Multibody dynamic analysis using a rotation-free shell element with corotational frame

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore,the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

Modeling joints with clearance and friction in multibody dynamic simulation of automotive differentials

Defects in kinematic joints can sometimes highly influence the simulation response of the whole multibody system within which these joints are included. For instance, the clearance, the friction, the lubrication and the flexibility affect the transient behaviour, reduce the component life and produce noise and vibration for classical joints such as prismatics, cylindrics or universal joints.In this work, a new 3D cylindrical joint model which accounts for the clearance, the misalignment and the friction is presented. This formulation has been used to represent the link between the planet gears and the planet carrier in an automotive differential model. C 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301303]

Fast simulation of flexible multibody dynamics with electric-hydraulic drive system

Hardware in the loop simulation （HILS） has been investigated in the field of the multibody dynamics （MBD）, which combined the MBD simulation with the actual mechanical system. The fast simulation is necessary for the HILS system in order to require the real time simulation. This paper presents a fast simulation technique using the domain decomposition method with the iteration in the flexible multibody system in which flexible linkage system and electro-hydraulic drive system are coupled with each other. C 2013 The Chinese Society of Theoretical and Applied Mechanics.[doi：10.1063/2.1301301]

Dynamic Damage Detection and Assessment on the Bogie Frame of High-Speed Train Based on the Coupled Elastic and Multibody Dynamics Scheme

The dynamic cumulative damage of rigid-flexible coupling model of high-speed train with flexible bogie frame is performed by using the coupled scheme of elastic and multibody dynamics theories.The motion equations of the present problem are firstly established by integrating the finite element method and floating frame of reference approach based on the virtual power principle and D'Alembert principle.The process of condensing the elastic DOFs of the obtained finite element model involving the incorporation of the substructure technique and sparse approximate inverse method is tentatively carried out.Then,the motion equations are further solved by virtue of the generalized α method and the Jacobian-free Newton-Krylov technologies.And the superiority of coupled scheme is proven by comparing with the traditional approach.Finally,besides the dynamic behaviors of the considered vehicle model,the time-variations of stresses on the elastic bogie frame's dangerous nodes and the distributions of stresses of bogie frame at some specified moments are synchronously calculated and analyzed.More importantly,the real-time and time-varying cumulative damages of some typical nodes on bogie frame are investigated.

Mechanical analysis of deepwater drilling riser system based on multibody system dynamics

A multibody system including a drilling riser system,tensioners and a floating platform is key equipment for offshore oil and gas drilling.Most of the previous studies only focus on the drilling riser system rather than the multibody system.Mechanical characteristics of the deepwater drilling riser system cannot be analyzed accurately in a simplified model.Therefore,a three-dimensional multibody analysis program is developed.The static and dynamic characteristics of the deepwater drilling riser system under different platform motions are analyzed based on the developed program.The results show that the static displacement of the riser system with tensioners is smaller than that without tensioners,which means the tensioners can suppress the deformation of the riser system.Under surge and sway motions of the platform,the dynamic displacement of the riser system with tensioners is also smaller than that without tensioners due to the tensioner suppression effect.Besides,the heave motion induces a uniform axial vibration of the riser system,while roll and pitch motions excite the riser system to vibrate laterally.Compared with the stress amplitude due to surge and sway motions,the stress amplitude of the riser system due to heave,roll and pitch motions is relatively small but cannot be neglected.

Coupled two-dimensional discrete element and multibody dynamic modeling for interaction of the soil and rough shaped rigid bodies

The study of soil and rigid body system interactions is very important for the exploration of the Moon and Mars worldwide.The discrete element method(DEM)is a relatively accurate simulation method to study dry sand soil mechanical properties.However,it is not suitable for bodies that are in mutual contact,connected due to constraints or have complex inertia properties due to their geometry.An efficient combination of the two-dimensional discrete element and multibody dynamic modeling method is proposed to solve the problem,in which the contacts and frictions among the granular spheres and the multibody system,including the smooth and rough rigid bodies,are taken into account.In this work,the soil field is modeled by a two-dimensional DEM,and the dynamics of the constrained rigid body system are modeled by the Cartesian method.A detection algorithm is developed to address the interactions between spherical discrete elements and roughly shaped rigid bodies.The advantage of this coupled method is that it enables the simultaneous capture of both responses.Finally,the program is verified by simulation experiments of the three-ball collision and the collision among the rectangular bars and the three balls.Based on this,the movement of the toothed wheel in the granular matter is analyzed,and the results show that the wheel with six teeth and 30°inclination has the fastest forward speed.In extraterrestrial objects,the wheel grip worsens,but the forward speed first increases and then decreases with decreasing gravity acceleration and loads on wheels,which proves that the coupled two-dimensional DEM and multibody dynamic program is effective in solving engineering problems.

