Three-dimensional Multi-body Model Research Articles

An efficient and accurate linearization approach for hydraulically actuated multibody systems with holonomic and nonholonomic constraints

Hydraulics is often used to actuate mechanisms in the applications of heavy machinery. In this work, a linearization approach for hydraulically driven multibody systems is presented. The approach allows linearizing the equations of motion of general multibody systems with holonomic and nonholonomic constraints, augmented with the hydraulic equations of the hydraulic subsystem. The derivation of this linearization approach is of interest in many applications, such as the performance of linear stability analyses. The procedure is tested with a three-dimensional multibody model of a hydraulically actuated four-bar mechanism. The validation of the approach is performed by means of the forward dynamics simulation of the linear and nonlinear systems. The results show the power of the approach, obtaining the linearized equations of motion around the equilibrium position of the four-bar mechanism multibody model in terms of the mechanical and hydraulic parameters. A comparison of the proposed procedure with a conventional counterpart approach is included, demonstrating the great accuracy and computational efficiency of the approach developed in this work.

An integrated three-dimensional powertrain-vehicle dynamics model for tracked vehicle analysis

A tracked vehicle employs a special transmission to generate a speed difference between the inner and outer tracks for steering. In this paper, the dynamic model of one of the most widely used steering transmissions called double differential steering has been derived and integrated with a multi-body tracked vehicle model. A simplified multi-body model for tracks has been proposed to reduce the computational and numerical difficulties arising from a detailed three-dimensional multi-body model. The accuracy of the proposed model is demonstrated by extensive comparison with a detailed multi-body model developed using the Tracked Vehicle module of the commercial software ADAMS. Simulations are carried out using the integrated tracked vehicle model to demonstrate the effects of changes in three-dimensional vehicle dynamic performance with design changes in powertrain systems.

Study of the forward locomotion of a three-dimensional multibody model of a Waveboard by inverse dynamics

This paper studies the forward motion of the Waveboard, a variant of the Skateboard that consists of two platforms and two caster wheels. This system exhibits a very interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms, without touching the ground.Because of the complex nature of the Waveboard dynamics, a three-dimensional multibody model is proposed, modeling the wheels as two rings first and as tori later on. Some holonomic constraints arise at the contact of the wheels with the ground, while some non-holonomic constraints appear from the assumption of rolling without slipping. The equations of motion of the system are derived and a kinematic and inverse dynamics simulation of a realistic meandering trajectory is carried out, in order to understand the necessary forces and torques to obtain the desired motion. Moreover, an analysis of the influence of the design parameters on the external actions exerted by the rider is made.Finally, the multibody model is enhanced by modeling the wheels as two tori, performing a comparison between the ring and toroidal models.

Dynamic analysis of varus knee using a subject-specific multibody model of the knee before and after osteotomy

Varus misalignment of the hip-knee-ankle angle causes greater loads on the medial compartment of the knee and increases the risk of developing knee osteoarthritis. High tibial osteotomy is a surgical method where the load-bearing axis is shifted laterally. The purpose of this study is to define a subject-specific three-dimensional multibody model of the knee to investigate the effect of osteotomy on cartilages and menisci during the stance phase of gait. It is assumed that osteotomy transfers load-bearing to the lateral parts of the knee. Magnetic resonance images of a patient with varus alignment were used to generate the geometries of the bones, cartilages, and menisci. Then, an experimental approach was used to determine the parameters for the stiffness matrices and compliant contact models of the tibio-menisco-femoral articulations with the use of finite element solutions. As indicated by the research findings, the contact force at the medial cartilage decreased as the load-bearing axis was transferred to the lateral parts. This subject-specific noninvasive analysis of contact force can be considered as a preoperative assessment tool for the surgeon. to predict the effects of high tibial osteotomy and the shifting of the load-bearing axis to the soft tissues of the knee.

Power dissipation modeling in wheel/rail contact: Effect of friction coefficient and profile quality

This work investigates the power dissipation in a wheel/rail system through friction work modeling. In order to identify the effect of the friction coefficient on the power dissipation in the wheel/rail contact, several simulations were performed using a three-dimensional multibody model of a railway vehicle implemented in the software package VI-Rail Adams. The power dissipation and wear rates of the inner and outer wheels of the first bogie of the vehicle running over a curve of a metro line were calculated for different friction coefficients varying from 0.2 to 0.7. The total frictional work was obtained from the resultant force and slip in a reference point. The wear was also analyzed according to the Tγ method including the spin, in combination with Kalker׳s simplified theory Fastsim, assuming that the wear is proportional to the frictional work. Two sets of rail and wheel profiles were studied in order to determine the effect of the profile׳s quality on the power dissipation and wear rates. To this end simulations and power calculations were performed with a friction coefficient of 0.4.

