Simulation Of Multibody Systems Research Articles

Control of a manipulation robot interacting with elastic objects using a software module for three-dimensional simulation of multibody mechanical systems

Control of a manipulation robot interacting with elastic objects using a software module for three-dimensional simulation of multibody mechanical systems

Wheel flat detection by using the angular domain synchronous averaging method and axle box acceleration: Simulation and experiment

Wheel flats (WFs) can generate periodic impact forces and aggravate the wheel-rail interaction. Therefore, the early detection of WFs is significant for railway operators to lower the maintenance cost. In this work, the angular domain synchronous averaging (ADSA) method is employed to detect WFs on railway vehicles since it can handle the non-stationary vibration process of rotating machines by processing the vibration data in the angular domain. Furthermore, the short-time irregular impulses, such as those caused by crossings and rail joints, can be attenuated by using synchronous averaging technology. The periodic impact caused by WFs can be easily observed in the polar coordinate using the ADSA method, which is verified by one multibody system (MBS) simulation and one field experiment. Besides, the sensitivity of this method to various flat dimensions and multiple flats is also studied in the MBS simulation.

A nonsmooth dynamics framework for simulating frictionless spatial joints with clearances

AbstractReal-world multibody systems do not have ideal joints; most joints have some clearance. The clearance allows the connected bodies to undergo a misalignment, and the resulting dynamics is governed by the contacts thus formed. Two approaches are typically taken to deal with contacts: the commonly used continuous dynamics approaches assume the Hertzian nature of the contact modeled by nonlinear unilateral spring-damper elements; while the nonsmooth dynamics approach results in a complementarity problem. This paper employs a nonsmooth dynamics approach to develop a coherent framework for the simulation of multibody systems having frictionless joints with clearances. Because clearances are of small magnitude relative to the dimensions of the mechanical components, the nature of the contact in the joints is assumed to be inelastic. Using this assumption and the general nonsmooth dynamics framework, the parametric formulations for cylindrical, prismatic, and revolute joints with clearances are derived. The equations of motion are formulated, and their time-discretized counterparts are cast as a nonlinear programming problem. The proposed scheme also enforces normalization constraint on Euler parameters in contrast to state-of-the-art methods that is conducive to stability of the solution for a suitable range of step sizes. In addition, a variable time-stepping scheme that includes the step size as an extra variable in the optimization is introduced and its stability properties are discussed. The versatility of the proposed framework is demonstrated through numerical experiments.

Dynamic Modeling, Dynamic Characteristics, and Slight Self-Guidance Ability at High Speeds of Independently Rotating Wheelset for Railway Vehicles

For better small-radius curve negotiation performance, the independently rotating wheelset has the potential to be equipped in urban rail transit. As a crucial part of the running gear, its dynamic characteristics directly affect the railway vehicle’s stability and curve negotiation ability. This study follows a model–simulation–experiment method to delve into the dynamic process and steady convergent process of the independently rotating wheelset. An improved mathematical dynamic model of the independently rotating wheelset is established, considering the gravitational restoring forces of the wheelset and different creepages between the left and right wheels. In addition, the gyroscopic effects on the independently rotating wheelset with positive wheel tread conicity and at high speeds are introduced and analyzed. With variations in the longitudinal speed and yaw suspension coefficients, three kinds of motions, derailment, hunting, and offset running, occur on the independently rotating wheelset. We find that the gyroscopic effects contribute to the slight self-guidance ability of the independently rotating wheelset, causing a hunting motion at high speeds. Through sufficient simulations, the improved mathematical dynamic model is verified to be closer to the dynamic model built in the general multibody system simulation software SIMPACK 2018 than the classical mathematical dynamic model. Further, we perform experiments on a scaled independently rotating wheelset experiment system. The dynamic characteristics derived from theoretical analysis, especially the slight self-guidance ability at high speeds, are verified.

