Dynamic Simulation Of Multibody Systems Research Articles

Rigid-flexible coupling modeling of the dual-rotor system for aero-engine

The dual-rotor system is the core component of advanced aero-engine. Establishing a reasonable, accurate, and efficient dynamics model is the key to studying the dynamics and vibration of the rotor system for aero-engine. This manuscript takes a representative aircraft engine dual-rotor system as a prototype, considers the rig-id-flexible coupling characteristics of different stiffness elastic supports and rotor structures, and establishes an analytical dynamic model of the dual-rotor system. Based on the established dynamic model, the natural char-acteristics of the dual-rotor system are analyzed. The model was validated using two different research methods: the rigid-flexible coupling multi-body system dynamics simulation platform ADAMS, and finite element analy-sis. The dynamic model of the dual-rotor system established in this paper can meet the requirements of hierar-chical rigid-flexible coupling of system and structure, overall mass distribution, and stiffness distribution. In particular, it can also effectively realize the simulation of multi-facet and multi-phase unbalanced vibration of the rotor system. The research methods of this paper can further enrich the basic theory of dynamics and vibration of the aero-engine rotor system.

Multibody system dynamics modelling and simulation of a high-speed train for its suspension optimization

Multibody system (MBS) dynamics modelling and simulation of high-speed train system is essential and meaningful in the context of train dynamics research and product design. In this work, MBS modelling of a CRH high-speed train is carried out, in the modelling process, nonlinear geometry of wheel-rail contact, nonlinear characteristics of the suspensions and nonlinear railroad irregularities are fully considered. With the obtained MBS model, simulation is performed and demonstrates that critical speed of the CRH train is 378 km/h, vertical ride comfort of the CRH train is in “Excellent” level and lateral ride comfort is in “Good” level, in addition, RMS derailment coefficient of the train is less than 0.5 which means curving performance of the train is good. Agreement of simulation result with actual test or running data validates the established MBS model, thus, the MBS model developed in this study is accurate and would be useful in the next step vibration analysis and suspension optimization of the CRH train.

Research progress in multi-body system dynamics modeling in stomatology

The stomatognathic system is an organic combination of bone, dentition, joints, masticatory muscles and innervation nerves. It is an organ system for the human body to perform mastication, speech, swallowing and other important functions. Due to the complex anatomical structure of stomatognathic system and ethical limitations, it is difficult to directly measure the movement and force by using the biomechanical experimental methods. Multi-body system dynamics is an important tool to study the kinetics and force of a multi-body system, which consists of several objects with relative motion. We can use the method of multi-body system dynamics simulation in engineering to study the movement, soft tissue deformation and force transfer of this complex stomatognathic system. This paper briefly introduces the history and application methods of multi-body system dynamics and the commonly used modeling methods. The application and research progress of multi-body system dynamics modeling methods in the field of stomatology was emphatically summarized, development prospects of current research and difficulties were put forward.

Determination of the critical defect and fatigue life of high-speed railway axles under variable amplitude loads

High-speed railway axles are suffered from extremely complex variable amplitude (VA) loads during operation. However, in the design codes and operation maintenance of railway axles, most of them are based on the equivalent constant amplitude (CA) load spectrum to perform the fatigue resistance design by using the traditional nominal stress method, and carry out the routine inspection based on running experiments and data. In this paper, an innovative time-domain stepwise fatigue assessment (TSFA) approach has been introduced to include the influence of VA loads on the accumulated damage and fatigue crack propagation. Based on this procedure, the fatigue load spectrum from the multi-body system (MBS) dynamics simulation was integrated into the fatigue damage and remaining lifetime assessment of the axles. The calculation indicates that the safe lifetime of the powered and non-powered axles under the time-domain loading is considerably larger than the design value, which shows that the axle could safely operate until they are retired. However, for an original crack with the morphology ratio of 0.6 propagating to 45.0 mm, the lifetime of the powered and non-powered axle is sharply reduced to 1.32, and 2.07 years, respectively. Compared with the classical nominal stress method, the newly-developed TSFA procedure could produce a more conservative but practical result.

A general framework for modeling and dynamic simulation of multibody systems using factor graphs

In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multibody systems. Although the motion of multibody systems is considered to be a well-studied problem and various methods have been proposed for its solution, a unified approach providing an intuitive interpretation is still pursued. We describe how to build factor graphs to model and simulate multibody systems using both, independent and dependent coordinates. Then, batch optimization or a fixed lag smoother can be applied to solve the underlying optimization problem that results in a highly sparse nonlinear minimization problem. The proposed framework has been tested in extensive simulations and validated against a commercial multibody software. We release a reference implementation as an open-source C++ library, based on the GTSAM framework, a well-known estimation library. Simulations of forward and inverse dynamics are presented, showing comparable accuracy with classical approaches. The proposed factor graph-based framework has the potential to be integrated into applications related with motion estimation and parameter identification of complex mechanical systems, ranging from mechanisms to vehicles, or robot manipulators.

