Multi-body Dynamics Method Research Articles

A validated co-simulation of grab and moist iron ore cargo: Replicating the cohesive and stress-history dependent behaviour of bulk solids

The traditional design approach of grabs and other bulk handling equipment consists of manufacturing and testing physical prototypes. A novel design approach is to use a co-simulation of MultiBody Dynamics (MBD) and Discrete Element Method (DEM), in which the virtual prototype of a new concept interacts with bulk solids. Therefore, this study develops and validates a full-scale co-simulation that models the grabbing process of cohesive and stress-history dependent iron ore. First, by executing in-situ measurements during the unloading of a vessel, grab-relevant bulk properties of the cargo, such as penetration resistance, are determined. Second, full-scale grabbing experiments are conducted in the cargo hold, which allows the process to be recorded in realistic operational conditions. Third, full-scale co-simulation is set up using the material model that has been calibrated based on an elasto-plastic adhesive contact model. Fourth, the co-simulation is validated by comparing its predictions to experimental data from various aspects, such as the force in cables and the torque in winches. The validated co-simulation proves that the stress-dependent behaviour of cohesive cargo as it interacts with the grab could be captured successfully. Valuable information such as a grab’s kinematics and dynamics, as well as the porosity distribution of collected bulk solids, can be extracted from the simulation, supporting engineers to enhance the design and operation of equipment.

Semi-Analytical Sensitivity Analysis for Multibody System Dynamics Described by Differential–Algebraic Equations

A large number of deployable space structures involve multibody system dynamics, and in order to effectively analyze and optimize dynamic performance, the sensitivity information of multibody systems is often required. At present, the sensitivity analysis methods of multibody system dynamics, which have been widely used, are mainly finite difference method, direct differentiation method, and adjoint variable method. Among them, the finite difference method is an approximate method; the direct differentiation method and the adjoint variable method are analytical methods. Based on the dynamic problems of the multibody system in the form of differential–algebraic equations, the semi-analytical sensitivity analysis method for multibody system dynamics is proposed in this paper, which combines the simplicity of the finite difference method with the accuracy of the analytical methods. It includes the local semi-analytical method based on the element level and the global semi-analytical method based on the system level, of which the latter has higher computational efficiency. Through two numerical examples, the effectiveness and numerical stability of the method are verified. This method not only retains the accuracy and efficiency of the analytical methods, but also simplifies the derivation and coding of analytical formulas by combining with the existing programs. It has stronger versatility and is beneficial to the sensitivity calculation of large-scale complex multibody systems.

Two-way coupled MBD–DEM modeling and experimental validation for the dynamic response of mechanisms containing damping particles

Damping particles can be used to attenuate vibrations in mechanisms. However, damping particles and mechanical parts interact in an extremely complex manner, which affects the energy dissipation of the mechanisms. This study proposes two-way coupled models based on Multi-Body Dynamics (MBD) and Discrete Element Method (DEM) to solve granule-structure interaction problems, and uses two sets of experiments to validate the numerical model. Subsequently, the validated coupled MBD–DEM model was used to further investigate the effects of cavity size and chamber number of particle dampers on the dynamic characteristics of mechanisms. Results show that the coupled MBD–DEM simulations reasonably agree with the corresponding experiments. In the mechanism with a particle damper, under the same mass but with different cavity sizes, the effect of vibration reduction follows the sequence: 1/4 box>1/8 box>1/16 box. Under the same mass but with different chamber numbers, the degree of damping follows the sequence: single-chamber box>double-chamber box>triple-chamber box. Adding damping particles to mechanisms does not affect the vibration period, but does reduce the acceleration amplitude.

Load distribution method in helicopter blade multibody dynamics system

The paper focuses on the loads applied to the helicopter blade cross-sections in the multibody dynamics system. The main objective is to simplify the blade aerodynamics calculation and avoid time-consuming CFD methods. For this reason, the way of computing blade aerodynamics is proposed by using multibody dynamics methods with a linear-elastic blade model. As the primary tool for further research, the MCS Adams software package is selected. Splitting the main rotor blade into a finite number of sections, each having its own average value of installation and coning angles, simplifies the calculation. Afterward, expressions for the total flow velocity around the blade section and its angle of attack are obtained through vector operations. This provides a measure of aerodynamic forces acting on each section in its cross-sectional coordinate system. In conclusion, the article provides the formalized method of aerodynamic force distribution between blade sections in the multibody model as well as the correlation between the flow coordinate system and the blade chord coordinate system.

