Multibody Research Articles

Smart Design of Hip Replacement Prostheses Using Additive Manufacturing and Machine Learning Techniques

The field of additive manufacturing, particularly 3D printing, has ushered in a significant transformation in the realm of joint arthritis treatment through prosthetic surgery. This innovative technology allows for the creation of bespoke prosthetic devices that are tailored to meet the specific needs of individual patients. These devices are constructed using high-performance materials, including titanium and cobalt-chrome alloys. Nevertheless, the routine physical activities of patients, such as walking, sitting, and running, can induce wear and tear on the materials comprising these prosthetic devices, subsequently diminishing their functionality and durability. In response to this challenge, this research has endeavored to leverage novel techniques. The primary focus of this study lies in the development of an algorithm designed to optimize hip replacement procedures via the mechanical design of the prosthesis. This optimization process exploits the capabilities of machine learning algorithms, multi-body dynamics, and finite element method (FEM) simulations. The paramount innovation in this methodology is the capacity to design a prosthetic system that intricately adapts to the distinctive characteristics of each patient (weight, height, gait cycle). The primary objective of this research is to enhance the performance and longevity of prosthetic devices by improving their fatigue strength. The evaluation of load distribution on the prosthetic device, facilitated by FEM simulations, anticipates a substantial augmentation in the useful life of the prosthetic system. This research holds promise as a notable advancement in prosthetic technology, offering a more efficacious treatment option for patients suffering from joint arthritis. The aim of this research is to make meaningful contributions to the enhancement of patient quality of life and the long-term performance of prosthetic devices.

Dynamic modeling and vibration analysis of an RV reducer with defective needle roller bearings

The rotate vector (RV) reducer's needle roller bearings (NRBs) are vulnerable to wear and flaws such as fatigue spalling of the raceway material. Studying the vibration mechanism and the excitation laws of NRB failures is essential to enhancing the RV reducer's performance and comprehending its operating state. This paper presents a dynamic model of the RV reducer based on the theory of contact multibody dynamics. It integrates internal and external raceway defects and takes into account the synchronous contact interaction between NRB groups and the crankshaft and cycloidal gears, as well as the time-varying mesh stiffness in the planetary gear transmission and cycloidal pin transmission. The study demonstrates that the rolling of bearings and the meshing of internal transmission components are the primary causes of vibration in a healthy RV reducer through experimental verification and dynamic simulation analysis of the system with and without NRB failures. Both the crankshaft rotation frequency and the cycloidal gear rotation frequency affect the vibration excitation source's characteristic frequency. The vibration amplitude of the RV reducer is influenced by bearing flaws on a periodic basis. The impact of internal raceway defects is greater than that of external raceway faults, resulting in a notable rise in vibration amplitude.

Backstepping model‐free adaptive control for a class of second‐order nonlinear systems

SummaryThis paper proposes a backstepping model‐free adaptive control (BS‐MFAC) algorithm for the trajectory tracking control problem of a class of second‐order nonlinear systems. Firstly, the model‐free adaptive control (MFAC) is employed to track the virtual desired velocity. Then, based on the measured state data at the current moment, a virtual desired velocity is designed, combining MFAC with backstepping control in a clever manner. By designing a discrete form of Lyapunov function, it is proven that the system velocity error under this algorithm converges asymptotically and stably. Furthermore, a nonhomogeneous difference equation solution related to the system position is obtained through calculations. The analysis of the solution indicates that the system position output error will slide into a neighborhood around zero. This algorithm possesses advantages such as simple structure, model independence, and strong robustness. Additionally, a planar two‐link space robot arm model is constructed using the Mbdyn platform, a multibody dynamics simulation software. Trajectory tracking control of joint angles is achieved under the proposed control algorithm in this paper. The simulation outcomes unequivocally establish the efficacy of the algorithm, which adeptly exploits the pseudo partial derivatives (PPD) estimation for second‐order nonlinear systems in MFAC. The algorithm yields expedited and superior trajectory tracking control of said systems.