Shape-locking in architected materials through 3D printed magnetically activated joints

Shape morphing is the ability of objects to adapt to different shapes and reduce stress concentrations through increased contact area. This is a common trait of natural and engineered objects and has several applications in, among others, soft robotics and orthopedic implants. Shape morphing is achieved through flexible materials or rigid components with either kinematic or compliant joints. An additional step, namely shape locking, is needed for sustained load support. Activation of a locking mechanism can be done with any energy, among which magnetism is one. Here, we present the implementation of a magnetic locking mechanism for kinematically deformable metamaterial structures that maintain shape and support loads upon locking. The structure consists of 3D printed rigid magnetic and non-magnetic components connected by hinges. We created several prototypes of the proposed designs using two additive manufacturing methods (i.e., material extrusion and multi-material jetting) and demonstrated its application in a closed-loop grid for arbitrary shapes. Moreover, we characterized the performance of the prototypes using mechanical tests and multibody kinematic system simulations. This work highlights the viability of the locking concept and provides design considerations for future applications. Further improvement and optimizations are needed for increased efficiency and effectiveness.

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.

Wavelet-Based Methods to Partition Multibody Systems With Contact in Dynamic Simulation

AbstractThe performance of physics simulation of multibody systems with contact can be enhanced by viewing the system as being composed of subsystems of bodies, and solving the dynamics of these subsystems in parallel. This approach to partition a system into subsystems, known as substructuring, is often based on topological information, such as the connectivity of a body in the system. However, substructuring based on topology may generate a potentially large number of equivalent decompositions, especially in highly symmetric systems, thus requiring a way to choose one partition over another. We propose that augmenting a topology-based partitioning scheme with dynamical information about the interactions between bodies may provide speedups by including temporal information about the constraint relationships between bodies. The simulation of multibody systems with contact typically exhibits nonstationary and multiscale interactions, which suggests a subsystem can be defined as a collection of bodies which have complex interactions with each other. We define complexity by introducing a novel metric based on the spread of time scales from a wavelet analysis of constraints between bodies. We show that for systems where purely topological information about the interaction between bodies is redundant, including dynamical information, not only removes redundancy but also can achieve significant computational speedups. Our results highlight the potential of using dynamical information to look at large-scale structures in multibody simulations.

Dynamic modelling and singularity-free simulation of closed loop multibody system driven by electric motors

This paper presents the dynamic model and singularity-free simulation of electromechanical systems including closed loop multibody systems, massless gear transmission and electric motors. The dynamic model of these systems is established in matrix form and written in a Differential-Algebraic Equations form by applying the Lagrangian equation with multipliers and substructure method. Moreover, this paper deals with two difficult issues in the simulation of closed-loop multibody systems which are to overcome smoothly the singular configurations and to stabilize the constrained equations due to accumulated errors. The singularity-free simulation is solved by using null-space of Jacobian matrix to eliminate the constraint forces – Lagrangian multipliers in equations of motion. The drift in the constraint equation during simulation is restricted by a combination of Baumgarte’s stabilization and post-adjusting technique. Some numerical experiments are carried out to the planar 3RRR parallel manipulator driven by electric motors. Simulation results confirm the effectiveness of the proposed approach in overcoming the singular configurations and in stabilization of the constraint.

Transient optical simulation by coupling elastic multibody systems, finite elements, and ray tracing

Transient dynamical–thermoelastic–optical system simulation is an important expansion of classical ray tracing through rigid, resting lenses because the operating performance of high-precision optical systems can be influenced by dynamical excitations or thermal gradients. In this paper an approach for an integrated optical system simulation using the coupling of elastic multibody system simulations, thermoelastic finite element analysis and gradient-index ray tracing is presented. Transient mechanical rigid body motions and elastic deformations, thermally induced refraction index changes, and thermal elastic deformations can be considered simultaneously in the ray tracing using the presented method. The calculation of the dynamical and thermal disturbances, the data transfer and coupling, and the gradient index ray tracing method are introduced. Finally, the approach is applied on a transient triplet lens optical system and some investigation results are shown.