Modeling and simulation of point contact multibody system dynamics based on the 2D LuGre friction model

The main purpose of this paper is to present a modeling method and algorithm for point contact non-smooth multibody system based on the 2D LuGre friction model. Firstly, parameter identification of the LuGre friction model is discussed. The identification method for micro-damping coefficient is given by analyzing the influence of it on the stiffness of the dynamic equations and the oscillation of the solution. The bristles stiffness coefficient is determined by comparing with the simulation results of the Coulomb dry friction model. The effectivity of the parameter identification method is verified by a numerical simulating example. Secondly, the dynamic model and algorithm of point contact multibody system with the 2D LuGre friction model are derived by using Lagranges equation of the first kind and Baumgartes stabilization method. Compared with the Coulomb dry friction model, the modeling method presented in this study can also describe the stick-slip motion very well, and greatly simplifies the numerical algorithm. Finally, the modeling method and algorithm are applied to the wheel mechanisms with single-point contact and multi-point contact, and the stick-slip motions of the systems are analyzed.

L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.

Simulating the anchor lifting maneuver of ships using contact detection techniques and continuous contact force models

Designing the geometry of a ship’s hull to guarantee a correct anchor maneuver is not an easy task. The engineer responsible for the design has to make sure that the anchor does not jam up during the lifting process and the position adopted by the anchor on the hull is acceptable when it is completely stowed. Some years ago, the design process was based on wooden scale models of the hull, anchor and chain links, which are expensive, their building process is time consuming and they do not offer the required precision. As a result of this research, a computational tool to simulate the anchor maneuver of generic ships given by CAD models was developed, and it is proving to be very helpful for the naval engineers. In this work, all the theory developed to simulate anchor maneuvers is thoroughly described, taking into account both the behavior of the anchor and the chain. To consider the contact forces between all the elements involved in the maneuver, a general contact algorithm for rigid bodies of arbitrary shapes and a particular contact algorithm for the chain links have been developed. In addition to the contact problem, aspects like the dynamic formulation of the equations of motion or the static equilibrium position problem are also covered in this work. To test the theory, a simulation of the anchor lifting maneuver of a ship is included as a case study. In spite of the motivation to develop the theory, the algorithms derived in this work are general and usable in any other multibody simulation with contacts, under the scope of validity of the models proposed. To illustrate this, the simulation of a valve rocker arm and cam system is accomplished, too. The computational and contact detection algorithms derived have been implemented in MBSLIM, a library for the dynamic simulation of multibody systems, and MBS model, a library for the contact detection and 3D rendering of multibody systems.

A Parallel Recursive Hamiltonian Algorithm for Forward Dynamics of Serial Kinematic Chains

This paper presents a novel recursive formulation for the simulation of multibody system dynamics based on Hamilton's canonical equations. Although Hamilton's canonical equations exhibit many advantageous features compared to their acceleration-based counterparts, it appears that there is a lack of dedicated parallel algorithms for multirigid body system dynamics based on this formulation. Serial kinematic chains are considered in this paper. Initially, the standard set of Hamilton's canonical equations is joined together with constraint equations at the velocity level. The reformulation determines the system's joint velocities and constraint force impulses in a divide and conquer manner resulting in logarithmic numerical cost for parallel implementation. Subsequently, the equations of motion are rearranged in order to obtain the time derivatives of the total joint momenta. In the case of the sequential implementation, the entire algorithm exhibits linear computational cost. Presented numerical method is exact and noniterative. Numerical test cases reveal negligible energy drift without the use of any additional constraint stabilization techniques. The results are compared against more standard acceleration based formulation and the outcome from real-life physical experiment.

Study on Coupling Dynamics Theory and Simulation of Advance Support and Tunnel Surrounding Rock

In order to study the dynamic coupling problem of tunnel advance support equipment and surrounding rock, the roof dynamics model based on thin plate theory is established in this paper; Advance support equipment is simplified, and the differential equations of motion of each component to establish the dynamic model of the whole; finally considering multi support conditions of advanced support roof system coupling dynamic model. The dynamic response of the coupling dynamic model under various working conditions is studied by using multi-body system dynamics simulation software RecurDyn. Through simulation we get the advance support top beam and retaining plate in dynamic response of collateral roadway conditions. The research conclusions of this paper can provide a theoretical basis for the research and design of advance support equipment in fully mechanized roadway.