Bidirectional vibration control for fully-coupled floating offshore wind turbines

The vast and stable wind resources present in deep waters have made deep-sea floating wind power the mainstream trend for future development. However, the operating environment of offshore floating wind turbines is complex and variable. The joint action of wind and waves causes significant platform motion and turbine vibration, reducing power generation efficiency, causing structural damage, and shortening the service life of turbines. Hence, this study focuses on the NREL 5 MW DeepCwind semi-submersible wind turbine and establishes a fully-coupled floating wind turbine model utilizing the SIMPACK multi-body dynamics software. The model includes aero-, hydro-, flexible body structure, mooring, control, and transmission chain components. 3D pendulum tuned mass dampers (3D-PTMD) and bilinear tuned mass dampers (2TMDs) are designed to control the bidirectional vibration causes due to wind-wave misalignment in the platform motion and nacelle displacement of the floating wind turbine. The research results show that: For the roll and pitch of the platform, there is only one platform roll or pitch main frequency, and the amplitude at the main frequency can be effectively reduced by setting the frequency of 2TMDs near the main frequency, thereby suppressing the vibration of the platform; For the displacement of the nacelle, in addition to the main frequency of platform roll or pitch, there is also a secondary frequency of first-order bending of the tower, 2TMDs corresponding to the main frequency can effectively reduce the amplitude at the main frequency, and 3D-PTMD corresponding to the secondary frequency can effectively reduce the amplitude at the secondary frequency, it is better to configure 2TMDs alone than 3D-PTMD alone, and it is best to configure both at the same time.

Predicting base Engine Vibrations using Flexible Multi Body Dynamics Simulation

Predicting the vibratory response of a base engine is appealing as it can speed up the engine development cycle and cut down testing cost. However, there are concerns regarding predictability of base engine vibration simulation models due to various factors. This study attempts to investigate this predictability and gives more insights on what factors can affect it. In the presented work, the vibratory response of a base engine is predicted through a flexible Multi Body Dynamics simulation. Cylinder pressure excitation on the cylinder head and pistons, and reciprocating inertia excitation, are considered as inputs in this flexible Multi Body Dynamics simulation. Effects arising from overhead moving components and gear train, have been excluded from this study. The predicted vibratory response of the base engine at particular locations, is compared with the vibratory response as measured using accelerometers mounted at those locations, during testing. A reasonable level of correlation can be seen between simulation and testing. Measures that can be taken to improve this correlation are also discussed.

Computational Investigation of a Flexible Airframe Taxiing Over an Uneven Runway for Aircraft Vibration Testing

<div>Ground vibration testing (GVT) is an important phase of the development, or the structural modification of an aircraft program. The modes of vibration and their associated parameters extracted from the GVT are used to modify the structural model of the aircraft to make more reliable dynamics predictions to satisfy certification authorities. Due to the high cost and the extensive preparations for such tests, a new method of vibration testing called taxi vibration testing (TVT) rooted in operational modal analysis (OMA) was recently proposed and investigated by the German Institute for Aerospace Research (DLR) as alternative to conventional GVT. In this investigation, a computational framework based on fully coupled flexible multibody dynamics for TVT is presented to further investigate the applicability of the TVT to flexible airframes. The time domain decomposition (TDD) method for OMA was used to postprocess the response of the airframe during a TVT. The framework was then used to examine the impact of the taxiing speed, shock absorber damping coefficient, and bump geometry on the outcome of the computational TVT. It was found that higher taxiing speed does not necessarily mean a better quality TVT, and one must find the optimal speed using the computational framework presented herein. A higher shock absorber damping coefficient was found to increase the amplitude of the response during the TVT without significantly impacting the extracted modes and their frequencies. Also, the quality of the TVT was found to be inversely proportional to the curvature of the bump cross section. The proposed TVT computational framework is validated against the normal modal analysis technique and certain experimental data.</div>

Particle swarm optimized fuzzy proportional-integral-derivative controller-based transverse leaf spring active suspension for vibration control