Passenger ride comfort in subway due to new subway excavation below

New tunnel excavation below existing tunnel deforms the rails inside the existing tunnel. The settlement-induced rail irregularity intensifies the wheel-rail interaction, which reduces passenger ride comfort of the existing tunnel. This research investigates the passenger ride comfort of the existing tunnel due to new tunnel excavation. A project of new twin tunnels excavation below existing triple tunnels is introduced. According to the field monitoring data, the settlement of each of the existing tunnels, although supported by different types of lining, can be fitted by the Gaussian function. Then numerical simulation is performed to study the deformation characteristics of the existing rails, which is difficult to monitor in the field. The simulation results show that the tunnel deformation can well represent the rail deformation. After that, train ride comfort is adopted to evaluate passenger comfort indirectly. The vehicle dynamic performance due to settlement-induced track irregularity is studied by a general multibody system simulation software. The results show that the vertical acceleration of the car body increases linearly with the increase of the settlement amplitude and decreases exponentially with the increase of the trough width i. When the trough width i is larger than 15 m, the vertical accelerations produced by new tunnel excavation are negligible compared to those produced by track irregularity. The settlement amplitude limits considering the passenger ride comfort in subway due to new subway excavation below are obtained.

FPGA acceleration of planar multibody dynamics simulations in the Hamiltonian–based divide–and–conquer framework

Multibody system simulations are increasingly complex for various reasons, including structural complexity, the number of bodies and joints, and many phenomena modeled using specialized formulations. In this paper, an effort is pursued toward efficiently implementing the Hamiltonian-based divide-and-conquer algorithm (HDCA), a highly-parallel algorithm for multi-rigid-body dynamics simulations modeled in terms of canonical coordinates. The algorithm is implemented and executed on a system–on–chip platform which integrates a general-purpose CPU and FPGA. The details of the LDUP factorization, which is used in the HDCA approach and accounts for significant computational load, are presented. Simple planar multibody systems with open- and closed-loop topologies are analyzed to show the correctness of the implementation. Hardware implementation details are provided, especially in the context of inherent parallelism in the HDCA algorithm and linear algebra procedures employed for calculations. The computational performance of the implementation is investigated. The final results show that the FPGA–based multibody system simulations may be executed significantly faster than the analogous calculations performed on a general–purpose CPU. This conclusion is a good premise for various model-based applications, including real-time multibody simulation and control.

An implicit asynchronous variational integrator for flexible multibody dynamics

To accurately capture the dynamic responses of flexible multibody systems with complex geometric shapes or with contact and collision problems, extremely fine meshes have to be used. However, most previous algorithms for simulating these systems adopt a single integration time step size. A way to improve computation efficiency is to use different integration time steps for different elements with different sizes. In this study, a novel implicit AVI (asynchronous variational integrator) is originally proposed to study dynamics of complex flexible multibody systems. The proposed integrator allows different integration time step sizes for different elements with different mesh sizes. The multipoint constraint method is utilized to glue non-matching elements. To establish the system’s discrete Euler–Lagrange equations (DELs) , the diagonal-scaling method is used to construct the lumped mass matrix of elements. Finally, seven numerical examples are presented to comprehensively validate accuracy and efficiency of the proposed integrator. Numerical results indicate that the proposed AVI is capable of accurately capturing the dynamic response of flexible multibody systems and preserving systems’ energy and momentum. Compared with the generalized-α algorithm with a single time step size, the proposed AVI can significantly improve the computation efficiency for the dynamic simulation of complex flexible multibody systems with clearance joints.

Research on dynamics software of transfer matrix method for multibody systems

The general and fast programmed dynamics modeling, computation and design method of complex mechanical multibody system have become the theoretical and technical problems that must be solved in the development of modern industry. The transfer matrix method for multibody systems (MSTMM) has become a powerful tool for dynamics modeling and simulation of multibody systems by virtue of its flexible modeling, such as no need for global dynamics equation, low matrix order, fast computational speed, automatic derivation of overall transfer equation and high degree of programming. In order to apply MSTMM to practical engineering problems quickly, the MSTMM is taken as the core theory of dynamics modeling and computation, and the visualization dynamics software of MSTMM is established by combining OpenCascade, Qt and other open source software. The software realizes the automatic derivation of the overall transfer equation and the fast computation of system dynamics. The engineering example of a tracked vehicle verifies the effectiveness of the software.