Mode decoupling concepts of an engine mount system for practical application

In recent years, appropriate engine mount system design has become increasingly important due to a consistent trend towards lighter car bodies combined with more power-intensive engines and often lower idle speed. Decoupling dominant vibration directions of the engine-gearbox assembly (EGA) from input excitation direction, in particular based on elastic axis decoupling and torque roll axis decoupling concepts, are often referred to in literature. However, their practical application remains scarce. Hence, multi-body system dynamics simulation and numerical optimization is used in order to introduce an easily applicable implementation of the referred concepts. Therefore, the modal kinetic energy distribution of the EGA with respect to physical directions is considered. Effects of coupling or decoupling of EGA eigenmodes regarding engine-excited (e.g. from engine run-up or idling) as well as road-induced vibrations (e.g. from rough road or cobblestones) are addressed in an engine mount system parameter design study for a small-sized engine. Decoupling modal kinetic energy fractions of all rigid body modes considerably reduces effects from engine-excited vibrations, while strong coupling might offer benefits for road-induced vibrations. As modal kinetic energy fractions can easily be varied by means of optimization and/or by using findings from correlation coefficients derived with design of experiment methods, the adaptation of design parameters (mount positions and inclinations, stiffnesses, and loss angles) is possible in a quite straightforward manner for an effective compromise.

Performance of automatic differentiation tools in the dynamic simulation of multibody systems

Within the multibody systems literature, few attempts have been made to use automatic differentiation for solving forward multibody dynamics and evaluating its computational efficiency. The most relevant implementations are found in the sensitivity analysis field, but they rarely address automatic differentiation issues in depth. This paper presents a thorough analysis of automatic differentiation tools in the time integration of multibody systems. To that end, a penalty formulation is implemented. First, open-chain generalized positions and velocities are computed recursively, while using Cartesian coordinates to define local geometry. Second, the equations of motion are implicitly integrated by using the trapezoidal rule and a Newton–Raphson iteration. Third, velocity and acceleration projections are carried out to enforce kinematic constraints. For the computation of Newton–Raphson’s tangent matrix, instead of using numerical or analytical differentiation, automatic differentiation is implemented here. Specifically, the source-to-source transformation tool ADIC2 and the operator overloading tool ADOL-C are employed, in both dense and sparse modes. The theoretical approach is backed with the numerical analysis of a 1-DOF spatial four-bar mechanism, three different configurations of a 15-DOF multiple four-bar linkage, and a 16-DOF coach maneuver. Numerical and automatic differentiation are compared in terms of their computational efficiency and accuracy. Overall, we provide a global perspective of the efficiency of automatic differentiation in the field of multibody system dynamics.

The Influence of Front Support on Vibration Behaviors of TBM Cutterhead under Impact Heavy Loads

Cutterhead is one of the key parts of Tunnel Boring Machine, TBM. The performance of cutterhead has a great impact on the boring capability of TBM. The impact heavy torque and thrust force bore by cutterhead during the tunneling process will cause severe vibration and lead to decline in its life even broken, which affect the boring efficiency. In this paper, a TBM mainframe model of Northwest Liaoning project has been built based on the multi-body system dynamics simulation platform ADAMS. It also has been discussed in the paper that the influence of front support on the vibration characteristics of cutterhead. The simulation results show that the front support will improve the vibration behaviors of cutterhead: The stabilization time of rotational and translational motion decreases 90% and 10% at least, the axial amplitude decreases 8%. All these conclusions have demonstrated that front support should be adopted when designing the TBM.

Simulation Study of Snake-like Robot's Serpentine Locomotion Based on Recurdyn

The snake-like robot is composed of nine joints and the robot is proposed in this study. The serpentine locomotion mechanism of snake-like robot is studied and its moving model is established in the multi body system dynamics simulation the Software Recurdyn. The joint angle functions of serpentine locomotion are set up. We add some restrictions for model in Recurdyn and set moving functions. The simulation introduced the input of the joint angle function's influence on the winding movement of the snake-like robot. The simulation results show that the snake-like robot can complete the serpentine locomotion set before.

A geometrically implicit time-stepping method for multibody systems with intermittent contact

Accurate dynamic simulation with robust handling of intermittent contact is necessary for a wide range of robotics problems, including the design of parts feeding devices, manipulation and kinodynamic planning, and designing grasp strategies. In this paper we present an implicit time-stepping scheme for dynamic simulation of multibody systems with intermittent contact by incorporating the contact constraints as a set of complementarity and algebraic equations within the dynamics model. We model each body as an intersection of convex inequalities and write the contact constraints as complementarity constraints between the contact force and a distance function dependent on the closest points on the bodies. The closest points satisfy a set of algebraic constraints obtained from the Karush–Kuhn–Tucker (KKT) conditions of the minimum distance problem. We prove that these algebraic equations and the complementarity constraints taken together ensure satisfaction of the contact constraints. This enables us to formulate a geometrically implicit time-stepping scheme (i.e. we do not need to approximate the distance function) as a nonlinear complementarity problem. The resulting time-stepper is therefore more accurate and does not rely on a closed-form distance function. We demonstrate through example simulations the fidelity of this approach to analytical solutions and previously described simulation and experimental results.

