Multibody Research Articles

Multibody Dynamics Modeling of a Continuous Rubber Track System. Part 2—Experimental Evaluation of Load Prediction

<div>Vehicles equipped with rubber track systems feature a high level of performance but are challenging to design due to the complex components involved and the large number of degrees of freedom, thus raising the need to develop validated numerical simulation tools.</div> <div>In this article, a multibody dynamics (MBD) model of a continuous rubber track system developed in Part 1 is compared with extensive experimental data to evaluate the model accuracy over a wide range of operating conditions (tractor speed and rear axle load). The experiment consists of crossing an instrumented bump-shaped obstacle with a tractor equipped with a pair of rubber track systems on the rear axle. Experimental responses are synchronized with simulation results using a cross-correlation approach.</div> <div>The vertical and longitudinal maximum forces predicted by the model, respectively, show average relative errors of 34% and 39% compared to experimental data (1–16 km/h). In both cases, the average relative error is lower for tractor speed from 1 to 7 km/h, namely 20% and 35%. The model and experimental amplitudes spectra of the force signals are compared using the coefficient of determination <i>r</i><sup>2</sup>. In the 1 to 7 km/h tractor speed range, the average vertical and longitudinal coefficients of determination are, respectively, 0.83 and 0.42. The coefficients, respectively, reduce to 0.27 and 0.14 for speeds over 7 km/h.</div> <div>In summary, the model can predict the maximum vertical and longitudinal forces in addition to the amplitude spectrum of those signals for operating conditions up to 7 km/h, regardless of the rear axle load, with accuracy acceptable for many applications, such as load case determination for preliminary structural design. Several factors affecting the accuracy of the model at higher tractor speed are identified for future work including suspension creeping, suspension compression characterization at high strain rates, and temperature dependence of material properties.</div>

Multibody Dynamics Modeling of a Continuous Rubber Track System: Part 1—Model Description

<div>Continuous rubber track systems for farming applications are typically designed using multiple iterations on full-scale physical prototypes which is costly and time consuming. The development of numerical design tools could speed up the design process and reduce development costs while improving product performance. In this article, a rigid multibody dynamics (MBD) model of a continuous rubber track system is presented. This article is the first part of a two-part study: Part 1 focuses on the model description and part 2 describes the experimental evaluation of the MBD model. The modeling methodology is based on a track discretization as a set of rigid body elements interconnected by 6 degrees-of-freedom bushing joints. The mathematical formalism and experimental characterization of all critical subsystems such as the roller wheels, tensioner, suspensions, and contact models are also presented. Several simulation results are presented to illustrate the capability of MBD models in design activities to rapidly evaluate new concepts as a result of the relative short-solving time of the model (approximately 3 h). The MBD model is shown to be a powerful design tool to provide input boundary conditions for structural analysis or as a design space explorer and optimization tool.</div>

Modeling De-Coring Tools with Coupled Multibody Simulation and Finite Element Analysis

De-coring is an essential process in the casting process chain, determining the quality and cost of production. In this study, a coupled multibody system (MBS) and finite element modeling (FEM) technique is presented to study the mechanical loads during the de-coring process. The removal of cast-in sand cores from the inner regions of the cast part by de-coring or knocking out is a complex process with dynamic loads. Currently, the process relies upon empirical knowledge and tests. Inorganic sand cores pose additional challenges in the success of the de-coring process. Increasing complexity in geometry and stringent environmental regulations compel a predictive process in the earlier stages of design. Predicting the process’ success is challenged by the dynamic non-linearities of the system. The dynamic characteristics and the interaction between hammer and casting were studied here for the first time using an industrial-based test rig, and a novel modeling approach was formulated. The results of the developed model are in good compliance with the experiments. The methodology presented in this study can be used to include a varying number of hammers and loads. The proposed approach presents the possibility to discretize the process and qualitatively assess the process parameters for optimization.