The transverse leaf spring (TLS) suspensions are a promising option for van vehicles due to their high load-carrying capacity and excellent handling stability. However, its ride comfort remains a major challenge. This paper investigates and compares the effects of semi-active and active control strategies to enhance the ride comfort of TLS suspensions. Firstly, a four-degree-of-freedom (4-DOF) half-car model and a multi-body dynamics (MBD) model of the TLS suspensions are established. The MBD model has higher accuracy and can describe the medium and high frequency characteristics of the TLS suspensions, such as the suspension offset frequency and the frequency response function of the body vertical acceleration (BVA). Therefore, based on the MBD half-car model with TLS suspensions, this paper proposes an optimal fuzzy PID active control strategy considering the left and right suspension coupling. The optimization objectives are the BVA, the left and right suspensions dynamic deflection, and the left and right wheels dynamic displacement. The integral absolute error is used as the evaluation criterion. The left and right fuzzy PID controllers’ parameters are obtained through particle swarm optimization. Simulation results demonstrate that the particle swarm optimization fuzzy PID active control strategy effectively controls the low-frequency vibration of the TLS suspensions and suppresses the medium- and high-frequency vibration characteristics compared with the traditional skyhook semi-active control strategy. This technology provides a reference for improving the ride comfort of the TLS suspensions.

Design and experiment of a shovel-tooth removal end-effector for abnormal plants in hybrid rape breeding based on MBD-DEM coupling.

In view of the problem that removing abnormal plants in breeding rape requires a large amount of labor and is inefficient, combined with the planting requirements of breeding rape, a shovel-tooth end-effector was designed, and a shovel-tooth removal test bench was built. A simulation model based on MBD (Multibody Dynamics)-DEM (Discrete Element Method) coupling was constructed. Then we conducted a Box-Behnken test with four factors and three levels. Taking the angle of soil penetration, speed of soil penetration, depth of soil penetration and speed of shovel-tooth gathering as the test factors, the soil penetration force and shovel-tooth gathering force as the test indicators. The mathematical regression model between test indicators and test factor was established. After optimizing the parameters of the model, the best combination of parameters with low soil penetration force and low shovel-tooth gathering force was obtained: angle of soil penetration of 84°, speed of soil penetration of 9 cm/s, depth of soil penetration of 8cm, and speed of shovel-tooth gathering of 6 cm/s. The simulation model was validated by field experiments. The average soil penetration force and average shovel-tooth gathering force of the three groups of pull-out tests were 34.8 N and 763.0 N, respectively. The removal rates were 96%, 92%, and 94%, all greater than 90%, indicating that the removal effect of the shovel-tooth end-effector was good, and the parameters were reasonably designed. The results can serve as reference for the design of rape abnormal plants removal device and the operation of MBD-DEM coupling simulation end-effector.

Modeling cable-pulley deployment systems of transformable rod structures

The aim of this article is to develop a simplified method for modeling cable-pulley deployment systems of rod structures based on the calculation of cable tensions and nodal driving forces with account for friction and other features of the system. Methods of theoretical mechanics, multibody dynamics, numerical integration of differential equations, and computer modeling were used during the research. The task of developing a simplified approach to modeling cable-pulley deployment systems for rod structures is considered. It is proposed to determine nodal driving forces by calculating cable tensions with account for friction and other features of the cable-pulley system, cables, and pulleys. To develop a model of cable-pulley deployment system, a rod system was chosen as the research object, which represents two sections of the transformable support truss of a reflector. Each section consists of diagonal and horizontal rods with tubular cross-sections. The sections are interconnected by hinge units. The structure is deployed using an upper and a lower cable, which pass through pulleys and are tensioned by an electric motor. The deploying forces are implemented by transferring the cable tension forces to the structure due to static friction and pressure between the cables and the pulleys. For further implementation of the model in an open-source software package, some simplifications were made due to the complexity of the design. A simplified method was developed for nodal driving force calculation in simulating rod structure deployment with the help of cables. The tensions, elongations, slacks, and neutral length of the cables and the forces transmitted from the cables to the pulleys were calculated as a function of time. Using them, the deployment of a rod structure was simulated for a constant cable speed. The results make it possible to control the rod system deployment time and rate depending on the characteristics and tension forces of the cables. The proposed approach is implemented using open-source software, and it provides modeling flexibility and reduces the model development and run time.