Dynamics of anchor last deployment of submersible buoy system

Submersible buoy systems are widely used for oceanographic research, ocean engineering and coastal defense. Severe sea environment has obvious effects on the dynamics of submersible buoy systems. Huge tension can occur and may cause the snap of cables, especially during the deployment period. This paper studies the deployment dynamics of submersible buoy systems with numerical and experimental methods. By applying the lumped mass approach, a three-dimensional multi-body model of submersible buoy system is developed considering the hydrodynamic force, tension force and impact force between components of submersible buoy system and seabed. Numerical integration method is used to solve the differential equations. The simulation output includes tension force, trajectory, profile and dropping location and impact force of submersible buoys. In addition, the deployment experiment of a simplified submersible buoy model was carried out. The profile and different nodes’ velocities of the submersible buoy are obtained. By comparing the results of the two methods, it is found that the numerical model well simulates the actual process and conditions of the experiment. The simulation results agree well with the results of the experiment such as gravity anchor’s location and velocities of different nodes of the submersible buoy. The study results will help to understand the conditions of submersible buoy’s deployment, operation and recovery, and can be used to guide the design and optimization of the system.

An improved three-dimensional multibody model of the human spine for vibrational investigations

In this paper, a three dimensional numerical model of the human spine, specialized for vibrational investigations, is presented. The model has been built using multibody dynamics techniques and includes the entire set of vertebrae, considered as rigid bodies. The interaction between vertebrae has been simulated using six component bushings, without the need of any kinematic constraint. This methodology allows a very relevant flexibility, and the fully three-dimensional deformation modes of the spine may be studied. The investigation has been focused on the assessment of the vibration modes and the computation of the transmissibility functions buttocks-to-head for acceleration inputs along three main directions. It has been observed that the first torsional modes with a relevant mass participation factors are present at very low frequencies. Most of the relevant modes, which involve the deformation of the spine with relevant participation factor, are within the range \(0{\div}5\ \mbox{Hz}\). These peaks are also visible in the transmissibility functions. Results have been also compared to those of other experimental and numerical studies.

Dynamic interaction of the monorail–bridge system using a combined finite element multibody-based model

To assess the dynamic behavior of monorail–bridge system, an innovative model of train–guideway interaction has been developed based on multibody dynamics and finite element simulation. A finite element model of guideway structure for a particular monorail system is built up using parametric design language, considering a specific length of straddle monorail line in three dimensions. Both straight and curved track geometries are modeled to simulate the actual bridge infrastructure. Flexible elements are adopted for the guideway beams consisting of reinforced concrete profiles to increase the accuracy of the numerical simulations in a more realistic way. The bridge model indeed, is simulated using a beam-frame structure of composite steel–concrete material. A multibody simulation of monorail vehicle is then introduced using the commercial multibody software MSC Adams. The three-dimensional multibody model of the monorail vehicle together with the bridge subassemblies is eventually implemented in multibody environment. The entire dynamic model of the vehicle-track system consists of all flexible and rigid body elements. Dynamic responses of the vehicle and bridge system are then extracted for different loading conditions. The proposed numerical model is validated using some dynamic simulation results of the system from the vehicle manufacturer in the selected case study. The model is further verified against several analytical and measurement results reported in the literature both for straight and curved track configurations. The result of dynamic simulations gives an overview about the dynamic forces and reactions that can appear in bridge structure due to the train movement.

Effect of Active Head Restraint on Cervical Vertebrae Injuries Lessening

A three-dimensional multi-body model of the 50th percentile male human and discretized neck was built to evaluate the effect of active head restraint on cervical vertebrae injuries lessening in vehicle rear impact. The discretized neck includes of cervical spine vertebrae, intervertebral discs, ligaments, and muscles. The BioRID-II adult male dummy restrained using safety belt was seated on a sled, whose longitudinal velocity measured from rear impact FEM simulation was applied to simulate the relative motion of the head and neck. According to the interspinous ligament loads and the ligamenta flava loads of the cervical spine, an active head restraint and an impact absorber were designed to lessening the neck injuries in vehicle rear end collisions.