Dynamic research on winding and capturing of tensegrity flexible manipulator

With the rapid development of social intelligence, flexible manipulator has become a typical representative of the intelligent era. However, due to the strong nonlinearity brought about by the high flexibility of the flexible manipulator, as well as the nonsmooth problems it faces during operation such as cable slacking and contact, it poses challenges to its modeling and dynamic analysis. Considering the above difficulties, this article first proposes a modeling strategy for flexible manipulator based on the theory of tensegrity, which can establish a highly flexible manipulator model. Then, based on the theory of nonsmooth multibody systems, a nonsmooth mathematical formula for cable slacking and contact is established to address the nonsmooth phenomena. Finally, a variable cross-section tensegrity flexible manipulator is designed, and the dynamic characteristics of winding and capturing are analyzed. Numerical results validate the effectiveness of the proposed method.

Quantification of soft tissue artifacts using CT registration and subject-specific multibody modeling

The potential use of gait analysis for quantitative preoperative planning in total hip arthroplasty (THA) has previously been demonstrated. However, the joint kinematic data measured through this process tend to be unreliable for surgical planning due to distortions caused by soft tissue artifacts (STAs). In this study, we developed a novel motion capture framework by combining computed tomography (CT)-based postural calibration and subject-specific multibody dynamics modeling to prevent the effect of STAs in measuring hip kinematics. Three subjects with femoroacetabular impingement syndrome were recruited, and CT data for each patient were collected by attaching marker clusters near the hip. A subject-specific multibody hip joint model was developed based on reconstructed CT data. Spring–dashpot network calculations were performed to minimize the distance between the anatomical landmark and its corresponding infrared reflective marker. The STAs of the thigh was described as six degrees of freedom viscoelastic bushing elements, and their parameter values were identified via smooth orthogonal decomposition. Least squares optimization was used to modify the pelvic rotations to compensate for the rigid components of STAs. The results showed that CT-assisted motion tracking enabled the successful identification of STA influences in gait and squat positions. Furthermore, STA effects were found to alter maximal pelvis tilt and hip rotations during a squat. Compared to other techniques, such as dual fluoroscopic imaging, the adopted framework does not require additional medical imaging for patients undergoing robot-assisted THA surgery and is thus a practical way of evaluating hip joint kinematics for preoperative surgical planning.

Dynamic transfer model and applications of a penetrating projectile‐fuze multibody system

AbstractIn modern warfare, fortifications are being placed deeper underground and with increased mechanical strength, placing higher demands on the target speed of the penetrating munitions that attack them. In such practical scenarios, penetrating fuze inevitably experience extreme mechanical loads with long pulse durations and high shock strengths. Experimental results indicate that their shock accelerations can even exceed those of the projectile by several times. However, due to the unclear understanding of the dynamic transfer mechanism of the penetrating fuze system under such extreme mechanical conditions, there is still a lack of effective methods to accurately estimate and design protection against the impact loads on the penetrating fuze. This paper focuses on the dynamic response of penetrating munitions and fuzes under high impact, establishing a nonlinear dynamic transfer model for penetrating fuze systems, which can calculate the sensor overload signal of the fuze location. The results show that the relative error between the peak acceleration obtained by the proposed multibody dynamic transfer model and that obtained by experimental tests is only 15.7%, which is much lower than the 26.4% error between finite element simulations and experimental tests. The computational burden of the proposed method mainly lies in the parameter calibration process, which needs to be performed only once for a specific projectile‐fuze system. Once calibrated, the model can rapidly conduct parameter scanning simulations for the projectile mass, target plate strength, and impact velocity with an extremely low computational cost to obtain the response characteristics of the projectile‐fuze system under various operating conditions. This greatly facilitates the practical engineering design of penetrating ammunition fuze.