Investigation on Aerodynamic Fluid–Structure Coupling Vibration of 160 km/h EMU Tail in Single-Track Tunnels

Recently, the phenomenon of tail-sustained swaying of the 160[Formula: see text]km/h EMU in single-track tunnels has gained much attention, especially for the rear-powered vehicle. This phenomenon is investigated from the perspective of aerodynamic fluid–structure coupling vibration in this study. The aerodynamics simulation model of the train in tunnels and the multi-body dynamics model of the rear-powered vehicle were respectively established through the software of XFlow and Simpack, and then the fluid–structure coupling vibration was simulated by using real-time data dynamic exchange between the two models. Moreover, the carbody’s vibration acceleration and the aerodynamic loads acting on the carbody under various wheel–rail contact geometrical conditions were discussed. Finally, the train tail swaying in field was tested, and the dominant frequencies were analyzed. The results show that the periodic aerodynamic loads and the frequency locking effect caused by the coupled vibration are the main factors for ride comfort deterioration. The violent vibration caused by fluid–structure coupling is named vortex-induced vibration (VIV) in some industries such as bridge and submarine pipeline. For the vehicle in this work, with the decrease of equivalent conicity in wheel–rail contact, the amplitude of carbody swaying increases owing to the carbody hunting, which enhances the fluid–structure coupling vibration, and further deteriorates the ride comfort. The swaying of the carbody is dominated by the vehicle hunting frequency, and the improvement of vehicle lateral stability can weaken this phenomenon.

Receptance-based model predictive control of multibody systems with time-varying references

Receptance-based model predictive control of multibody systems with time-varying references

Analysis of lateral running of small crawler transporter on slope

The lateral climbing force of a crawler transporter is analyzed with the help of relevant theoretical formulas. Discrete element software and multi-body dynamics software were used to carry out coupling simulation for tracked vehicles, and orthogonal test was used to analyze the main and secondary factors affecting the lateral climbing of tracked vehicles. The results show that the main factors affecting the lateral climbing of tracked transporters are respectively the track gauge, the lateral deviation of the center of gravity and the vertical height of the center of gravity.

Redundant Serial Manipulator Inverse Position Kinematics and Dynamics

AbstractA redundant serial manipulator inverse position kinematic mapping is employed to define a new manipulator operational space differentiable manifold and an associated system of well posed operational space differential equations of manipulator dynamics. A review of deficiencies in the conventional generalized inverse velocity approach to manipulator redundancy resolution and a numerical example show that the conventional approach is incompatible with kinematics of redundant serial manipulators. The inverse position kinematic mapping presented is shown to define a differentiable manifold that is parameterized by either input or operational space coordinates. Differentiation of the inverse position mapping yields an inverse velocity mapping that is a total differential, in contrast with generalized inverse velocity mappings, hence avoiding the deficiencies identified. A second differentiation yields an inverse acceleration mapping that is used, without ad-hoc derivation, to obtain well posed operational space ordinary differential equations of redundant manipulator dynamics that are equivalent to the equations of multibody dynamics.

A Novel Physics-Informed Hybrid Modeling Method for Dynamic Vibration Response Simulation of Rotor–Bearing System

For rotor–bearing systems, their dynamic vibration models must be built to simulate the vibration responses that affect the safe and reliable operation of rotating machinery under different operating conditions. Single physics-based modeling methods can be used to produce sufficient but inaccurate vibration samples at the cost of computational complexity. Moreover, single data-driven modeling methods may be more accurate, employing larger numbers of measured samples and reducing computational complexity, but these methods are affected by the insufficient and imbalanced samples in engineering applications. This paper proposes a physics-informed hybrid modeling method for simulating the dynamic responses of rotor–bearing systems to vibration under different rotor speeds and bearing health statuses. Firstly, a three-dimensional model of a rolling bearing and its supporting force are introduced, and a physics-based dynamic vibration model that couples flexible rotors and rigid bearings is constructed using multibody dynamics simulation. Secondly, combining the simulation vibration data obtained using the physics-based model with measured vibration data, algorithms are designed to learn vibration generation and data mapping networks in series connection to form a physics-informed hybrid model, which can quickly and accurately output the vibration responses of a rotor–bearing system. Finally, a case study on the single-span rotor platform is provided. By comparing the signal output by the proposed physics-informed hybrid modeling method with the measured signal in the time and frequency domains, the effectiveness of proposed method under both constant- and variable-speed operating conditions are illustrated.

