Computational Multibody Dynamics Research Articles

Development and trials of a novel deep-sea multi-joint autonomous underwater vehicle

To realize fine exploration in the deep sea, this paper designed a highly maneuverable multi-joint autonomous underwater vehicle (MJ-AUV). MJ-AUV is composed of three cabins in series, which are connected mechanically and electrically through two joint systems. The rotation of the joints drives the deformation of MJ-AUV, thereby realizing a variety of maneuvering modes. Each connecting joint is driven by a two-stage bevel gear, which is compact in structure and has good strength and rigidity, and can drive the cabins to achieve two degrees of freedom (i.e., pitch and yaw) motion. Computational fluid dynamics (CFD) technology was used to build a numerical pool and calculate the added mass coefficient and drag coefficient of each cabin. The kinematics model of MJ-AUV was established and the force analysis was carried out. On this basis, the simulation environment was built through computational multi-body dynamics (MBD) software MSC Adams, which was used to systematically analyze the multiple motion states of MJ-AUV. Lake and sea trials conducted in Thousand Islet Lake, the South China Sea, Qingdao Coast, and other places have validated the actual performance of the designed MJ-AUV, including cruising mode, vertical profile motion, deep diving and water surface motion.

A novel nonsmooth approach for flexible multibody systems with contact and friction in 3D space

For computational multibody system dynamics, contact and friction problems are very complex and important problems. Therefore, this paper proposes a novel nonsmooth method for flexible multibody systems with contact and friction in 3D space. Considering the nonsmooth effect of contact and friction on the state variable of the multibody systems, the proposed method is divided into two parts: (i) the change of state variables under the action of smooth force and (ii) the change of state variables caused by contact and friction. Furthermore, for the contact part, the Newton’s impact law and the classical Coulomb friction model are employed to deal with normal impact contact impulse and tangential friction contact impulse, respectively. In addition, Fischer–Burmeister function and Karush–Kuhn–Tucker conditions are also used to solve the normal impact contact impulse and tangential friction contact impulse. What’s more, since the symplectic discrete format performs well robustness to numerical results, the discrete format of the proposed method is based on the symplectic discreteness, and it is expected to obtain the robust numerical results. Finally, several numerical examples are tested by the proposed nonsmooth method, and the numerical simulation results verify the effectiveness of the proposed approach.

Reduced-order thermomechanical modeling of multibody systems using floating frame of reference formulation

In this study, a reduced-order thermomechanical coupling model, which accounts for the inertia coupling of the thermoelastic deformation and the large reference body motion, is proposed using the floating frame of reference formulation for the transient thermomechanical analysis of constrained multibody systems. In this approach, the reduced-order heat equations are fully embedded in the final form of the equations of motion. Accordingly, the transient thermal response as well as the resulting thermoelastic behavior of constrained multibody system can be predicted within the general multibody dynamics computer algorithm. It is demonstrated that appropriate selection of the thermal interface coordinates is crucial for describing the thermal modes (i.e. temperature distribution) induced by external heat sources using the Craig–Bampton component mode synthesis approach generalized for thermomechanical systems. Furthermore, a systematic procedure for imposing prescribed surface temperature given, for example, from thermal-fluid dynamics simulations is proposed for the thermomechanical floating frame of reference formulation. Using several numerical examples, simulation capabilities of the thermomechanical floating frame of reference formulation model are demonstrated for multibody dynamics applications. Numerical results show good agreement with the nonlinear thermomechanical finite element solutions considering the large rotational motion with substantial reduction in the model dimensionality and computational time.

Combined simulation of heavy truck stability under sudden and discontinuous direction change of crosswind with computational fluid dynamics and multi-body system vehicle dynamics software