Innovative Management of Wheel-Rail Adhesion Conditions in Localization Algorithms for the Automatic Train Protection

In the modern railway network, Automatic Train Protection and Control (ATP-ATC) systems are fundamental to increase the infrastructure capacity, maintaining a proper level of operation safety. Odometry is a relevant on-board module, since it estimates the speed and the travelled distance of a railway vehicle along the track. Its reliability affects the definition of allowed speed profiles, in order to prevent collisions from a driver's failure to observe a signal. Typically the dead reckoning relies on encoders providing an accurate estimation of the train speed only when good adhesion conditions between wheel and rail occur. In presence of wheel sliding the estimation error may become very high. In this paper the management of adhesion conditions is enhanced using an Inertial Measurement Unit (IMU) which improves the adhesion condition detection and the speed and travelled distance estimation. The testing of the proposed algorithm is performed through a testing simulator, set up by the MDM Lab and used to speed up the algorithm tuning, capable of replicating in a realistic way the motion dynamic effects of a railway vehicle on inertial sensors. The Hardware-In-The-Loop test rig is composed of a Matlab-Simulink TM three-dimensional multibody model of a railway vehicle, a commercial anthropomorphic manipulator with spherical wrist and an IMU designed by ECM Spa (Pistoia, Italy). The experimental results are compared to the performance requirements fixed by the European Rail Traffic Management System (ERTMS).

Evaluation of odometry algorithm performances using a railway vehicle dynamic model

In modern railway Automatic Train Protection and Automatic Train Control systems, odometry is a safety relevant on-board subsystem which estimates the instantaneous speed and the travelled distance of the train; a high reliability of the odometry estimate is fundamental, since an error on the train position may lead to a potentially dangerous overestimation of the distance available for braking. To improve the odometry estimate accuracy, data fusion of different inputs coming from a redundant sensor layout may be used. Simplified two-dimensional models of railway vehicles have been usually used for Hardware in the Loop test rig testing of conventional odometry algorithms and of on-board safety relevant subsystems (like the Wheel Slide Protection braking system) in which the train speed is estimated from the measures of the wheel angular speed. Two-dimensional models are not suitable to develop solutions like the inertial type localisation algorithms (using 3D accelerometers and 3D gyroscopes) and the introduction of Global Positioning System (or similar) or the magnetometer. In order to test these algorithms correctly and increase odometry performances, a three-dimensional multibody model of a railway vehicle has been developed, using Matlab-Simulink™, including an efficient contact model which can simulate degraded adhesion conditions (the development and prototyping of odometry algorithms involve the simulation of realistic environmental conditions). In this paper, the authors show how a 3D railway vehicle model, able to simulate the complex interactions arising between different on-board subsystems, can be useful to evaluate the odometry algorithm and safety relevant to on-board subsystem performances.

Research on Flexibility of Bearing Rings for Multibody Contact Dynamics of Rolling Bearings

The flexibility of bearing rings is very important to calculate the characteristics of rolling bearings in some rolling bearing applications such as planetary gear, rolling mill and aircraft. It may cause significant changes in dynamics characteristics, bearing deflections, contact stresses, and fatigue endurance, especially under heavy applied load, large size bearing, hollowed shaft and nonrigid bearing housing. The purpose in the work presented is to research a new approach and multibody model of bearing rings for MBS of mechanical system with rolling bearings. The flexibility and three-dimensional multibody model of bearing rings have been developed using equivalent rigid elements and curved Timoshenko beam elements. The simulation of the bearing rings vibration response will be presented. In addition to the presented multibody model, the FEM model and analytical model are also used to perform the vibration analyses of the bearing ring. An investigation of the actual static deformation field of the outer ring loaded by 5 balls has been carried out for the radial displacement field using the presented model. The total number of the discrete equivalent rigid elements and CTB elements has an important effect on the predicted frequencies, however the results will be minimal changes when the elements are achieved a certain number. In such situations, the presented approach can provide multibody rings model for contact dynamics of rolling bearings with acceptable accuracy and considerably less computational effort. The calculated radial static deformation is critical to load distribution, life fatigue and dynamics characteristics of rolling bearings. The three-dimensional multibody model of bearing rings developed here and the predicted frequencies agree well with the analytical results and FEM.