Einsatzgebiete der numerischen Simulation in der muskuloskelettalen Forschung und ihre Bedeutung für die Orthopädische Chirurgie

Finite element analyses (FEA) as well as multibody system dynamics (MSD) are the main tools used for numerical simulation in the field of musculoskeletal research. While FEA is utilized for field problems, such as calculation of stress and strain distribution, MSD is applied for solving kinematic analyses, such as calculation of muscle and joint forces. Depending on the focus of investigation, modelling of biological tissue may vary from simple homogeneous behavior to modelling biochemical processes on the microscale and nanoscale. An important milestone in biomechanical research was the analysis of stress shielding, which led to further research on bone remodelling. Various models of implant-bone fixation used for the prediction of micromotion have been published. New possibilities for biomechanical analyses are achieved by consideration of complex muscle forces which are generated by MSD simulation and imported into FEA models as limiting conditions. A numerical model always requires experimental validation. If the results are confirmed experimentally, various advantages of numerical simulation apply and problems can be analysed isolated from many influencing factors. Therefore, straightforward parameter variation is possible, enabling studies which would be impossible in an experimental or clinical setup.

Beam Layout Optimization for Vehicle Body Stiffness

In this paper we research the beam layout optimization to strengthen the stiffness of a tracked vehicle’ body. Based on CAD models of vehicle parts, a rigid-flexible coupling virtual prototype of the vehicle is constructed through body finite element meshing and modal analysis. The multi-body system dynamics simulation is conducted under several typical driving conditions. Loads acting on the vehicle body at several typical moments are exported and then imposed on the body finite element model to carry out the static analysis, such that the multi-load steps topology optimization for the hull is achieved. On the basis of the optimization results the local beam layout is modified and the vehicle virtual prototype is reconstructed. By re-executing the dynamics simulation, the change of the stress and deformation are compared. The simulation result shows the strength and stiffness of the body are improved. So the proposed scheme is effective for the body stiffness and could provide references for similar structural optimization problems.

Application of Counter-Rotary Counterweights to the Dynamic Balancing of a Spatial Parallel Manipulator

The dynamic balancing of a spatial parallel manipulator of three degrees-of-freedom, CaPaMan-2 (Cassino Parallel Manipulator 2), by the application of Counter-Rotary Counterweights (CRCW) is analyzed. To accomplish this objective the mass and inertia of the moving platform are dynamically replaced by point masses located at the points of attachment of the legs to the platform and the mechanism is balanced by considering each of the legs independently. This fully parallel manipulator has three identical legs, each one composed by a four-bar mechanism (an articulated parallelogram) connected to the fixed base, and a link supported by the coupler that connects to the mobile platform. This link, seen as a pendulum, is transformed to a dynamic balancer using a Counter-Rotary Counterweight in order to compensate the motion of the moving platform. In a second stage the articulated parallelogram is modified by adding Counter-Rotary Counterweight plus a Counterweight to dynamic balance its part of the system. As a final result it is obtained a new design, with a parallel manipulator dynamic balanced. The resulting model of the manipulator is validated by dynamic simulation, using general purpose software for the analysis and dynamic simulation of multi-body systems (ADAMS).

Partitioned Dynamic Simulation of Multibody Systems

Partitioned dynamic simulation of multibody systems offers the benefit of increased modularity over direct simulation, thereby allowing for the use of softwares tailored to the needs of each physical subsystem. In this paper, the partitioned simulation of multibody systems is accomplished by deriving an explicit expression for the constraint forces acting between subsystems. These constraint forces form the basis of a coupling module that communicates results between subsystems, each of which can be simulated independently using tailored numerical solvers. We provide details of how this partitioned solution approach can be implemented in the framework of implicit and explicit time integrators. The computational efficiency of the proposed partitioned simulation approach is established, in comparison with direct simulation, by solving three suitable problems containing both rigid and deformable components.

Optimum Design of Local Cam Profile of a Valve Train

In this paper, optimization of the local cam profile of a valve train modelled by a parameterized Bezier curve is described. Dynamic responses of the valve train are simulated through its multi-body system dynamics model built using ADAMS software. The kriging method is used to build the surrogate model, which presents the relationship between dynamic responses resulting from the multi-body system dynamics simulation and the parameters of the local Bezier profile. The local cam profile is optimized through a generic algorithm, such that the acceleration peak at the valve open phase is reduced significantly.