The method of yaw model is used to establish aerodynamic property of heavy truck in computational fluid dynamics and wind tunnel test. A model of multi-body system simulation for heavy truck is built based on design and measure data from body, driving system, steering system, braking system, and powertrain system with TruckSim. Aerodynamic reference point of Society of Automotive Engineers (SAE) and aerodynamic coefficients are as the interface to integrate computational fluid dynamics and multi-body system simulation. A sudden and discontinuous direction change of crosswind is set up in multi-body system simulation, and dynamic performance of the heavy truck is performed by open-loop and closed-loop simulation. Under the given simulation case, lateral offset of the truck for open-loop simulation is 1.55 m and more than that for closed-loop simulation; the roll rate range of both simulations is −1.49°/s to 1.695°/s, the range of lateral acceleration is −0.497 m/s2 to 0.447 m/s2 in open-loop simulation, the range of lateral acceleration is −0.467 m/s2 to 0.434 m/s2 in closed-loop simulation; the range of yaw rate is −1.36°/s to 1.284°/s in open-loop simulation, the range of yaw rate is −0.703°/s to 0.815°/s in closed-loop simulation. The results show that combined simulation of the heavy truck stability can be completed by computational fluid dynamics and multi-body system software under sudden and discontinuous direction change of crosswind.

Multibody system dynamics interface modelling for stable multirate co-simulation of multiphysics systems

Many industrial applications benefit from predictive computer simulation to reduce costs and time, and shorten product development cycle. Computational multibody system dynamics formalisms and software tools have proved to be particularly useful in the simulation of machinery and mechanical systems. Nowadays, however, the complexity of the applications under study often makes it necessary to consider the interaction of mechanical systems with other components of different nature, physical behaviour, and time scale, such as hydraulics or electronics. Co-simulation is an increasingly important approach to formulate and solve the dynamics of these multiphysics setups. In these, modelling techniques and solvers that are tailored to the requirements of each subsystem execute in parallel and are coupled via the exchange of a limited number of inputs and outputs at certain communication times. Co-simulation has clear potential in the modelling of complex engineering systems. On the other hand, there are also challenges. The use of co-simulation may compromise the stability of the numerical solution, especially when non-iterative coupling schemes are used.In this work, we introduce a modelling technique to improve the dynamic interfacing of mechanical systems in co-simulation setups, based on a reduced representation of multibody systems. This reduced order model is used to obtain a physically meaningful prediction of the evolution of the multibody subsystem dynamics that enables the improvement of the solution of other subsystems. The technique is illustrated in the co-simulation of some examples that include both mechanical and hydraulic components. Results show that dynamic interfaces based on reduced models can be used to improve the stability of non-iterative co-simulation schemes in multiphysics engineering systems, enabling the use of larger communication step-sizes.

Physics-Based Deformable Tire–Soil Interaction Model for Off-Road Mobility Simulation and Experimental Validation

A physics-based deformable tire–soil interaction simulation capability that can be fully integrated into the monolithic multibody dynamics computer algorithm is developed by extending a deformable tire model based on the flexible multibody dynamics approach to off-road mobility simulations with a moving soil patch technique and it is validated against test data. A locking-free nine-node brick element is developed for modeling large plastic soil deformation using the multiplicative finite strain plasticity theory along with the capped Drucker–Prager failure criterion. To identify soil parameters including cohesion and friction angle, the triaxial compression test is carried out, and the soil model developed is validated against the test data. In addition to the component level validation for the tire and soil models, the tire–soil interaction simulation capability developed in this study is validated against the soil bin mobility test results. The tire forces and rolling resistance coefficients predicted by the simulation model agree well with the test results. It is shown that effect of the wheel loads and tire inflation pressures is well captured in the simulation model. Furthermore, it is demonstrated that the moving soil patch technique, with which soil behavior only in the vicinity of the rolling tire is solved to reduce the soil model dimensionality, leads to a significant reduction in computational time, thereby enabling use of the high-fidelity physics-based tire–soil interaction model in the large-scale off-road mobility simulation.

Geometric methods and formulations in computational multibody system dynamics

Multibody systems are dynamical systems characterized by intrinsic symmetries and invariants. Geometric mechanics deals with the mathematical modeling of such systems and has proven to be a valuable tool providing insights into the dynamics of mechanical systems, from a theoretical as well as from a computational point of view. Modeling multibody systems, comprising rigid and flexible members, as dynamical systems on manifolds, and Lie groups in particular, leads to frame-invariant and computationally advantageous formulations. In the last decade, such formulations and corresponding algorithms are becoming increasingly used in various areas of computational dynamics providing the conceptual and computational framework for multibody, coupled, and multiphysics systems, and their nonlinear control. The geometric setting, furthermore, gives rise to geometric numerical integration schemes that are designed to preserve the intrinsic structure and invariants of dynamical systems. These naturally avoid the long-standing problem of parameterization singularities and also deliver the necessary accuracy as well as a long-term stability of numerical solutions. The current intensive research in these areas documents the relevance and potential for geometric methods in general and in particular for multibody system dynamics. This paper provides an exhaustive summary of the development in the last decade, and a panoramic overview of the current state of knowledge in the field.