Assessment of influence of considering the flexibility of the front loader frame on the emerging loads in the multibody system

BACKGROUND: Dynamic models are widely used for vehicle dynamics simulation. Increase of simulation accuracy is achieved with adding flexible bodies in a model, making problem solving more complicated. Therefore, assessment of influence of considering the flexibility of the front loader frame on the emerging loads in the multibody system becomes necessary.
 AIM: Assessment of considering the flexibility of the front loader frame on the emerging loads in the multibody system becomes necessary.
 METHODS: The solution of the problem is presented with the example of a multibody model of a 14.5-ton front loader (FL) with a frame coupled with wheel movers rigidly fixed to the front half-frame and a swinging axle at the rear half-frame. This method of coupling makes it possible to assess the effect of the flexibility of the elements of the FL by comparing the vertical forces that occur in the contact patch of the wheels with the support surface. The multibody models are built in the NX Motion application of the NX 2206 software package.
 RESULTS: The comparison of vertical wheel forces in given load conditions (symmetrical and skew-symmetric) using absolutely rigid and flexible models of the frame is carried out. It is found that the forces for skew-symmetric loading modes can differ by up to 20% depending on the frame stiffness.
 CONCLUSION: As a result of the conducted research, it can be stated that taking into account the suppleness of the load-bearing system of the vehicle significantly affects the results obtained in the process of modeling.

Dynamics analysis of a rigid-flexible-liquid coupled satellite antenna system via absolute nodal coordinate formulation curvature continuity constraints

Typically, Euler and Lagrangian approaches are primarily used in fluid dynamics and multibody system (MBS) dynamics models, respectively. Absolute nodal coordinate formulation (ANCF), as a Lagrangian nonlinear finite element method (FEM), can effectively handle large deformation problems and incorporate the arbitrary Lagrange-Eulerian (ALE) method for fluids turbulence and breaking. Therefore, we have established a rigid-flexible-liquid coupled satellite antenna system dynamics model via ANCF. Navier-Stokes equations and virtual work principle are applied to formulate the fluid-structure interaction (FSI) dynamics equations. A penalty function is used to describe liquid incompressibility. Bi-directional FSI effects are solved simultaneously and brick fluid element elastic force is validated with reference experiments. Moreover, we introduce curvature continuity constraints to make the liquid free surface continuous. Results indicate that curvature continuity constraints can smoother liquid free surface and eliminate the protrusions and depressions caused by assembling brick fluid elements. Furthermore, we achieve simulation results consistent with reference experiments by using fewer elements with curvature continuity constraints. In addition, due to bi-directional FSI effects, liquid sloshing will magnify satellite antenna vibrations and simultaneously oscillate the advancing tank.

The method of virtual bench tests conducting to analyze the vehicle technical characteristics compatibility to detect and prevent the risk of resonant phenomena in the sprung cab

BACKGROUND: A relevant issue when designing vehicles with multiple levels of suspension systems is collaborative operation of these systems, which ensures the required vehicle dynamics and smoothness parameters, as well as the absence of risk for the occurrence of resonance phenomena. The vehicle cab is a dynamic system with 6 degrees of freedom, so its oscillatory motions have a complex spatial character with the oscillation energies overflow from one direction to another. The solving of problems of the sprung cab dynamics should be conducted in a spatial nonlinear formulation, which makes it possible to take into account the phenomena of redistribution of oscillation energy between the directions of space. This approach can be put into operation with simulation modeling methods through creating a spatial virtual rig of the cab with a suspension system and modeling its dynamics with the application of appropriate external inputs.
 AIM: Development of the method of using virtual tests to analyze the compatibility of technical characteristics of the cab suspension system, the frame system and the primary vehicle suspension systems to detect and prevent the risk of resonant phenomena in the cab.
 METHODS: Building a virtual test rig of a vehicle cab as a multibody dynamics system of connected bodies in space, mounted at the movable vehicle frame with spring-dampers. Virtual tests are conducted by simulation modeling methods according to the method for analyzing nonlinear phenomena when spatial resonances occur in the secondary suspension system of a vehicle cab.
 RESULTS: The method of vehicle cab virtual tests conducting for analyzing oscillatory processes occurring in the cab, including resonances, using a virtual test rig in a multibody dyamics software package.
 CONCLUSION: The developed method ensures an ability to take measures to detect and prevent the risk of spatial resonance phenomena in the vehicle cab at all stages of the components design and the cab suspension systems study.

