This study presents a computational investigation of longitudinal tire slip dynamics and their influence on vehicle motion using a parameterized tire model within an integrated four-wheel vehicle framework. Existing analytical, reduced-order, and experimental studies frequently treat the governing sub-systems in a decoupled or simplified manner, imposing load transfer quasi-statically, assuming a constant rolling radius, or computing slip from a rigid kinematic relationship. The contribution of this work is a closed, self-consistent formulation, in which four independently parameterized Magic Formula tires are dynamically coupled with the vehicle body, wheel rotational dynamics, dynamic axle load transfer, and braking dynamics, and solved simultaneously as a single differential-algebraic system. In this coupling, the instantaneous slip determines the tire force, which drives wheel rotation and longitudinal load transfer, which in turn updates the normal load and the speed- and load-dependent effective rolling radius governing the subsequent slip. The model incorporates drive torque, braking inputs, road inclination, and aerodynamic drag, and simulates a complete driving cycle consisting of acceleration, steady-state motion, and braking. Key performance parameters, including the longitudinal slip ratio of the front and rear tires, vehicle velocity, travel distance, and axle normal loads, are evaluated under varying torque inputs. The results reveal distinct slip characteristics between the front and rear wheels during transient acceleration and braking, a pronounced increase in negative slip during braking corresponding to potential wheel-lock tendencies, and a braking-phase rear-axle slip that converges to a nearly constant value independent of the initial drive torque. The coupled analysis of vehicle speed, travel distance, and dynamic load transfer further establishes the relationship between slip dynamics and vehicle kinematics. The findings provide insight into vehicle stability and the design of traction and braking control strategies, particularly for electric vehicles characterized by rapid torque delivery.
The axisymmetric vector nozzle is a critical component of aircraft engines. Its moving mechanisms exhibit hinge clearance and structural flexible deformation during manufacturing, assembly, and operation. These nonlinear factors significantly influence the nozzle's dynamic performance. This study aims to establish a high-precision rigid-flexible coupled multi-body dynamics model that comprehensively considers hinge clearance and component flexibility, revealing their mechanisms of action on nozzle motion accuracy and dynamic response. The innovation lies in employing an absolute node coordinate method, a Flores contact force model, and an improved Coulomb friction model to construct a nozzle mechanism model incorporating clearance hinges and flexible triangular tie rods. Experimental validation confirms the model's effectiveness. Simulation results indicate that hinge clearance induces lag in the expansion blade motion response, significantly reducing deflection efficiency; while component flexibility also reduces motion precision, its negative impact is less than that of clearance; flexible components can partially absorb high-frequency vibrations caused by clearance collisions, resulting in smoother velocity responses. Furthermore, the coupled effects of external loads with clearance and flexibility further increase driving resistance. This study provides important references for the dynamic design and analysis of nozzle mechanisms.
This study explores the development and characterization of palm oil-based magnetorheological fluid (MRF) behaviour and its dependency on dynamic conditions through a semi-analytical approach. Magnetorheological fluid viscosity can be rapidly adjusted by applying a magnetic field to control and modulate the damping force in various mechanical systems. The effectiveness of the prepared magnetorheological fluid was analysed through experimental rheological characterization, and the obtained properties were incorporated into a semi-analytical rotor dynamic model to evaluate vibration attenuation. The rheological behaviour of the magnetorheological fluid was tested under varying currents supplied to the magnetorheological damper from 0 to 1 A. Magnetorheological fluid exhibited shear-thinning behaviour with increasing shear rate and current. The storage modulus and the loss modulus both increased with frequency and current increment, which enhances the material's viscoelastic properties at higher current. Yield stress tests showed a significant rise in yield force with increasing current, from 65 N at 0 A to 586 N at 0.9 A, due to the alignment of magnetic particles enhancing resistance to fluid movement. The vibration amplitude of the rotor system was attenuated from 12.82 to 2 mm with the increase of the current supply to the magnetorheological damper. This study is helpful to those applications where adjustable viscosity and stress are controlled through a magnetic field for vibration attenuation of the rotor dynamic system.