On the use of computational multi-body dynamics analysis in SLS-based 3D printing

In the context of additive manufacturing, we illustrate how computational multi-body dynamics (CMBD) analysis can (a) increase printing throughput; and, (b) play a role in improving the quality of 3D printed parts. Throughput is increased by packing the printing volume with as many parts as possible. The problem becomes one of determining where each component that needs to be printed finds itself inside the printing volume. Finding the position and orientation of each part is accomplished through CMBD analysis, a point illustrated through an example in which an open-source dynamics engine called Chrono is used to simulate the filling of the active printing volume with a dress that is subsequently 3D printed. This approach, which is general in purpose, enables one to print in one pass multiple parts that are virtually; i.e., through simulation, dropped inside the printing volume to fully fill it up, thus improving efficiencies. In relation to (b), we use million-body dynamics simulations to gauge how various granular mixture parameters and rolling regimes combine to ultimately control the roughness of the surface being sintered.

Patient-specific bone geometry and segment inertia from MRI images for model-based analysis of pathological gait

Patient-specific modeling is a vital component in the translation of computational multibody dynamics into clinical practice. Recent research has focused on ways to derive such models from medical imaging, but the process is usually time consuming and sensitive to operator skill. Here, we present methods to derive kinematic and inertial properties of body segments from MRI images, and condense them into a dynamically consistent patient-specific multibody model (PSM). We develop a semi-automated tool chain to classify bone, muscle and fat in the lower body and use optimization and geometrical methods to derive personalized bone meshes and segment inertial properties. The tool chain is applied to investigate the gait of a 12-yr old female with bone deformities. The patient-specific results are compared to those arising from generic scaled models with parameters based on regression equations. We found several kinematic and inertial differences between the two models, and overall the PSM resulted in markedly smaller angular and force residuals. The PSM was able to capture vital aspects of this patient׳s gait in the transverse plane that were overlooked by the generic model. These results are relevant to the use of multibody dynamics in the planning of surgical interventions, and form the basis for developing efficient and automatic methods to create patient-specific models.

Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model

In this investigation, the flexible tire model based on the absolute nodal coordinate formulation (ANCF) is integrated with LuGre tire friction model for evaluation of the longitudinal tire dynamics under severe braking scenarios. The ANCF-LuGre tire model developed allows for considering the nonlinear coupling between the dynamic structural deformation of the tire and its transient tire force distribution in the contact patch using general multibody dynamics computer algorithms. To this end, the contact patch obtained by the ANCF elastic ring tire model is discretized into small strips and the state of friction at each strip is defined by the differential equation associated with the discretized LuGre friction parameters. The normal contact pressure distribution predicted by the ANCF elastic ring elements that are in contact with the road surface are mapped onto the LuGre strips in the contact patch to evaluate the tangential tire force distribution and then the tire forces evaluated at LuGre strips are fed back to the generalized tangential contact forces of the ANCF elastic ring tire model. By doing so, the structural deformation of the ANCF elastic ring tire model is dynamically coupled with the LuGre tire friction in the final form of the governing equations. Furthermore, the systematic and automated parameter identification procedure for the LuGre tire force model is developed. It is shown that use of the proposed procedure with the modified friction curve proposed for wet road conditions leads to accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Several numerical examples are presented in order to demonstrate the use of the in-plane ANCF-LuGre tire model for the longitudinal transient dynamics of tires under severe braking scenarios.

Air Suspension System Model Coupled With Leveling and Differential Pressure Valves for Railroad Vehicle Dynamics Simulation

In this investigation, a nonlinear air suspension system model that accounts for the coupling between air springs, leveling valves, and differential pressure valves is developed and integrated into general-purpose multibody dynamics computer algorithms. It is demonstrated that the proposed model can capture highly nonlinear air suspension characteristics resulting from the coupling with leveling and differential pressure valves, and good agreements are obtained between the numerical and on-track test results. Furthermore, the effect of flow characteristics of leveling valves on the wheel load unbalance on spiral curve sections is discussed. The numerical results obtained by the proposed model clearly indicate the importance of modeling the nonlinear flow characteristics of the leveling and differential pressure valves for assessing the vehicle safety in low speed operations on a small radius curved track.