Development and research of the model of a wheel-legged robot

BACKGROUND: The development of robots capable of moving in both walking and wheeled modes and distinguishing with a simple design from the already developed robots is a relevant task for some recent years. In order for such a robot to have scientific and commercial success, it is necessary for it to be as structurally complex, smooth, reliable and inexpensive as its wheeled equivalent and, in addition, to be able to move stably and quickly over terrain that is impassable for wheeled robots. The robot dynamics is modeled with the Universal Mechanism and the MATLAB/Simulink software packages. The results of virtual tests of the robot in main motion modes (straight-line motion, turning, step climbing) are given in the paper.
 AIM: Increasing the mobility of a wheel-legged robot, equipped with the pseudo-walking propulsion system, using reasonable control laws.
 METHODS: In order to evaluate ride performance of the studied robot, methods of numerical simulation of its motion based on the multibody dynamics software packages are used.
 RESULTS: The maximal velocity of stable straight-line motion, the turning velocity and the height of the largest climbed step were obtained for the robot with given power of engines.
 CONCLUSION: The model of the new mobile robot equipped with the simple-designed propulsion system has been developed. This model demonstrated high cross-country abilities and other mobility indicators according to the results of virtual tests.

Study on Lateral Vibration of Tail Coach for High-Speed Train under Unsteady Aerodynamic Loads

As the speed of high-speed trains increases, the vehicle’s lateral stability steadily deteriorates. There have been observations of abnormal vibrations in the tail car, particularly on certain sections of the railway line. This study built a high-speed train aerodynamic simulation model for a three-car consist, and a multibody dynamics simulation model for an eight-car consist based on numerical simulations of train aerodynamics and multibody dynamics. It investigated both steady and unsteady aerodynamic loads, flow field characteristics, and the dynamic performance of vehicles under varied aerodynamic loads at 400 km/h. The results indicate that the aerodynamic loads generated during high-speed train operation exhibit highly unsteady characteristics. Steady aerodynamic loads have a relatively minor impact on the vehicle’s dynamic performance, whereas unsteady loads exert a more significant influence. Under unsteady aerodynamic forces, the tail car experiences severe lateral vibrations. The lateral stability index, displacement, velocity, and acceleration of the tail car under unsteady conditions were measured at 2.26, 7.54 mm, and 0.53 m/s2, respectively. These values represent increases of over 17.71%, 148.84%, and 111.24%, respectively, compared to the steady loads. Large oscillation amplitudes result in more significant lateral displacements and accelerations of the vehicle. This phenomenon is a crucial factor contributing to the “tail swing” effect observed in high-speed trains. This study emphasizes the importance of considering unsteady aerodynamic effects in assessing the lateral stability of high-speed trains and highlights the significance of mitigating the adverse impacts of such dynamic responses, particularly in the tail car.

Electromechanical coupling characteristics analysis of vertical stirred mill based on ECS-MBD-DEM

This paper focuses on the start-up and steady-state operation stages of a vertical stirred mill, and the electromechanical coupling characteristics are thoroughly investigated based on the ECS-MBD-DEM coupling method. Firstly, according to the driving and working principles of the vertical stirred mill, the electrical control system (ECS) and multibody dynamics (MBD) model of the vertical stirred mill are separately established. Subsequently, a discrete element method (DEM) model is developed for the grinding media inside the mill. On this basis, the ECS-MBD-DEM coupling model of the vertical stirred mill is constructed, and its feasibility is validated through experiments. Then, the pitch, screw diameter, grinding media filling, and mill rotation speed of the helical agitator are considered as influential factors, with average value and coefficient of variation used as evaluation indicators for the level and fluctuation of changes. The load torque and current amplitude during the start-up and steady-state stages of the vertical stirred mill are analysed separately based on the ECS-MBD-DEM coupling method. The results indicate that the pitch, screw diameter, and grinding media filling have a significant effect on the average value of load torque. The screw diameter, grinding media filling, and mill rotation speed significantly influence the coefficient of variation of the load torque. The mill speed has a significant effect on the average value and coefficient of variation of the current amplitude. Finally, the cumulative volume velocity difference is proposed as an evaluation indicator for the grinding efficiency in the annular region, and the impact of influential factors on it is discussed, the results show that the grinding media filling and mill speed have a significant impact on the cumulative volume velocity difference.