Multibody System Discrete Time Transfer Matrix Method for Nonlinear Shear Dynamic analysis of Immersed Tunnels

Shear seismic response analysis is critical for seismic design of immersed tunnels. According to the structural characters of immersed tunnels and shear dynamic response of their joints, a multibody dynamic model consisting of multi-rigid body, shear hinge, and viscous damping hinge is proposed for shear response analysis, in which the dynamic stiffness of the shear hinge is divided into two stages based on a threshold. Following the discrete time transfer matrix method for multibody system dynamics (MS-DT-TMM), the mechanical model and mathematical expression of each tunnel element is derived first and then assembled for the whole tunnel system. A solution procedure is proposed to solve the shear dynamic response of immersed tunnels using the proposed multibody system model. It is shown that the MS-DT-TMM has the same computational accuracy as the finite element method (FEM) and the modeling process is more efficient and flexible when compared to FEM. Although the MS-DT-TMM discussed herein is only applied to shear response analysis, it can easily be extended to analyze axial force and bending moment of immersed tunnels leading to a complete, rapid yet accurate enough seismic analysis of immersed tunnels suitable for engineering practices.

A Dynamic Investigation of the Impact Failure Analysis of the Friction Plate in a Planetary Transmission System

A clear understanding of both vibrations and the impact forces of planetary transmission systems is very helpful for decreasing impact failures of their friction discs and preventing serious accidents of the system. This study presents a multibody dynamic (MBD) investigation based on a commercial MBD software to predict the vibrations and impact forces of the friction disc in a planetary transmission system. In the MBD model, the radial clearance of the planet bearing is formulated, as well as the backlash between the outer gear teeth of the ring and friction disc teeth. However, the previous works in the literature only considered single radial clearance or backlash. The influences of the radial clearance of the planet bearing and backlash between the outer gear teeth of the ring and friction disc teeth on the vibrations and impact forces of the friction disc in the planetary transmission system are studied. The results give that a smaller radial clearance and backlash can be useful for decreasing both the vibrations and impact forces of the friction disc in the planetary transmission system. The MBD method can be applied to predict the vibrations and impact forces in the planetary transmission system as well.

ИССЛЕДОВАНИЕ ДИНАМИЧЕСКОЙ УСТОЙЧИВОСТИ МАШИННО-ТРАКТОРНОГО АГРЕГАТА НА ВИРТУАЛЬНОМ СТЕНДЕ

The questions of studying the dynamic stability of machine-tractor unit by the methods of multi-body dynamics (MBD) are considered. The study used a virtual stand created in CAD SolidWorks and CAE application SolidWorks Motion. It simulated the movement of the machine-tractor unit on the basis of the MTZ-82.1 tractor equipped with mounted modular implements. The motion surface has four different types of obstacles located in series in separate sections. To analyze the stages of the machine-tractor unit movement, we used the parameter of the lift height of the geometric center of each of the wheels above the supporting surface and the fact of the unit rollover. He showed that overcoming a single linear, single sequential and group linear obstacles at a speed of 3.22 m/s occurs without loss of stability. Only when overcoming a group sequential obstacle, significant fluctuations in the tractor frame are observed, however, due to the balancing suspension of the front wheels, they do not always lead to the rollover of the unit. In the future, using the developed virtual stand, it is possible to conduct studies of the dynamic stability of various configurations of the machine-tractor unit. In addition to the MTZ 82.1 tractor, models of other tractors can be used. It is also possible to change the geometry of obstacles, the angles of inclination of the supporting surface, speed mode, contact parameters, etc.

A Dynamic Model of Inertia Cone Crusher Using the Discrete Element Method and Multi-Body Dynamics Coupling

The cone crusher is an indispensable equipment in complex ore mineral processing and a variant of the cone crusher is the inertia cone crusher. A real-time dynamic model based on the multibody dynamic and discrete element method is established to analyze the performance of the inertia cone crusher. This model considers an accurate description of the mechanical motions, the nonlinear contact, and the ore material loading response. Especially the calibration of ore material simulated parameters is based on the Taguchi method for the Design of Experiments. For model verification, the industrial-scale experiment was conducted on a GYP1200 inertia cone crusher. Two different drive speeds were included in the experiments, and the testing devices were used to acquire crusher performances, for instance, displacement amplitude, power draw, product size distribution, and throughput capacity in order to accurately compare simulation results. The preliminary model can be qualitatively evaluated the flow pattern of particles and quantitatively evaluated the crushing force distribution in the concave. Furthermore, the simulation predicts the variety of crusher performances using the drive speed and the fixed cone mass as input variables. The simulation model provides novel insight regarding the improvement of linings wear period, lowering manufacturing cost, and obtaining optimal operation parameters.