Enhanced modelling of planar radial-loaded deep groove ball bearings with smooth-contact formulation

AbstractBearings are mechanical components designed to restrict the relative rotary motion between moving parts and transmit loads with low friction. Their performance directly impacts the durability, efficiency and reliability of various machinery. Therefore, bearing failures can lead to economic costs, repair/stoppage times, accidents and regulatory compliance issues. In the context of Industry 4.0, the development of detailed and reliable computational models for simulating bearings’ dynamics plays a crucial role in establishing digital twins and implementing advanced predictive maintenance strategies.This work focuses on modelling radial-loaded deep groove ball bearings under the multibody systems dynamics framework and the components of the bearing (inner and outer rings, rolling elements, and cage) are treated as separate bodies. A smooth contact approach is utilised to characterise the contact/impact phenomena, providing flexibility and efficiency in monitoring the whole contact event. In this sense, suitable normal and friction contact force models are used to describe those interactions between the contacting bodies. The main contribution of this work relies on the modelling strategies to represent the cage/rolling element interaction.Having that in mind, several multibody models of radial-loaded deep groove ball bearings are developed considering different modelling assumptions, resulting in dynamic analyses with various levels of complexity. The underlying simplifications are described, and their main advantages and shortcomings are discussed. The simulation results demonstrated the significant impact of accurately selecting the modelling parameters. The promising results of this study pave the way for future investigations, extending to other geometries of rolling contact bearings and working conditions.

Effect of a rotational damper on a moored and articulated multibody offshore system in waves

Motions and loads of an articulated and moored floating platform consisting of multiple bodies in waves are investigated through numerical analysis. The wave–structure interaction (WSI) problem is solved using a high-fidelity viscous–flow solver that couples nonlinear rigid body motions, multibody interactions with an internal connection, and mooring dynamics. The study focuses on two modular floating structures (MFSs) connected by a flexible joint, with and without a rotational damper, and positioned using four symmetrical mooring lines. Multibody responses and the corresponding loads acting on the mooring lines and hinged joints are analyzed. Our results reveal that the influence of the damper on heave motions is less significant. Notably, the presence of the rotational damper has a noticeable impact on pitch motions between the two hinged MFSs. Introducing a rotational damper on the flexible joint effectively dampens the highly dynamic pitch motions while not imposing additional loads on the flexible joints.

A multidirectional pendulum kinetic energy harvester system for low-power appliances in new energy buses

Wireless sensors play a crucial role in vehicle operations. The effective energy harvesting for self-powering these sensors has emerged as a critical area of interest in recent years. This paper presents a multidirectional pendulum kinetic energy harvester system (MP-KEHS) designed to power low-power sensors in vehicles. The MP-KEHS consists of four main components: an energy capture module, a motion transfer module, an energy conversion module, and an electric energy storage module. The energy capture module, comprising a mass ball and a turntable, captures omnidirectional inertial kinetic energy during vehicle acceleration, deceleration, and turning. In the motion transfer module, a one-way gear module converts the multidirectional rotations of the energy capture module into unidirectional rotations, while the planetary gear train enables speed coupling during simultaneous vehicle acceleration and turning. The energy conversion module utilizes a generator to transform rotational kinetic energy into electric energy. The electric energy storage module stores the electric energy in a supercapacitor after passing through a voltage regulator circuit, providing power to low-power devices. Using of multi-body dynamics software and Simulink, the swing angle of the mass ball was determined under four real driving cycles. Experimental results demonstrated that the average output power of the MP-KEHS reached 116.8 mW. Charging the capacitors of 220 μF, 470 μF, and 1000 μF from 0 V to 1 V takes 8 s, 24 s, and 93 s, respectively. Finally, the MP-KEHS was applied to a bus on the Liaocheng University campus, achieving an average output power of approximately 176 mW, which satisfied the power requirements of the sensors. These findings indicate that the MP-KEHS effectively harnesses the vehicle's otherwise wasted inertial energy, enabling wireless sensor self-powering.

A transfer learning-based method for marine machinery diagnosis with small samples in noisy environments

The operating conditions of marine machinery are demanding, and their operational state significantly affects the safety of marine structures. Detecting faults is crucial for machinery health management and necessitates a highly precise diagnostic method. In this paper, we propose a fault diagnosis framework that employs transfer learning and dynamics simulation. A denoising convolutional autoencoder is used to reduce noise when monitoring vibration data in marine environments. To address the challenge of limited sample sizes in marine machinery fault data, a multibody dynamics simulation model is developed to acquire data under fault conditions. The fault features are extracted using a convolutional neural network model. Parameter transfer is applied to enhance the accuracy of fault diagnosis. The effectiveness and applicability of the framework are demonstrated through a case study of a bearing fault dataset.