An approach for the coupled simulation of machining processes using multibody system and smoothed particle hydrodynamics algorithms

The prediction accuracy of a simulation method is limited by its theoretical background. This fact can lead to disadvantages regarding the simulation quality when investigating systems of high complexity, e.g. containing components showing a fairly different behavior. To overcome this limitation, co-simulation approaches are used more and more, combining the advantages of different simulation disciplines. That is why we propose a new strategy for the dynamic simulation of cutting processes. The method couples Lagrangian particle methods, such as the smoothed particle hydrodynamics （SPH） method, and multibody system （MBS） tools using co-simulations. We demonstrate the capability of the new approach by providing simulation results of an orthogonal cutting process and comparing them with experimental data. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301305]

Dynamic Investigations on the Wear Behavior of a 3D Revolute Joint Considering Time-Varying Contact Stiffness: Simulation and Experiment

The existence of the relative radial and axial movements of a revolute joint’s journal and bearing is widely known.The three-dimensional(3D)revolute joint model considers relative radial and axial clearances;therefore,the freedoms of motion and contact scenarios are more realistic than those of the two-dimensional model.This paper proposes a wear model that integrates the modeling of a 3D revolute clearance joint and the contact force and wear depth calculations.Time-varying contact stiffness is first considered in the contact force model.Also,a cycle-update wear depth calculation strategy is presented.A digital image correlation(DIC)non-contact measurement and a cylindricity test are conducted.The measurement results are compared with the numerical simulation,and the proposed model’s correctness and the wear depth calculation strategy are verified.The results show that the wear amount distribution on the bearing’s inner surface is uneven in the axial and radial directions due to the journal’s stochastic oscillations.The maximum wear depth locates where at the bearing’s edges the motion direction of the follower shifts.These find-ings help to seek the revolute joints’wear-prone parts and enhance their durability and reliability through improved design.

Numerical and experimental studies on impact dynamics of a planar flexible multibody system

In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.

AN AUTOMATIC CONSTRAINT VIOLATION STABI- LIZATION METHOD FOR DIFFERENTIAL/ ALGEBRAIC EQUATIONS OF MOTION IN MULTIBODY SYSTEM DYNAMICS

A new automatic constraint violation stabilization method for numerical integration of Euler_Lagrange equations of motion in dynamics of multibody systems is presented. The parameters α,β used in the traditional constraint violation stabilization method are determined according to the integration time step size and Taylor expansion method automatically. The direct integration method, the traditional constraint violation stabilization method and the new method presented in this paper are compared finally.

Dynamic Analysis of Flexible Multibody Systems for High-Rise Building Window Cleaning Gondola

A virtual prototype of high-rise building window cleaning gondola based on multibody system dynamics software MS（2. ADAMS is presented. The rigid bodies are modeled by CAD software and flexible bodies are modeled by discrete beam method. The whole machine＇s natural characteristics are analyzed and changed to frequency field. According to the results, the dangerous frequencies are avoided and the design can be optimized and the performance can be improved.

A METHOD FOR SOLVING THE DYNAMICS OF MULTIBODY SYSTEMS WITH RHEONOMIC AND NONHOLONOMIC CONSTRAINTS

The solution of the dynamic problem of multibody systems subject to rheonomic and nonholonomic constraints is achieved by applying singular value decomposition of the constraint matrix and projections of the dynamic equations of the systems along the feasible and unfeasible directions of the constraints. Formula to solve the constraint reaction forces and a method to avoid the violation of the constraints are also given.The solution does not rely on coordinates used to describe the systems and is computational efficitive example is finally presnted.

A GENERAL PROCEDURE TO CAPTURE THE "DYNAMIC STIFFNESS

A general procedure to capture the 'dynanmic Stiffness' is presented in this paper. The governing equations of motion are formulated for an arbitrary flexible body in large overall motion based on Kane's equations . The linearization is performed peroperly by means of geometrically nonlinear straindisplacement relations and the nonlinear expression of angular velocity so that the 'dynamical stiffness' terms can be captured naturally in a general tcase. The concept and formulations of partial velocity and angular velocity arrays of Huston's method are extended to the flexible body and form the basis of the analysis. The validity and generality of the procedure presented in the paper are verified by numerical results of its application in both the beam and plate models.