Reconstruction of a real-world car-to-pedestrian collision using geomatics techniques and numerical simulations

The aim of this study is to provide an improved method for traffic accident reconstruction based on geomatics techniques and numerical simulations. A combination of various techniques was used. First, an unmanned aerial vehicle (UAV), laser scanner and structured-light scanner were used to obtain information on the accident scene, vehicle and victim. The collected traces provided detailed initial impact conditions for subsequent numerical simulations. Then, multi-body system (MBS) simulations were conducted to reconstruct the kinematics of the car-to-pedestrian collision. Finally, a finite element (FE) simulation using the THUMS model was performed to predict injuries. A real-life vehicle-pedestrian collision was used to verify the feasibility and effectiveness of this method. The reconstruction result revealed that the kinematic and injury predictions of the numerical simulations effectively conformed to the surveillance video and investigation of the actual accident. UAV photogrammetry was demonstrated to be more efficient in accident data collection than hand sketch and measurement, and 3D laser scanning enabled an easier and more accurate modeling process of vehicle. The present study shows the feasibility of this method for use in traffic accident reconstruction.

Exponential integration for efficient and accurate multibody simulation with stiff viscoelastic contacts

The simulation of multibody systems with frictional contacts is a fundamental tool for many fields, such as robotics, computer graphics, and mechanics. Hard frictional contacts are particularly troublesome to simulate because they make differential equations stiff, calling for computationally demanding implicit integration schemes. We suggest to tackle this issue by using exponential integrators, a long-standing class of integration schemes (first introduced in the 1960s) that in recent years has enjoyed a resurgence of interest. This scheme can be applied to multibody systems subject to stiff viscoelastic contacts, leading to integration errors similar to implicit Euler, but at much lower computational costs (between 2 to 100 times faster). In our tests with quadruped and biped robots, our method demonstrated a stable behavior with large time steps (10 ms) and stiff contacts (\(10^{5}\) N/m). Its excellent properties, especially for fast and coarse simulations, make it a valuable candidate for many applications in robotics, such as simulation, model predictive control, reinforcement learning, and controller design.

An innovative stepwise time-domain fatigue methodology to integrate damage tolerance into system dynamics

With the development of vehicle system dynamics, the multi-body system simulation has been proven as an effective and cost-saving way to obtain fatigue loads of high-speed railway bogies. However, the application of simulated dynamic stress spectra is usually limited to the classical damage accumulation design. Moreover, the advanced damage tolerance philosophy for railway bogies are mainly based on standard prescribed loads or measured loads. To this end, a novel time-domain stepwise fatigue assessment (TSFA) methodology was proposed to effectively bridge the vehicle system dynamics with fracture mechanics. The research results indicate that the welded butt joints of gearbox bracket are the most critical positions for bogie frames made of S355J2W steel with an estimated life of 162.7 years. This is conservative enough for the conventional safety life design. However, the residual life abruptly decreases to 26.4 years once a crack with the length of 6 mm initiates near the weld toe, and the service lifetime of 30 years cannot be covered yet. This agrees well with the practical maintenance cases and full-scale benchmark tests. Therefore, the newly-proposed TSFA approach is suggested while determining the damage tolerance and maintenance strategy of defective bogie frames under complex dynamic vibration responses.

Singularity-Free Lie Group Integration and Geometrically Consistent Evaluation of Multibody System Models Described in Terms of Standard Absolute Coordinates

Abstract A classical approach to the multibody systems (MBS) modeling is to use absolute coordinates, i.e., a set of (possibly redundant) coordinates that describe the absolute position and orientation of the individual bodies with respect to an inertial frame (IFR). A well-known problem for the time integration of the equations of motion (EOM) is the lack of a singularity-free parameterization of spatial motions, which is usually tackled by using unit quaternions. Lie group integration methods were proposed as an alternative approach to the singularity-free time integration. At the same time, Lie group formulations of EOM naturally respect the geometry of spatial motions during integration. Lie group integration methods, operating directly on the configuration space Lie group, are incompatible with standard formulations of the EOM, and cannot be implemented in existing MBS simulation codes without a major restructuring. The contribution of this paper is twofold: (1) A framework for interfacing Lie group integrators to standard EOM formulations is presented. It allows describing MBS in terms of various absolute coordinates and at the same using Lie group integration schemes. (2) A method for consistently incorporating the geometry of rigid body motions into the evaluation of EOM in absolute coordinates integrated with standard vector space integration schemes. The direct product group SO(3)×ℝ3 and the semidirect product group SE(3) are used for representing rigid body motions. The key element is the local-global transitions (LGT) transition map, which facilitates the update of (global) absolute coordinates in terms of the (local) coordinates on the Lie group. This LGT map is specific to the absolute coordinates, the local coordinates on the Lie group, and the Lie group used to represent rigid body configurations.