This work uses Cross-Williamson fluid model to investigate hemodynamics in a trapezoidally stenosed artery. Cross-Williamson fluid model, which explains rheological behavior of blood, captures its shear-thinning and time-dependent properties quite well. For accurate hemodynamic modeling, these features are crucial, especially in arterial disorders like stenosis. Investigating the effects of two significant rheological parameters, power index and relaxation time, on the velocity, pressure, shear rate, heat flux, Reynold number and temperature profiles within stenosed artery is the aim of study. Understanding how these characteristics affect heat transfer and hemodynamic forces is intended to shed light on potential outcomes for cardiovascular disorders. The momentum, energy, and continuity equations are among the mathematical formulas that are constructed. Weak formulation of these equations is produced using the finite element method (FEM) for the mathematical solution. The FEM provides a robust foundation for handling complex geometries and boundary conditions. According to the study, the model significantly alters the various temperature, pressure, and velocity profiles under different conditions. Shear-thinning behavior resulted in higher velocities and decreased wall pressure in the stenotic area. Furthermore, the trapezoidal form emphasizes the impact of non-Newtonian behavior on hemodynamics. These findings expand our knowledge and help to develop better diagnostic strategies.
The dynamic behavior of heavy vehicles is significantly influenced by suspension design, which governs both ride comfort and road-holding characteristics. Conventional passive suspension systems exhibit inherent limitations in isolating the vehicle from road-induced vibrations, especially under high-speed operating conditions. To address this issue, the present study developed a comprehensive bond-graph-based dynamic model of a semi-active suspension system integrated with a magnetorheological damper. The model is experimentally validated using a quarter-car test rig, capturing the nonlinear hysteretic response of the magnetorheological damper through a modified Bouc–Wen formulation. Simulation results are compared with the measured data to confirm model accuracy across varying excitation frequencies and input currents. Subsequently, the response surface methodology is applied to determine the optimal configuration of suspension parameters, namely spring stiffness, damper current, tire stiffness, and tire pressure, to achieve enhanced ride comfort and road-holding. An optimized ride comfort value of 0.679545 m/s 2 and an optimized road holding value of 21.81 mm were obtained with a corresponding desirability value of 0.785. The proposed methodology effectively integrates analytical modeling, experimental validation, and optimization to evaluate and enhance the performance of heavy vehicle suspension systems.
This study presents a comprehensive three-dimensional (3D) analysis of wire-rope mechanisms in crane systems, with a particular focus on mobile harbor cranes during luffing, slewing, and hoisting operations. The developed model incorporates bending and transverse vibrations of wire ropes, while accounting for variations in wire-rope length during complex 3D movements. Additionally, a real-time interactive simulation framework is introduced, enabling precise and stable real-time modeling of crane dynamics. This framework integrates a joystick-based control system, allowing users to control virtually crane operations. The accuracy of the real-time interactive simulation is validated against offline simulations. Moreover, the system dynamics are further verified through theoretical analysis. The developed model offers some insights into payload behavior during combined crane operations, addressing potential oscillations caused by the elasticity of the wire ropes and the rigid-body motion of the payload. Furthermore, the mathematical model developed in this study can be used to predict the payload’s motion trajectory, which helps in preventing system failures and damage during complex and heavy-load operations. The proposed framework is applicable across the entire lifecycle of crane systems, from the initial design phase to the final stages of motion control in various transport applications.
This article provides a review of the state-of-the-art techniques for collision detection in multibody dynamics, highlighting the unique requirements and constraints of engineering simulations. Specifically, the article compares the most popular narrow-phase algorithms which are widely used for distance computation and intersection testing between convex shapes. Additionally, broad-phase algorithms are examined in detail, emphasizing their role in reducing computational complexity during pairwise collision checks. Part of the article is dedicated to the collision detection of concave shapes, frequently encountered in multibody dynamics where geometries are often imported from CAD tools as highly detailed and complex models. Furthermore, the article identifies several open problems in the field, such as the need for scalable algorithms capable of handling large-scale systems with high degrees of freedom, handling of deformable bodies, better integration with modern CAD workflows and GPU computing.
With the continuous increase in the size and flexibility of wind turbine blades, conventional fatigue testing methods are facing severe challenges. Although some studies have proposed using a planar 5R parallel mechanism as an alternative loading system, most of the existing work has focused on the mechanism itself without adequately considering the coupling interaction between the blade and the mechanism. To address this gap, the blade is simplified in this study as a two-degree-of-freedom spring-mass-damper system, and the kinematic equations and workspace of the mechanism are derived. On this basis, a coupled blade-mechanism dynamic model is developed using the Lagrangian formulation. Finally, simulations are conducted under flapwise, edgewise, and biaxial loading conditions. The results reveal that, when blade effects are included, the torque and power demands of the driving joints increase significantly. The novelty of this work lies in incorporating blade characteristics into the dynamic analysis of the 5R parallel mechanism, thereby uncovering the critical influence of blade effects on mechanism performance. This research provides a theoretical foundation for advancing wind turbine blade fatigue testing equipment.