A Study on the Dynamic Analysis of A Tracked Vehicle for Ocean Mining on the Deep Seabed

A study is presented on the dynamic analysis of a tracked vehicle for mining on the deep seabed of very soft soil. Equations for the interaction between the track and extremely soft seabed are employed to develop a track/soil interaction module called TVAS. The vehicle is modeled as a multibody dynamic system by the use of a multibody dynamic analysis program. The module developed is cooperated with the multibody dynamic analysis program with a user-defined subroutine. The dynamic behavior and the conceptual design of the mining vehicle on the deep seabed are investigated.

A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems

Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multibody systems involving impact should consider the local plastic deformation and the strict requirements of the spatial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlinear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.

Dynamic Response of Functional Virtual Prototyping of Motorcycle under Combined Excitations

This paper developed 3D product models of motorcycle and engine by UGNX as well as virtual prototyping by ADAMS program with road roughness generated by MATLAB. Under the straight-line running condition, the dynamic responses of motorcycle multibody system to both road and engine excitations were compared with those to only road excitation in terms of vertical acceleration response, amplitude frequency response and power spectral density. The comparisons of simulation data showed that the response due to flat road excitation was around 20 Hz, while that to the combined excitations was in a wide frequency band, of which the major components focused on 10 Hz, 15 Hz, 35 Hz ,70 Hz, 100 Hz and even higher frequencies, reflecting the characteristics of engine excitation based on its unbalanced inertia force and torque. It is concluded that the high fidelity virtual prototyping can simulate the dynamics of motorcycle product well in investigating the vibration and ride comfort performance.

Improving the dynamic stability of a workpiece dominated turning process using an adaptronic tool holder

In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability.A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue. C 2013 The Chinese Society of Theoretical and Applie-d Mechanics. [doi：10.1063/2.1301308]

Dynamic analysis of rotating flexible disk subjected to double slider loading systems

Rotating disk subjected to stationary slider loading system is a very common mechanical structure. This paper investigates the multibody dynamics of a rotating flexible annular thin disk subjected to double slider loading systems. Along the rotating disk radial and circumferential directions, two stationary slider loading systems are distributed. System dynamic model is solved by Galerkin＇s method, and then natural frequency, dynamic stability and mode shape are determined with a quadratic eigenvalue problem. Effects of the distributing positions and interaction mechanism of the double slider loading systems on natural frequency, dynamic stability and mode shape are discussed and investigated.

Quantum Entanglement and Cryptography for Automation and Control of Dynamic Systems

This paper addresses the application of quantum entanglement and cryptography for automation and control of dynamic systems.A dynamic system is a system where the rates of changes of its state variables are not negligible.Quantum entanglement is realized by the Spontaneous Parametric Down-conversion process.Two entangled autonomous systems exhibit correlated behavior without any classical communication in between them due to the quantum entanglement phenomenon.Specifically,the behavior of a system,Bob,at a distance,is correlated with a corresponding system,Alice.In an automation scenario,the"Bob Robot"is entangled with the"Alice Robot"in performing autonomous tasks without any classical connection between them.Quantum cryptography is a capability that allows guaranteed security.Such capabilities can be implemented in control of autonomous mechanical systems where,for instance,an"Alice Autonomous System"can control a"Bob Autonomous System"for applications of automation and robotics.The applications of quantum technologies to mechanical systems,at a scale larger than the atomistic scale,for control and automation,is a novel contribution of this paper.Notably,the feedback control transfer function of an integrated classical dynamic system and a quantum state is proposed.

COMPUTER AIDED ANALYSIS OF FLEXI－BLE MEMBER IN CONSIDERATION OF THE EFFECTS OF DYNAMIC STI－FFEN－ING

A recently developed procedure to capture the dynamic stiffening of an arbitrary flexiblemember in large overall motion accompanied by small elastic vibrations is presented. A mechanicalsystem that consists of one or more flexible members is called a flexible mechanical system. If thesystem is considered as a multibody system, the flexiblemember can be considered as a flexible bodyin a flexible multibody system. Having retained the nonlinearitites up to an appropriate point in theanalysis, the linearization is then performed properiy so that the dynamic stiffening terms can befound naturally, while the explicit formulation of the governing equations for the deformation mo-tion is ultimately linear. Based on the procedure, the effects of dynamic stiffening are investigatedqualitatively and quantitatively with analytical and numerical examples. The results are useful incomputer aid analysis of the dynamic behavior of flexible mechanical systems.