Modelling and control of an autonomous articulated mining vehicle navigating a predefined path

This research is conducted on machine dynamics and steering control of an articulated surface mining large wheel loader (LWL) navigating a predefined path. Modelling a LWL based on computational multibody dynamics is achieved by modelling each system of the articulated vehicle separately then merging them to form an overall system of an articulated vehicle navigating a predefined path. This model includes the front and rear frames, articulated hinge, steering actuators, tyre model, steering controller and a predefined path. Fuzzy and PID steering controllers are developed and simulated. Results show that it is possible to model large articulated vehicles as a multibody mechanical system. Both of the developed controllers are able to control the lateral and longitudinal motion of the vehicle and drive the machine over the desired path accurately. The fuzzy logic controller has longer rising time but shorter settling time when compared with the PID controller.

Binding Force Analysis of Multiple Pairs of Bars Space RCCR Mechanism without Inertia Force

In close to the rigid body condition,to solve the binding force of multiple pairs of bars space RCCR mechanism,first, starting from solving main binding force of three-pair bars space RCCR mechanism by the theoretical analysis, to have obtained the change law of the main binding force without the inertial force (extremely low speed) by using the computational multibody dynamics software ’COSMOSMotion’ and then summed up the equivalent tangential force through the investigation of the simulation data. Finally the concept of equivalent tangential binding force was expanded to 4, 5, 6 pairs of bars space RCCR mechanism.

The Computational Multi-Body Dynamics for Motorcycle on its Oscillation Properties

Based on 3D digital model of motorcycle constructed in UGNX, motorcycle multi-body model was established for dynamic behavior analysis under inbuilt assembling of coefficient matrix of dynamical equation in computation code of ADAMS. Through the comparison of simulation analysis for dynamics of different models in accelerations in time and frequency domains, it is concluded that realistic multi-body model better represents the dynamic behavior of motorcycle while simplified one with less physical parameters only provides qualitative analysis for the dynamic behavior. The simulation results shows that model IV with accurate parameters of components influences the dynamic response of frame, simplified models could not represent the influence of mass and inertia moment of subsystems on dynamic behavior, which means advanced motorcycle multi-body improves simulation effectiveness and approximates the dynamic behavior of motorcycle well so that the simulation developed to replace experiments in bad working conditions will promote the advancement of engineering.

Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems

The aim of this study is to provide a comprehensive review of the finite element absolute nodal coordinate formulation, which can be used to obtain efficient solutions to large deformation problems of constrained multibody systems. In particular, important features of different types of beam and plate elements that have been proposed since 1996 are reviewed. These elements are categorized by parameterization of the elements (i.e., fully parameterized and gradient deficient elements), strain measures used, and remedies for locking effects. Material nonlinearities and the integration of the absolute nodal coordinate formulation to general multibody dynamics computer algorithms are addressed with particular emphasis on visco-elasticity, elasto-plasticity, and joint constraint formulations. Furthermore, it is shown that the absolute nodal coordinate formulation has been applied to a wide variety of challenging nonlinear dynamics problems that include belt drives, rotor blades, elastic cables, leaf springs, and tires. Unresolved issues and future perspectives of the study of the absolute nodal coordinate formulation are also addressed in this investigation.

COMFORT AND INTERFACE FORCES IN ANKLE-FOOT ORTHOTICS

The use of orthoses can lead to discomfort due to the abnormal loading of skin in areas that are unaccustomed to support forces. To promote the comfort of the users a standard recommendation for the design of these devices, is to lower these forces. Different strategies can be applied: increase the area of contact and lower the pressure or limit the area of contact to prescribed locations. Although pressure pain thresholds and indications for suitable locations to apply force are available [Pons, 2008], still it is essential to calculate the forces to infer about comfort. The present methodology allows the calculation of the interface forces, in this case between the lower limb and an Ankle-Foot Orthosis (AFO), using a two-dimensional computational multibody dynamics model. The input of this model encompasses the patient’s pathological data from a lab gait. With the ability to calculate the interface forces in the indicated locations, it is possible to design the orthotic device to the required function and comfort.