Development and performance evaluation of lateral control simulation-based multi-body dynamics model for autonomous agricultural tractor

Development and performance evaluation of lateral control simulation-based multi-body dynamics model for autonomous agricultural tractor

Two-body dynamic simulations of a combined semi-submersible floating offshore wind turbine and torus wave energy converter

Dynamic responses of a combined wind and wave energy system which consist of a 5MW semi-submersible floating offshore wind turbine (FOWT) and a torus-shaped wave energy converter (WEC) are investigated. In the investigated configuration, the torus WEC is constrained to move only in the heave direction with respect to the FOWT. This results in a two-body dynamic system that allows for the extraction of wave energy through the relative heave motion. A Modelica-based multi-body system (MBS) code is used to perform fully coupled dynamic analyses of the combined system. The wind turbine loads are calculated using the state-of-the-art Blade Element Momentum (BEM) method, while the wave power take-off (PTO) system is modelled as a linear spring and a viscous damper. A case study is presented where the mass of the torus is varied to investigate the impact on the two-body dynamics of the combined system. The system performance is assessed in terms of the maximum wave power absorption and the quality of wind power production.

Development of a contact force model with a fluid damping factor for immersed collision events

Impact behavior in a fluidic environment is an inevitable phenomenon in multibody systems. This investigation studies the motion of a contact body in an unbounded and incompressible Newtonian viscous fluid. In allusion to the physical impact in immersed fluid, a dissipated coefficient is introduced to describe the dissipated energy caused by the hydrodynamic forces, including the drag force, added mass force, and history force. To attain the fluid damping factor during impact, the kinetic energy corresponding to the physical impact has four discrepant destinations at the end of the compression phase. According to this principle, a new fluid damping factor is derived based on the energy conservation during impact for simultaneously depicting the coupling between liquid and solid and the coupling between solid and solid. More importantly, to determine the coefficient of restitution (CoR) corresponding to the actual physical impact, a new CoR is proposed according to the definitions of dry and wet CoRs. Subsequently, since both compression and recovery phases happen in the presence of hydrodynamic forces, fluid damping force should be imposed on the Hertz contact model. Consequently, a new contact force model with a fluid damping factor tailored for immersed collision events is proposed. Although the viscosity of the fluid is not explicitly exhibited in the hysteresis damping loop from the new contact force model, the effect of fluid on the immersed collision cannot be neglected, especially for the initial distance of contact bodies. Finally, the rationality and correctness of the proposed model are validated by the reference solution obtained from the solitary wave propagation of a horizontal one-dimension granular chain.

Analysis of Catapult-Assisted Takeoff of Carrier-Based Aircraft Based on Finite Element Method and Multibody Dynamics Coupling Method

Catapult-assisted takeoff is the initiation of flight missions for carrier-based aircrafts. Ensuring the safety of aircrafts during catapult-assisted takeoff requires a thorough analysis of their motion characteristics. In this paper, a rigid–flexible coupling model using the Finite Element Method and Multibody Dynamics (FEM-MBD) approach is developed to simulate the aircraft catapult process. This model encompasses the aircraft frame, landing gear, carrier deck, and catapult launch system. Firstly, reasonable assumptions were made for the dynamic modeling of catapult-assisted takeoff. An enhanced plasticity algorithm that includes transverse shear effects was employed to simulate the tensioning and release processes of the holdback system. Additionally, the forces applied by the launch bar and holdback bar, nonlinear aerodynamics loads, shock absorbers, and tires were introduced. Finally, a comparative analysis was conducted to assess the influence of different launch bar angles and holdback bar fracture stain on the aircraft’s attitude and landing gear dynamics during the catapult process. The proposed rigid–flexible coupling dynamics model enables an effective analysis of the dynamic behavior throughout the entire catapult process, including both the holdback bar tensioning and release, takeoff taxing, and extension of the nose landing gear phases. The results show that higher launch bar angle increase the load and extension of the nose landing gear and cause pronounced fluctuations in the aircraft’s pitch attitude. Additionally, the holdback bar fracture strain has a significant impact on the pitch angle during the first second of the aircraft catapult process, with greater holdback bar fracture strain resulting in larger pitch angle variations.

