Coupling Dynamic Model Research Articles

Real-time wheel-rail adhesion anti-skid control model for high-speed articulated trains on long downhill slopes during braking

To improve the braking efficiency of articulated trains on long-steep downhill gradients under different wheel-rail adhesion levels, this paper develops a real-time train braking control system equipped with an optimal adhesion anti-slip controller. Simulation validation is conducted under both dry and wet wheel-rail contact conditions with different braking torques applied on a steep downhill slope. The anti-slip adhesion control system comprises two modules: an adhesion optimization module using a forgetting factor recursive least squares (FFRLS) method to determine creep force function slopes for enhancing wheel-rail adhesion utilization, and a controller employing a neural network with a Levenberg–Marquardt (L-M) algorithm. Through the co-simulation of the train-track coupling dynamic model and the anti-skid control system, the real-time adjustment of the braking torque of the train can be quickly corrected. The results indicate that the anti-skid control system demonstrates excellent self-adjustment capabilities under various operating conditions. It effectively controls wheel slip, achieving optimal wheel-rail adhesion. This ensures the shortest possible braking distance while maintaining train stability and improving train transmission efficiency.

Surrogate modeling of pantograph-catenary system interactions

The smooth interaction between the pantograph and the catenary is crucial for the operational safety of railway vehicles. Coupled dynamic models of the pantograph–catenary system (PCS) constructed based on physical principles are important tools for analyzing their interactions; however, these models rely on accurate system parameters (such as stiffness, damping, and mass). Under actual operating conditions, the system parameters of the PCS exhibit time-varying characteristics and are difficult to measure, making it challenging for dynamic models to accurately represent the system’s behavior. Data-driven intelligent algorithms, with powerful feature extraction and nonlinear fitting capabilities, provide new approaches for solving system response prediction and state identification problems of the PCS. However, excessive reliance on large amounts of data for training may lead to poor generalization ability and pose challenges to model robustness, such as sensitivity to input noise or outliers. To address these issues, this paper proposes a surrogate model for the interaction of the PCS by integrating physical information with deep neural networks. The model introduces a novel neural operator that combines Transformers and convolutions (Convs), capable of capturing complex mapping relationships among various parameters within the dynamic model of the PCS in the frequency domain. A residual network incorporating physical information is designed to simulate the intricate correlations among system parameters. Additionally, a dynamic weighting balance algorithm is proposed to adjust the losses of different physical equations dynamically, ensuring the balance of physical information during training. The proposed model effectively performs response prediction and state identification of the PCS. It demonstrates excellent performance on both simulation and real-world data, providing new insights and methodologies for studying PCS interactions.

Influence of the driving environment on the dynamic characteristics of a DCT vehicle starting considering the longitudinal and vertical coupling model

The most significant external excitation affecting the dynamic characteristics of a vehicle is its driving environment. This type of excitation leads to issues such as slow initial response during starting, significant vibrations in the transmission system, and overall performance instability. A longitudinal–vertical coupled dynamics model has been developed to analyse the impact of driving conditions on the dynamic characteristics of vehicles with Dual-Clutch Transmission (DCT) during starting. This model takes into account factors such as the engine’s harmonic torque, the time-varying meshing stiffness of the gear system, the nonlinear torsional behaviour of the dual-mass flywheel, the deformation and torsion of the powertrain mounts, tire deformation, and random road excitations. Utilizing the established coupled model for DCT vehicle transmission systems, the impact of varying road roughness, adhesion coefficients, and road slope on the dynamic performance of DCT vehicles. To verify the accuracy of the simulation results of the influence of the driving environment on the dynamic characteristics of the DCT vehicle starting process, the experimental and simulation results of the influence of the driving environment on the vehicle dynamic characteristics of flat road surfaces, B-level uneven road surfaces, wet road surfaces, and 10% road slopes were compared. The overall trend of the simulation results of the clutch master and slave end speeds, vehicle longitudinal and vertical impact degrees, etc., was in good agreement with the experimental results, confirming the accuracy of the established DCT vehicle transmission system coupling dynamic model.

Dynamic simulation and adaptive heave compensation control of a wave-compensated gangway under random wave excitation

For high-precision position control of wave-compensated gangways under random wave excitation, the kinematic model is established based on the Denavit–Hartenberg parametric method. Desired motion parameters for each degree of freedom (DOF) are solved through multi-DOF motion decoupling calculations. The telescopic arm, pitching arm, and slewing seat are simplified as mechanical-hydraulic motor-driven systems or cylinder-driven systems. The nonlinear dynamic models for each system are deduced based on their structural composition and adaptive motion controllers are designed with the desired motion parameters as control targets. The gangway base's heave motion under random wave excitation is reconstructed and the electromechanical-hydraulic coupling dynamic model of the wave-compensated gangway under random wave excitation is coupled. Comparative testing with the traditional Proportional-Integral-Derivative control method shows that the displacement stabilization accuracy of the telescopic arm's tip in the x-axis and y-axis directions under the condition of scale 4 wave improved by 93.05% and 97.38%, respectively. This research provides a technical reference and reliable approach for dynamic analysis and high-precision control of wave-compensated gangways.