This study investigates the impact of interchanging the shaft-bearing roles between the crank and the connecting rod on the dynamics of a planar four-bar mechanism containing a revolute joint with clearance. Two configurations are compared with identical geometry, material and clearance: (i) crank as shaft and (ii) crank as bearing. First, the study establishes a theoretical framework that details how both cases behave differently. Afterward, high-fidelity simulations in MSC Adams are used to quantify mean/RMS/peak accelerations, normal contact forces, flight time, and contact area probability over 100 to 2000 RPM. The results indicate a significant dependence on the configuration. Case 1 exhibits higher peaks and longer flight intervals, while case 2 produces more localised contact and concentrated wear. An experimental setup was used to validate acceleration trends at 100 and 130 RPM. The findings of this study have significant implications for applications that require high accuracy and provide useful information on vibration analysis for clearance joints mechanisms. Although fundamental mechanical design norms establish baseline joint configurations, this study provides a complementary quantitative framework demonstrating how the assignment of the motion-applying versus motion-receiving body alters penetration depth, contact pressure, dynamic response and wear progression.
This study investigates the stability characteristics of a lemon bore hydrodynamic journal bearing utilizing micropolar fluid lubrication. This study examines the influence of micropolar parameters on the dynamic stability of the bearing system via nonlinear transient analysis. The Reynolds equation, adapted to incorporate micropolar fluid theory, is solved numerically through the finite difference method utilizing the Successive Over-Relaxation technique alongside Swift-Stieber boundary conditions. The static and dynamic performance characteristics are evaluated computationally and validated with published results. The stability parameters, such as critical mass, threshold speed, and whirl frequency ratio, are computed for both Newtonian and micropolar lubricants to evaluate the impact of microstructural fluid characteristics. The trajectories of journal centres are determined by solving the nonlinear equations of motion using the fourth-order Runge-Kutta method, which facilitates a precise assessment of the system's stability margin. The findings demonstrate that the inclusion of micro-polar effects significantly improves the stability margin of the journal bearing, especially in high load scenarios. Increased eccentricity results in a higher coupling number (N2) and a reduced characteristic length (l(m)), which enhance micropolar effects, thereby improving damping and expediting the convergence of journal trajectories to equilibrium.
Ball bearings are vital elements in rotary machinery, and their premature failure can cause severe operational disruptions and unplanned downtime. The present work proposes a dual-model framework for simulating and analysing bearing faults to support the predictive maintenance strategies. The first model is a physics-based seven degrees of freedom model developed in MATLAB-SIMULINK environment, and the second is a detailed multibody dynamics model built in MSC ADAMS, providing a physically grounded, high-fidelity counterpart to the physics-based model. Both models are deliberately seeded with the most frequently encountered bearing faults, allowing for comprehensive virtual testing. To validate the simulation results, controlled experiments are conducted using a machine-fault simulator. The results of both models are analysed qualitatively in time, frequency and time-frequency domains. To quantify similarity between the models and experiments, the Pearson correlation coefficients for the envelope spectra indicate strong agreement between the MSC ADAMS multibody model and the experimental responses. However, both models successfully extract most of the fault-related symptoms, except in the ball fault case, where the MSC ADAMS model's response is more closely aligned with the experiments.
This study proposes a new analytical framework for identifying the optimal parameters of a tuned mass damper (TMD) aimed at mitigating torsional oscillations in steam turbine shafts. Improper TMD design may induce eccentric shaft rotation, which becomes particularly hazardous for high-speed shafts due to the substantial Coriolis and centrifugal forces generated during operation. These inertial forces can significantly degrade shaft performance and structural integrity. To address this issue, the present work formulates an analytical approach based on the exact solution of the equivalent frequency equation, enabling the determination of the optimal TMD parameters in closed form. Obtaining analytical expressions for these parameters is crucial, as it allows designers to configure an optimal TMD directly from the initial physical characteristics of the turbine shaft, without relying on computationally expensive numerical optimization. Numerical simulations are conducted to validate the proposed method, demonstrating that the analytically optimized TMD can effectively eliminate torsional oscillations in steam turbine shafts.