Muscle dynamics analysis by clustered categories during jogging in patients with anterior cruciate ligament deficiency

BackgroundPatients with anterior cruciate ligament (ACL) deficiency (ACLD) tend to have altered lower extremity dynamics. Little is known about the changes in dynamic function and activation during jogging in patients with ACLD.MethodsTwenty patients with an injured ACL before ACL reconstruction (ACLD group) and nine healthy male volunteers (control group) were recruited. Each volunteer repeated the jogging experiment five times. Based on the experimental data measured, a musculoskeletal multibody dynamics model was employed to simulate the tibiofemoral joint dynamics during jogging. Eighteen muscles were used for analysis. The obtained dynamics data were used for clustering and curve difference analysis.ResultsThe 18 muscles studied were divided into 3 categories. All the quadriceps, the soleus, the gastrocnemius, and the popliteus were classified as label 1. All the hamstrings were classified as label 2, and the sartorius muscles were classified as label 3. Among them, the classification of the short head of the biceps femoris was significantly different between the two groups (P < 0.001). The force curves of all 18 muscles and the between-group differences were studied according to clustered categories. Most muscle force in label 1 was approaching zero in the terminal stance phase, which was significantly lower than that in the control group (P < 0.05). The muscle force in label 2 had areas with significant differences in the stance phase. Muscle force in label 3 was significantly lower than that in the control group in the pre-swing phase.ConclusionsThis study showed that there are various changes of muscle function and activation in patients with ACLD. Through clustering and curve analysis, the joint reactions and changes of different muscle forces in the gait cycle between the ACLD and control groups could be further clarified.

Geometric error modeling and compensation for high precision composite optical measurement systems

Composite optical measurement systems are widely used in the field of precision measurement due to their combination of inspection with high accuracy, speed, wide range, real-time, and other advantages. Whereas errors are prevalent in measurements, in order to improve detection accuracy, the systems must be compensated for geometric errors in three-dimensional space. Aiming at the complex situation of multi-probes and multi-zooms in the composite optical measurement system, the current error modelling methods are difficult to be directly applied, so this paper establishes a unified three-dimensional volumetric error model based on the theory of multi-body system and combined with the principle of geometric optics, performs the error verification through the direct measurement method, and finally realises the compensation of geometric error in the continuous space of the whole measurement range. Eventually, the accuracy of the proposed error model and the effectiveness of the error compensation method were verified by a laser interferometer and standard objects to be measured, and the integrated geometric error of the system was decreased by 76.55%, which effectively improved the accuracy of the system. The error modelling and compensation method proposed in this paper provides a new idea for the error compensation of the zoom measurement system, and at the same time, it is universal for the measurement systems of different structures and motion forms, which can be widely used in the field of precision measurement.

A general FSI framework for an effective stress analysis on composite wind turbine blades

The fluid-structure interaction (FSI) technique has been extensively used and developed in the past decades. Commonly, the reduced-order models are used in FSI analyses to assure the numerical robustness and efficiency. However, due to the increasing demand for higher numerical resolutions in modern wind turbine composite blade applications, intrinsic limitations of reduced-order models, such as their inability to account for complex aerodynamic flow interactions, multi-motion couplings, and sophisticated composite properties, have become the weaknesses in existing reduced-order FSI approaches. In this study, we propose a general FSI framework, which combines the advantages of high-fidelity Computational Fluid Dynamics (CFD) and robust Multi-Body Dynamics (MBD) methods, and detailed Finite Element Analysis (FEA) for analysing the detailed stress distributions on the composite structures. The results of predicted dynamics and the Von Mises stress on the composite blade structures under given operation condition are compared and reasonably agreed with the literature results, with a significant computational cost reduction by nearly 25% is achieved. The proposed FSI framework can be a general approach to investigate the multi-physical interactions where the composite structure specifications are involved, coupling with complex dynamic motions in three-dimensional space.