Numerical modeling of nonstationary hydrodynamic forces and induced motions of a coupled offshore floating installation system

Offshore installations always involve multi-body systems in which the hydrodynamic and mechanical interactions are complicated for the properties keep changing under certain operation procedures. Float-over deck (FOD) installation is a typical example, where the draft of barge continuously varies during the load transfer operation. Numerical analysis of such continuous operation is crucial to identify the extreme responses, but it's difficult to model the nonstationary properties involved in the hydrodynamic loads and motions and contact loads of the system. In the study, a numerical modeling methodology is developed to calculate these nonstationary hydrodynamic forces and induced responses, considering an active update of the hydrodynamic properties with the time varying body boundary conditions. The effects of time varying body boundary conditions on hydrodynamic forces and induced nonstationary motions and contact loads of a FOD installation system is studied. The results indicate that the dynamic analysis of the continuous load transfer operation could be effectively carried out with one update of hydrodynamic forces at the end of the operation. The barge roll motions and its natural period are the most affected. The proposed method could be used in intensive simulation of offshore multi-body systems with obvious draft variation during operations.

РАЗРАБОТКА ДИНАМИЧЕСКОЙ МОДЕЛИ ДЛЯ ОЦЕНКИ ПРОФИЛЬНОЙ ПРОХОДИМОСТИ ДВУХЗВЕННОГО ВНУТРИТРУБНОГО РОБОТА

The ability of a multi-unit in-pipe robot to drive through curved sections of a pipeline is an importantindicator of its capability to move through the pipeline. At the design stage, this indicatorcannot be verified without mathematical simulation of the robot spatial movement and interaction ofits running gear with the pipeline. The objective of this work is to create a dynamical model for evaluationof the two-link in-pipe wheeled robot capability to drive through a pipeline. The model wasdeveloped in the Universal Mechanism multibody system simulation program with the use of itsstandard elements of the mechanical system modeling and a special-purpose wheel – pipeline contactmodel developed by the authors. The wheel – pipeline contact model was created in MATLAB andcompiled as a DLL. The developed multibody model was verified by the robot behavior during itsmotion through a bent section of the pipeline and by the time histories of the indicators of its capabilityto drive through the pipeline. Two directions of the pipeline bend were studied. The minimumdistance from the extruding electric motors of the robot actuators to the internal surface of the pipelinehas been offered as an indicator of the robot ability to move through the pipeline. The analysis ofthe simulation results has proved the adequacy of the model behavior and showed that the developedmultibody model can be used for the evaluation of the robot capability to move through the pipelineat the early design stages before fabrication of its prototype.

A hybrid data-driven model order reduction strategy for flexible multibody systems considering impact and friction

The numerical simulation of flexible multibody systems (FMBSs) with contact is important. Meanwhile, the contact problem is always a key and difficult point for FMBSs; and when impact and friction affect FMBSs, the computational efficiency will dramatically decline. In this work, the nonsmooth contact method (NSCM) for FMBSs is briefly introduced. Moreover, in order to save the computational costs of a contact FMBS, a novel hybrid model order reduction (MOR) strategy based on the idea of data-driven method is proposed. For the hybrid MOR strategy, the reduced-order models (ROMs) based on the NSCM in smooth force part and nonsmooth force part are derived using proper symplectic decomposition and proper orthogonal decomposition, respectively. In addition, in order to adapt the ROMs to parameter variation, the parameter interpolation method on the tangent space of Grassmann manifold is studied. Finally, several numerical examples are tested using the proposed methodology, the results show that compared with the original model, the ROM can save 65.89% of the computing time, and the root-mean-square error between the ROM and original model can reach the order of 10−12.