Walking dynamics from mechanism models to parameter optimization

The paper deals with the historical development of human body dynamics, and it presents results received for simple models by parameter optimization. The scientific research on human walking dynamics started already in the 19th century and was later promoted by the physicist and physiologist Otto Fischer who published in 1906 his fundamental book. Fischer used the mechanism theory for modeling and analysis of human walking. His research was based on the barycenters of the corresponding reduced mechanisms. By the end of the 20th century computational multibody dynamics provided more complex models which were applied to human body dynamics, too. More recently parameter optimization has been used to deal with the overactuation of biomechanical systems still a very active research topic in biomechanics. As an example a gait disorder simulation is presented showing that even today mechanism models, muscle group selection, inverse dynamics approaches and parameter optimization techniques using energy and aesthetics criteria are essential tools.

Sliding Joint Constraints for the Large Deformation Analysis of Multibody Systems

In this investigation, a numerical procedure that can be effectively used for modeling sliding joint constraints for the absolute nodal coordinate formulation is developed. To this end, the arc-length coordinates are introduced to define the time-variant location of the constraint definition point on flexible bodies, while the intermediate coordinates are introduced to derive a mapping between the generalized gradient coordinates and the rotational coordinates. With this mapping, sliding joint constraints can be efficiently formulated for a flexible body modeled using the absolute nodal coordinate formulation. Furthermore, existing constraint libraries formulated for rigid bodies can be employed for the absolute nodal coordinate formulation without modifications. It is also demonstrated that the arc-length coordinates and intermediate coordinates used for formulating sliding joint constraints can be systematically eliminated from the equations of motion and standard differential algebraic equations used for general multibody dynamics computer algorithms can be obtained.

Evaluation of the contact forces developed in the lower limb/orthosis interface for comfort design

Ankle-Foot Orthoses (AFOs) are technical aids that promote locomotion and rehabilitation of individuals with gait pathologies. Every pathology has its own requirements and this has led to classical solutions that are far from optimal in terms of comfort and overall performance for restoring the human gait. Formal scientific approaches are therefore necessary to take full advantage of the available technological potential and produce more efficient modern devices that can significantly improve the quality of life of people with locomotion impairment. In this work, a computational multibody dynamics approach is adopted. A multibody model of an active AFO is developed and integrated in a whole-body multibody human model developed in the MATLAB environment. In the adopted procedure, normal gait motion data is used as input to the biomechanical model. The experimental data was obtained in the gait lab by acquiring the kinematic and kinetic data of a stride of a healthy female subject. The aim of this integrated model is to estimate the loads transmitted at the foot-leg-orthosis interface. To achieve this, it is essential to decide where the contact between the lower limb and the orthosis should occur, and what are the forces generated in such interface. A contact model between a sphere and a plane is applied together with a friction model to determine the contact forces, and the properties used for the surfaces in contact were based on the available data in the literature and on experimental tests. The results revealed that the contact pressures obtained are below the PPTs (Pain Pressure Thresholds), which represent the patient’s comfort. However, the pressure is dependent on the contact properties between surfaces, meaning that these must be experimentally determined for each material. It was also uncovered that the weight of the orthosis is an important issue in the design of an active AFO as it greatly influences the moments at the ankle, knee, and hip and, therefore, the patient effort when wearing the orthosis.

The Vehicle Dynamical Analysis of a High-Speed Train Passing through a Tunnel

As the speed of train increases, flow-induced vibration of trains passing through tunnels has become a subject of discussion, to investigate this phenomenon, a simplified geometric model and a vehicle dynamics model of a high-speed train traveling through a tunnel were built. To analyze the unsteady three-dimensional flow around the train, the 3-D, transient, viscous, compressible Reynolds-averaged Navier-Stokes equations combined with the k- two-equation turbulence model were solved with the finite volume method. The motion of the train was carried out using the technique of sliding grid method. The dynamics response of the train was obtained by means of the computational multi-body dynamics calculation. Meanwhile the running safety and riding comfort of the train were analyzed. With the numerical simulation, the variation of aerodynamic forces was obtained. The research founds that, vibration of the train increases drastically during it passing through a tunnel. The running safety and riding quality of the train are reduced greatly but they are in the safe range.