In-Service Detection and Quantification of Railway Wheel Flat by the Reflective Optical Position Sensor.

Railway wheel tread flat is one of the main faults of railway wheels, which brings great harm to the safety of vehicle operation. In order to detect wheel flats dynamically and quantitatively when trains are running at high speed, a new wheel flat detection system based on the self-developed reflective optical position sensor is demonstrated in this paper. In this system, two sensors were mounted along each rail to measure the wheel-rail impact force of the entire circumference by detecting the displacement of the collimated laser spot. In order to establish a quantitative relationship between the sensor signal and the wheel flat length, a vehicle-track coupling dynamics analysis model was developed using the finite element method and multi-body dynamics method. The effects of train speed, load, wheel flat lengths, as well as the impact positions on impact forces were simulated and evaluated, and the measured data can be normalized according to the simulation results. The system was assessed through simulation and laboratory investigation, and real field tests were conducted to certify its validity and correctness. The system can determine the position of the flat wheel and can realize the quantification of the detected wheel flat, which has extensive application prospects.

Simulation of layout schemes of soil-throwing machine-tractor units based on articulated load-bearing machines

The work is devoted to the study of possible layout options for various soil-throwing machine-tractor units using the 3D-CAD SolidWorks system. In the process of research, three basic mass-produced models of wheeled traction devices were selected. This is the T-150K tractor, the DZ-122 grader and Amkodor 2661-01 forwarder. Its simplified 3D models were created, while all the basic geometric parameters were saved. At the next stage, the mass-inertial characteristics of the main moving elements were set by applying the properties of materials from standard libraries to it. These are wheels, suspension elements, linkage mechanisms of working equipment, front and rear frames. To compensate for the mass-inertial characteristics of the stationary elements located on the front and rear half-frames, spherical elements were added, with the possibility of changing the spatial position and mass. To study the possibilities of aggregation, simulation 3D models of three types of soil throwers were created: heavy mounted, mounted medium, light manipulator. Also, various types of additional tillage equipment were modeled: stripper harrows, strip cultivators. Next, ten versions of the most promising soil-throwing machine-tractor units were arranged. The coordinates of the center of gravity of the aggregates and the mass-inertial characteristics were obtained and analyzed. In the future, the developed models can be studied on static and dynamic virtual stands using the methods of multibody dynamics (MBD), for example, in the integrated environment for engineering calculations SolidWorks Motion, or exported to specialized programs, for example, MSC.ADAMS.

Frame loads accuracy assessment of semianalytical multibody dynamic simulation methods of a recreational vehicle

The design of a vehicle frame is largely dependent on the loads applied on the suspension and heavy parts mounting points. These loads can either be estimated through full analytical multibody dynamic simulations, or from semi-analytical simulations in which tire and road sub-models are not included and external vehicle loads, recorded during field testing, are used as inputs to the wheel hubs. Several semi-analytical methods exist, with various modeling architectures, yet, it is unclear how one method over another improves frame loads prediction accuracy.This study shows that a semi-analytical method that constrains the vehicle frame center of gravity movement along a recorded trajectory, using a control algorithm, leads to an accuracy within 1% for predicting frame loads, when compared to reference loads from a full analytical model. The control algorithm computes six degrees of freedom forces and moments applied at the vehicle center of gravity to closely follow the recorded vehicle trajectory. It is also shown that modeling the flexibility of the suspension arms and controlling wheel hub angular velocity both contribute in improving frame loads accuracy, while an acquisition frequency of 200 Hz appears to be sufficient to capture load dynamics for several maneuvers. Knowledge of these loads helps engineers perform appropriate dimensioning of vehicle structural components therefore ensuring their reliability under various driving conditions.