Study on Cervical Spine Injuries in Vehicle Frontal Impact

The human spinal column is a highly complex and sophisticated system both from an engineering and neurological point of view, and provides a source of biomimetic inspiration for analysis of its function in trauma scenarios. A three-dimensional multi-body model of the 50th percentile male human and discretized neck were built for the study on cervical spine injuries in vehicle frontal impact. The discretized neck includes of cervical spine vertebrae, intervertebral discs, ligaments, and muscles. Following motor front crash evaluations, a finite element vehicle model was propelled straight ahead into a concrete barrier at a speed of 50 km/h. The longitudinal velocity of driver seat was decreased due to the absorbing energy function of the crumple zones. A Hybrid III adult male dummy was seated on a sled, restrained using safety belt, and longitudinal velocity measured from frontal impact was applied to simulate cervical spine injuries. The disk bending loads, interspinous ligament loads and disk shear strain of the cervical spine were analyzed in this paper.

Study on Cervical Spine Injuries in Vehicle Side Impact

This paper presents the development and study of a three-dimensional multi-body model of the 50th percentile male human and discretized neck for the study of cervical spine injuries in vehicle side impact. The neck is composed of cervical spine vertebrae, inter-vertebral discs, ligaments, and muscles. Following motor crash evaluations, an impactor with a deformable front end representing the front of a car was propelled straight ahead into the sides of the vehicles being assessed. A EuroSID-2 adult male dummy was seated on a sled, restrained using safety belt, and lateral velocity measured from side impact was applied to simulate cervical spine injuries. The results show that the methods used in this paper have the potential to provide a costeffective and versatile platform to examine local loadings on the cervical spine and soft tissues, including the kinetics and the kinematics of the cervical spine and its components, as well as the mechanical response of the intervertebral discs under other complex dynamic loading environment.

Viscoelastic finite element analysis of the cervical intervertebral discs in conjunction with a multi-body dynamic model of the human head and neck

This article presents the effects of the frontal and rear-end impact loadings on the cervical spine components by using a multi-body dynamic model of the head and neck, and a viscoelastic finite element (FE) model of the six cervical intervertebral discs. A three-dimensional multi-body model of the human head and neck is used to simulate 15 g frontal and 8.5 g rear-end impacts. The load history at each intervertebral joint from the predictions of the multi-body model is used as dynamic loading boundary conditions for the FE model of the intervertebral discs. The results from the multi-body model simulations, such as the intervertebral disc loadings in the form of compressive, tensile, and shear forces and moments, and from the FE analysis such as the von Mises stresses in the intervertebral discs are analysed. This study shows that the proposed approach that uses dynamic loading conditions from the multi-body model as input to the FE model has the potential to investigate the kinetics and the kinematics of the cervical spine and its components together with the biomechanical response of the intervertebral discs under the complex dynamic loading history.

A computational model of the human head and neck system for the analysis of whiplash motion

This paper presents the development and validation of a three-dimensional multi-body model of the human head and neck for the study of whiplash motion. The model is composed of cervical spine vertebrae, intervertebral discs, ligaments, and muscles, and has been validated against experimental data for small and large static loading conditions. The resulting main and coupled displacements of the individual motion segments have been shown to be accurate and the moment generating capacity of the neck muscle elements to be realistic. The model has been used for the dynamic simulation of impacts in frontal, lateral and rear-end directions. For rear-end impacts the characteristics of ‘whiplash’ motion have been accurately reproduced in terms of head and vertebral kinematics. The model results with active musculature suggest that, for rear-end impact, the influence of active muscle response is unable to significantly alter the head and neck kinematics of an initially unaware occupant but will affect the forces developed in the cervical soft-tissues.

A Study of Standards for Child Restraint System Sled Tests

A method is developed for finding the best and worst possible responses of a child dummy in a child seat sled test where the sled deceleration pulse must follow a prescribed corridor. Constrained optimization techniques are applied to a two-degree-of-freedom lumped mass model of the sled test to determine the best and worst sled deceleration pulses, within the prescribed corridor, that produce the minimum and maximum child chest decelerations. A three-dimensional multi-body model is used to predict the values of the peak child chest g's in sled tests with the best and worst sled deceleration pulses. The results are useful as a measure of the variability of child dummy response that can be expected for a prescribed sled deceleration corridor. The standards for child seat safety testing can be evaluated and compared quantitatively using this sensitivity information. Results indicate that some prescribed sled deceleration corridors are too wide, allowing extreme variations in occupant responses, and some are too narrow, or perhaps unnecessarily complex.