Addressing the complexity of system-level modeling and computation in transmission systems, this paper investigates an Aerospace Three-Ring Reducer (ATRR) and proposes a coupled dynamic modeling approach basd on Component Mode Synthesis (CMS), within which Multi-Point Constraint Coupling and Automated Model-Order Reduction are incorporated to balance modeling accuracy and computational efficiency. Regarding the mechanical characteristics of the aeronautical electromechanical actuators, the whole aeronautical TRR is divided into subcomponents such as the crankshaft, the output shaft, and the internal gear disc. According to the coupling relationship between gears, output shaft and the internal gear disc are further divided into the gear meshing unit and the linkage unit. The crankshaft and linkage unit adopts beam unit theory to establish the nodal model, the output shaft adopts the combination of mass equivalence method and beam unit theory to establish the nodal model. The condensation model of internal gear disc is established based on the super unit theory. Thus, the rigid-flexible coupling dynamics model of the drive system of the ATRR was established. The model was solved: quasi-static and dynamic results were obtained, which verified that the comprehensive modeling strategy of this paper is superior to the traditional concentrated mass method. This paper provides a new method for dynamic modeling and analysis of complex gear transmission systems similar to three ring reducers and provides a high-precision and efficient model foundation for optimizing the dynamic characteristics of transmission systems.
Accurately integrating stiff ordinary differential equations (ODEs) and index-1 differential-algebraic equations that govern constrained multibody systems remains computationally demanding, especially for real-time applications. This article proposes an improved parsimonious physics-informed random-projection neural-network (PIRPNN) integrator that embeds explicit velocity- and position-correction into a single-hidden-layer random-feature framework and employs a vectorized assembly of system matrices for computation efficiency. Two illustrative examples are utilized to demonstrate the proposed algorithm and advantages. For the multibody dynamics benchmark problems examined, the improved PIRPNN demonstrates improved accuracy in terms of L2-trajectory error and energy drift, together with a notable reduction in computational cost compared with the original PIRPNN. At peculiar tolerances from 10-6 to 10-10, it also outperforms the implicit MATLAB solvers ode15s and ode23t, further lowering both trajectory error and total-energy drift. The results underscore the potential of random-projection neural integrators as lightweight, constraint-preserving integration method alternative to classical integrators or more complex learning-based approaches in real-time multibody simulation.
Although various reduced-order models (ROM) have been developed for the dynamics of multibody systems modeled based on the Absolute Nodal Coordinate Formulation (ANCF), there still remain issues concerning the efficiency of model reduction. The traditional Proper Orthogonal Decomposition (POD) method can effectively reduce the dimensionality of the ANCF dynamic equations, but it necessitates mapping the generalized nodal coordinates back to their original dimension at each time step to calculate the nonlinear terms of the elastic internal forces. This leads to limited time savings in equation solving despite the dimensionality reduction achieved by the POD method. To enhance the efficiency of equation solving using the POD method, this study proposes the POD-L model reduction approach. Firstly, we apply POD to the collected snapshot matrix and retain dominant POD modes to construct a linear basis. Next, leveraging local linearization, we approximate the system stiffness matrix as constant within a limited displacement range. And iteratively obtain the elastic internal forces using the improved local linearization method, reducing error accumulation. The computed forces are then incorporated into the dynamic equations, which are projected onto the linear basis to reduce their dimensionality. The POD-L approach not only significantly reduces the dimensionality of ANCF dynamic equations and simplifies the computation of nonlinear elastic internal forces, but also reduces the error accumulation associated with the local linearization approach. It demonstrates good accuracy in prolonged simulations. It is well suited for ANCF dynamics problems involving planar triangular element modeling. The effectiveness and accuracy of the POD-L method are validated through three numerical examples.
This article takes 6306 deep groove ball bearing as the research object, considering the influence of time-varying displacement caused by variable stiffness vibration of rolling bearing on vibration response characteristics. Firstly, the bearing roller is reduced to a nonlinear spring-damping structure based on Hertzian contact theory, and a dynamic model of the rolling bearing is created. Second, the coupling solution of the motion controlling equation is found using the Runge-Kutta approach. Finally, numerical simulation is used to examine the vibration characteristics of bearings under single fault of the rolling element and outer ring and compound fault of the rolling element and outer ring, respectively. The observed signal attests to the model's correctness that was developed in this research. The modeling signal and the experimental vibration signal agree well. In the meantime, the spectrum diagram makes the defect characteristic frequency and its frequency doubling signal quite evident. The results show that the model may be used to analyze and forecast the vibration of a deep groove ball bearing with a fault, and they also provide a theoretical framework for studying the vibration response of a compound fault involving both the rolling element and the outer raceway.