Analysis and Selection of Deployment Methods for a Wave Glider System

A wave glider is a novel unmanned marine vehicle which can convert marine energy into kinetic energy. In practice, it is crucial for the wave glider system to deploy into the ocean environment efficiently and safely. Hence, the present work establishes the wave glider motion equations to analyze the deployment method. Firstly, the wave glider model is simplified in the vertical plane and the cable model is defined as mass nodes connected with a massless spring. Then, two typical deployment methods (Method 1 and Method 2) are proposed based on the multibody dynamic method, and the numerical simulation model is established to investigate the kinematic performance of two deployment methods. Lastly, the dynamic characteristic analysis is conducted to select the determined deployment method. We explain the practical advantages of Method 1, which would provide the reference for the deployment method selection.

A comprehensive assessment of bus rollover crashes: integration of multibody dynamic and finite element simulation methods

Rollover crashes have the highest fatality rate and exhibit complex and unpredictable mechanisms in terms of vehicle-ground and vehicle-occupant interactions. The objective of this study is to evaluate the tilt table and modified dolly rollover (MDR) crash tests in terms of how these crash tests can represent those interactions and compare their results with two real-world rollover crashes. An application of combined dynamic and finite element (FE) simulations was presented to assess the cutaway bus rollover crash. First, the numerical models were validated against the experimental MDR test. Then, two real-world rollover crashes were simulated in PC-Crash to find the kinematics of the bus prior to the first vehicle-to-roof impact phase. Next, the impact phase of these real-world crashes was simulated using LS-DYNA and the results were compared with the two rollover crash tests. The FE simulations were conducted using a 2-point belted 50th Hybrid III FE model. The results of this study indicate that the common impact mechanism among these rollover scenarios was the impact between the bus’s roof corner (roof connection to the sidewall) and ground which caused lateral deformation patterns. Furthermore, unlike passenger cars where the vertical roof deformation can cause severe injuries in rollover crashes, the intrusion of the bus’s passenger compartment was not identified as a main source of injury. In addition, the highest head, neck, and chest injury risk were predicted during the MDR simulation where the ATD was partially ejected through the side window. Lastly, possible future works and limitations were explained.

Comparative performance of granular scaling laws for lightweight grouser wheels in sand and lunar simulant

Recently developed granular scaling laws create new opportunities to evaluate particle dynamics between environment and wheel shapes. We investigate the performance of straight grousered (i.e. protrusions added to the wheel rim to better engage the soil) wheels and helical grousered wheels in both silica sand and crushed basalt lunar simulant. Mechanical power draw and velocity of the wheels are compared in both materials for performance assessment. The scaling laws are evaluated for Earth gravity experimentally and reduced gravity through coupled multi-body dynamic and discrete element method (MBD-DEM) simulations. Experimental results show general power prediction error between 20 and 35% for crushed basalt and 15–25% error for silica sand. Velocity prediction error showed high dependence on material, with silica sand error generally between 4 and 10% and crushed basalt varied between 0 and 27%. Simulation results match theoretical predictions more closely with power error under 8% and velocity error under 4% for most speeds. The experimental error was further investigated and shows a new scaling dependency on sinkage (depth which the wheel rim sinks below the terrain surface) thresholds.

A scalable computational platform for particulate Stokes suspensions

We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric ‘non-overlapping’ constraints imposed at each time-step. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to 8×104 particles with approximately 4×107 degrees of freedom on 1792 cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.

A study of the static lateral stability of a tillage machine-tractor unit on a virtual stand

The problems of studying the static lateral stability of machine-tractor units by the methods of multi-body dynamics (MBD) are considered. To create a simulation model, the virtual modeling method in CAD SolidWorks and CAE SolidWorks Motion was used. A 3d model of the MTZ-82.1 tractor was created, equipped with front and rear mounted three-point linkage. At the same time, all the basic structural elements and their geometric and mass-inertial parameters were preserved. The tractor was aggregated with front and rear mounted modular implements. To study the lateral stability, the tractor is mounted on a virtual stand consisting of a fixed base and a platform that changes the angle of inclination. Using a virtual stand, the lateral stability angles of three typical configurations of a machine-tractor unit and a tractor without attachments were obtained. For a tractor without attachments, the rollover angle was 34°, it was equipped with a single-beam rear mounted implement 36° (scheme 0 + 1), with a double-beam rear mounted implement 25° (scheme 0 + 2), with a front mounted implement and a double-beam rear mounted implement 36° (scheme 1 + 2). Verification of simulation data was carried out by comparing with experimental data obtained at a stationary stand. The difference in the values of the critical angles of lateral stability of the tractor, obtained by the results of virtual modeling and using the method of rollover the tractor on a stationary stand, is 3 … 5°.

