks very well because it integrates the FEM and multi-body system dynamics theory. It is therefore a complete method for solving discontinuous deformation problems through balance equations of the contact surface and for simulating the displacement of whole blocks. In this study, this method was successfully used for deformation analysis of underground caverns in stratified rock. The simulation results indicate that the multi-body FEM can show contact forces and the stress states on contact surfaces better than DDA, and that the results calculated with the multi-body FEM are more consistent with engineering practice than those calculated with DDA method.

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.

Engine Noise Prediction by Using Multi-body Simulation

Abstract： This paper presents a coupled multi-body and FEM （finite element method）-BEM （boundary element method） methodology used to carry out a comprehensive NVH （noise, vibration and harshness） investigation of a four-cylinder internal combustion engine prototype. Firstly, a MBDS （multi-body dynamic simulation） of the internal combustion engine has been carried out, at a defined operating condition, in order to determine the excitation force of the powertrain exciting the cylinder block. In this way, the dynamics of the engine powertrain have been described taking into account both the effects of the gas forces of the combustion process and the inertia forces of the moving parts. Afterwards, the cylinder block excitation forces have been used to evaluate the engine block vibrations and to predict the external noise radiated with both the well-known ATV （acoustic transfer vectors） and MATV （modal acoustic transfer vectors） methodologies at a distance of 1 m from the engine, according to the standard ISO 3744. The dynamics of the engine powertrain and its vibro-acoustic behaviour have been described using LMS （learning management system） Engineering Innovation Virtual.Lab tools.

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.

Advantages of Multi-body Simulation within the Design Process of Heavy Drivetrains

For the further design of the particular gearbox components, the alternating cycles of the respective application mean an often insufficient knowledge of the actual loads occuring in use. Especially for the application within lifting units, such dynamic load cycles are very difficult to pre-estimate. The so-called slack rope test represents the most critical point in the load cycle and provides a special challenge for the gearbox design. Because of this missing expert knowledge, a test bench of such an application is installed and applied to practical movement cycles. Besides the test bench, a multi-body simulation model of the whole system is mapped within the MBS （multi-body simulation） environment SIMPACK. To verify this simulation model, the results are compared with the respective measurements of the test bench. These comparisons show very good agreements. Thus, one of the major advantages of using such simulation tools is the possibility to re-evaluate the internal and external loads during the whole design process. Finally, these simulations serve as a clarification of the load spectrum of the different drivetrain components. Gearbox series or different modifications of the design can now be analyzed prospectively without extensive testing.