DDPG-Based Adaptive Sliding Mode Control with Extended State Observer for Multibody Robot Systems

This research introduces a robust control design for multibody robot systems, incorporating sliding mode control (SMC) for robustness against uncertainties and disturbances. SMC achieves this through directing system states toward a predefined sliding surface for finite-time stability. However, the challenge arises in selecting controller parameters, specifically the switching gain, as it depends on the upper bounds of perturbations, including nonlinearities, uncertainties, and disturbances, impacting the system. Consequently, gain selection becomes challenging when system dynamics are unknown. To address this issue, an extended state observer (ESO) is integrated with SMC, resulting in SMCESO, which treats system dynamics and disturbances as perturbations and estimates them to compensate for their effects on the system response, ensuring robust performance. To further enhance system performance, deep deterministic policy gradient (DDPG) is employed to fine-tune SMCESO, utilizing both actual and estimated states as input states for the DDPG agent and reward selection. This training process enhances both tracking and estimation performance. Furthermore, the proposed method is compared with the optimal-PID, SMC, and H∞ in the presence of external disturbances and parameter variation. MATLAB/Simulink simulations confirm that overall, the SMCESO provides robust performance, especially with parameter variations, where other controllers struggle to converge the tracking error to zero.

A unified analytical expression of the tangent stiffness matrix of holonomic constraints

While an accurate computation of the tangent stiffness matrix of multibody systems is usually of critical importance in various numerical analyses, one contribution often neglected in dynamics is represented by the tangent stiffness matrix of constraints. This term, resulting from the change of joints reactions with respect to the coordinates of the connected bodies, is indeed easily discarded for the sake of performance due to its slight effect on dynamic simulation results. On the contrary, it plays a critical role when static or eigenvalue analyses are required, especially for those cases featuring free motions. While the topic of holonomic constraint equations and their respective Jacobian matrix is not new in literature, this article aims to provide a general and unified formulation based on quaternion parametrization together with a consistent analytical expression of the tangent stiffness matrix derived through linearization. The article includes also the rheonomic contribution to holonomic constraints. The formulations presented in this work are built on a mixed-basis formulation, in use in many engineering applications, and allow to easily derive specialized versions (e.g. revolute, cylindrical, prismatic joints, etc.) from the same equation set. Examples demonstrate the doubly-positive effect of this additional stiffness term: first, static analyses are able to converge to the actual equilibrium position and second, the eigenvalues analyses proved to be more consistent. For this latter set of tests the non-linear dynamic results, observed in the frequency domain, are compared against those coming from eigenvalue analysis, in order to prove the augmented accuracy of the results.

Study on the vibration characteristics of deep groove ball bearings under time-varying loads

A general methodology for dynamic modeling and analysis of deep groove ball bearing used in the crank-slider mechanism of punching machine is presented in this paper. The time-varying loads applied at the inner ring of this bearing can be obtained by analyzing the planar multibody systems. The bearing joint has been modeled by introducing a nonlinear constraint force system, which takes into account the contact stiffness interaction between the rolling elements and the raceways. The four-degree-of-freedom dynamic equations for the inner and outer rings of the bearings is established by Newton's second law. By numerical calculation, the variations of the load, trajectory, FFT frequency domain response, and x direction phase trajectory and Poincare of the inner ring, and the contact force on each ball element are discussed. The results indicate that the present methodology can not only be used to analyze the overall dynamic behavior of crank-slider mechanism and the deep groove ball bearing used in punching machine, but also to obtain the dynamic loads of the inner ring and ball in bearing. Therefore, the dynamic loads on ball elements can provide a basis for the strength checking, fatigue life calculation and wear analysis of the deep groove ball bearing.