Study driving dynamics of the machine-tractor unit on a virtual stand with obstacles

The problems of studying the dynamic stability of machine-tractor units by the methods of multi-body dynamics (MBD) are considered. To create a simulation model, the virtual modeling method in CAD SolidWorks and CAE SolidWorks Motion was used. A 3d model of the MTZ-82.1 tractor was created, equipped with front and rear mounted three-point linkage. The tractor was aggregated with modular implements. To test the machine-tractor unit, a test track was simulated, consisting of four sections with various non-movable obstacles: single linear; single sequential; group linear; group sequential. In the process of modeling, the following parameters were recorded: lifting height of the geometric center of the wheels; displacement of the machine-tractor unit center of gravity in the transverse direction; linear speed. An analysis stages movement of the machinetractor unit showed that overcoming a single linear, single sequential and group linear obstacles at a speed of 0.9 m/s occurs without loss of stability. Only when overcoming a group sequential obstacle, significant oscillations in the tractor frame are observed, however, due to the balancing suspension of the front wheels, they do not always lead to the rollover of the tractor. In the future, using the developed virtual stand, it is possible to carry out studies of the dynamic stability of various configurations of a machine-tractor unit. It is also possible to change the geometry of obstacles, the angles of inclination of the support surface, the speeds of motion, the contact parameters of the wheels, etc.

Formation of the law of steering angle control to maintain a trajectory of the vehicle movement

The object of the study is a control system for changing and maintaining the trajectory of the vehicle. Methods of maintaining a trajectory of the vehicle are the subject of research. Multi-body dynamics (MBD) methods are used to solve this problem. The purpose of the study is development of management model change the trajectory of the vehicle. On the example of a two-axle four-wheel drive truck, a mathematical model of the vehicle includes subsystems-transmission, springing system and steering. The study of the influence of the transmission and suspension to change the trajectory of the car is not considered. The paper deals with the formation of the steering angle control law to maintain a given trajectory. A detailed description of the developed control model and analytical dependencies for setting the parameters of the model. An example of selection of coefficients for its setting is shown, recommendations for other types of calculation modes are offered. In this paper, the calculation of one calculation case corresponding to the rearrangement of the car, followed by a return to the original lane. This example proves the adequacy of the model. The developed mathematical model can be used in the systems of calculation of solid body dynamos in the simulation of driver-driven cars, unmanned vehicles and adaptive driver assistance systems. The vehicle was described as a system of solid bodies connected by hinges and force interactions from the library of typical elements of the software package. According to this description of the system, the software package automatically formed a system of equations of motion and connections. The equations were solved using an implicit numerical method with variable pitch and automatic accuracy control.

The Aero-elastic-wake Coupling Behavior for a Two-wind-turbines Case with Power Control Process

This study focuses on the aero-elastic-wake coupling behavior of wind turbines. A newly developed code called FALM (Flexible Actuator Line Model), which combines the wake simulation ability of the actuator line mothed (ALM) and the structural simulation ability of the flexible multibody dynamics method, was employed to achieve these simulations. The power output and thrust, the natural frequency and deformation and the wake characteristics of a single NREL 5MW wind turbine were studied to validate this code. It shows that nonlinear effects such as spin softening and stress stiffening were fully considered by FALM and it can also guarantee a reliable prediction of power and thrust of wind turbines. Furthermore, a case of two-wind-turbines with the inlet wind speed of 14m/s (exceeding the rated wind speed) were carried out to study the aero-elastic-wake coupling behavior in a wind farm. It shows that FALM is able to simulate multiple wind turbines with power control system involved. The pitch control process of the upstream wind turbine was predicted and the dynamic loads of the downstream wind turbine caused by the wake effect were studied. These results will contribute to the study of reducing the fatigue load caused by wake effect.

State-of-the-art and challenges of railway and road vehicle dynamics with multibody dynamics approaches

A review of the current use of multibody dynamics methods in the analysis of the dynamics of vehicles is given. Railway vehicle dynamics as well as road vehicle dynamics are considered, where for the latter the dynamics of cars and trucks and the dynamics of single-track vehicles, in particular motorcycles and bicycles, are reviewed. Commonalities and differences are shown, and open questions and challenges are given as directions for further research in this field.