This paper proposes a dynamic model of the flexible rotor system in a centrifugal pump with the fluid excitations to investigate the vibrations caused by typical shafting faults including the shaft misalignment and impeller unbalance. The elastic deformation of the shaft and the time-varying excitations of the support bearings are considered. The effects of the shaft misalignment and impeller unbalance on the time- and frequency-domain vibrations of the system are discussed. Note that the shafting faults not only increase the amplitude of the system vibration, but also change the spectral components of the frequency-domain vibrations of the system. The shaft misalignment introduces an additional peak at the second harmonic of the system's rotating frequency. The impeller unbalance introduces some additional peaks at the second and third harmonics, respectively, in the system's rotating frequency. This research may offer some significant values for enhancing the operational reliability of centrifugal pump systems.
This research proposes DiSCNet (Dual-input Spectrogram-Scalogram Convolutional Network), a dual-input convolutional neural network (CNN) designed for robust and highly accurate bearing fault diagnosis using time-frequency representations of vibration signals. Unlike traditional single-input models, DiSCNet employs a dual-branch architecture that processes both spectrograms, derived via the short-time Fourier transform, and scalograms, computed using the continuous wavelet transform, in parallel. Each modality is passed through a pre-trained ResNet-50 backbone to extract rich 2048-dimensional deep features, which are concatenated and fed into a custom classification head consisting of fully connected layers with dropout regularization to enhance generalization. The model is trained end-to-end on matched spectrogram-scalogram image pairs generated from vibration signals acquired experimentally from a bearing test rig. Training utilizes the Adam optimizer and cross-entropy loss, resulting in a low validation loss of 0.0183. Extensive evaluation against seven state-of-the-art CNN models - AlexNet, GoogLeNet, MobileNetV3, EfficientNet-B0, DenseNet-121, ResNet-50, and ConvNeXt-Tiny - demonstrates DiSCNet's superior performance. It achieves a validation accuracy of 99.38%, with outstanding results across additional metrics: F1-score (0.9932), precision (0.9946), recall (0.9938), Matthews correlation coefficient (0.9937), and Cohen's kappa (0.9936). The results highlight the advantages of integrating spectral and wavelet-domain features into a unified deep learning framework. By effectively leveraging complementary information from both domains, DiSCNet enhances feature discriminability and class separability, making it a highly promising approach for practical industrial condition-monitoring and fault-diagnosis applications.
An accurate mathematical model serves as a fundamental analytical tool for examining the behavior response of mechanical systems. In order to investigate the kinetic behavior of a bearing-rotor-bearing coupled multibody system with localized failures, the mathematical models of flexible rotor and flexible disk based on Timoshenko beam theory and Kirchhoff plate theory are developed in this study, as well as the bearing model considering the time-varying misalignment factor. Then these components are integrated into a novel modeling framework for bearing-rotor-disk systems, which is employed for a detailed analysis of modal responses, operational mechanisms, and the effects of bearing faults and unbalance on system dynamics. The result demonstrates a pronounced coupling relation between rotor structure and rolling bearings, the rotor bending places the bearing in a persistently misaligned operational state, leading to the unavoidable generation of bearing contact angles. The maximum contact angle exceeds 10 degrees when the rotor systems are operated under heavy-load and high-speed and conditions, and the bearing clearance becomes negative, resulting in severe degradation of system stability and nonlinear characteristics. Severe shock is produced due to the bearing raceway defect, and high-frequency fluctuations in bearing contact angle are generated as a result of oscillations in radial displacement of rollers, while the minimum clearance of the bearing is lost by 32.21%, and the contact stiffness is increased by 0.249%. The vortex motions of rotor system will be induced by unbalance faults, node orbit are characterized by circular geometry, and a positive linear correlation is observed between ball-ring contact frequency and rotor working frequency.
Effective control of flexible systems is a challenge in the design and implementation of control strategies. In this study, a systematic approach in the framework of multibody dynamic modeling was developed in order to control and stabilize a flexible inverted pendulum. In this approach, the dynamic behavior of the flexible inverted pendulum was replicated by an equivalent multibody system of rigid segments with rotational spring connections. Thus, it would be possible to derive an approximate nonlinear dynamic state space model for the flexible inverted pendulum and design a model-based control system. The state space model of the equivalent system was derived using Lagrange's equations, and the control system was designed using a linear-quadratic regulator along with a Kalman filter state observer. The dynamic behavior of the flexible inverted pendulum was simulated using the Simscape tools. Results of numerical simulations signify that the designed control system can effectively control the states of the flexible inverted pendulum. Moreover, increasing the number of rigid bodies enhances the effective flexibility of the equivalent multibody system and consequently improves the control performance.