Design and modeling of three-mode nonlinear hybrid piezoelectric-electromagnetic vibration energy harvester for harvesting multi-band vibration energy on the freight wagon axle box

Abstract With the rapid development of rail transit system, it is becoming more demanding for structural health monitoring (SHM) of the train. It is crucial to supply power for sensing devices on the freight wagon to ensure the safe operation of rail transit systems. Three-mode nonlinear hybrid piezoelectric-electromagnetic vibration energy harvester (TNHVEH) with a three-layer pickup system has been designed and applied to efficiently harvest vibration energy on the axle box of freight wagons for providing the power of the sensors for online SHM. Dynamic coupling model of the vehicle-harvester system is built to devote the relationship between the operation bandwidth and the nonlinear degree of TNHVEH for broadening the operation frequency band. Simulation and experimental results demonstrate that the resonant frequencies of the three pickup systems of TNHVEH are concentrated around 27, 70, and 120 Hz, matching the representative frequencies of axle box vibrations. A maximum output voltage of 2.97 V and output power of 29.4 μW under an optimal load of 300 kΩ at 0.5 g acceleration is achieved. It successfully lights up 53 LEDs with ‘ECJTU’ patterns, providing a solution to the power supply problem of microelectronic devices on freight wagons.

Operational Adaptability Improvement of High-Speed Trains Through Multi-Objective Control on Carbody Lateral Vibration

To improve the operational adaptability of high-speed trains, a control method is proposed to mitigate carbody lateral vibration by leveraging the dynamic vibration absorption effect of multi-suspended equipment. A comprehensive analysis of five typical wheel/rail contact relationships, closely related to vehicle operational status in the long-term service, is conducted and incorporated into the established rigid-flexible coupling dynamic model. Based on the proposed improved niche genetic algorithm (INGA), an objective function, which holistically assesses the vibration of the carbody and suspended equipment, is constructed to undertake the optimization analysis. The results show that the dynamic vibration absorption effect of the suspended equipment proves effective in controlling carbody lateral vibration, thereby enhancing operational adaptability. However, the improvement in vehicle performance varies under different operating conditions, influenced by the competitive relationship between multiple control objectives. While carbody lateral vibration performance could be further improved without considering equipment vibration tolerance, such improvements are limited, indicating that it is reasonable and necessary to consider equipment vibration tolerance in the research of carbody vibration control. This study furnishes valuable insights for improving the adaptability of high-speed train operations and provides ideas for further research on carbody vibration control using the suspended equipment.

Research on the Wheel Wear and Rolling Contact Fatigue of Metro Vehicle Induced by Rail Corrugation

Rail corrugation is a common characteristic of track wear and exacerbates wheel–rail interaction and accelerates wheel wear and crack propagation. This study focuses on wheel wear and rolling contact fatigue of a metro vehicle under rail corrugation. Firstly, the characteristics of rail corrugation under service conditions are determined by statistical analysis of field data, and rail corrugation is applied to the established vehicle–track coupled dynamics model. Then, the wear index and the work of friction force as indicators of wheel wear are studied. Finally, based on the shakedown map and the criterion of maximum amplitude of shear stress, a simulation analysis of wheel rolling contact fatigue under rail corrugation is carried out. The results show that the increases in superficial fatigue index and accumulated fatigue are respectively 1.52 and 6.16 times in the wavelength range of 30 to 90 mm larger than those in the range of 90 to 210 mm. Furthermore, the cracks more easily occur 2 to 4 mm from the outer surface of wheel and expand along the wheel tread.

Thermo-electric coupling dynamic modeling and response behavior analysis of PEMEC based on heat current method

Complete analysis of the dynamic characteristics of the proton exchange membrane electrolytic cell (PEMEC) is significant for its efficient and flexible utilization. To fully reflect the dynamic process including thermo-electric interactions within PEMEC, this paper disassembles this process and simplifies it for representation through a clear diagram of dynamic power flow. On this basis, we proposed a novel combined qualitative and quantitative analytical method for the comprehensive response by defining the evaluating indexes for PEMEC's response performance. Meanwhile, we analyzed the change pattern of dynamic response behavior, response time and the influence of thermo-electric interaction under multi-scenarios, like different voltage abrupt change magnitudes, different cathode operating pressures, and different inlet water temperatures. The results show that the PEMEC has the biggest response behavior with the longest response time under the largest external voltage variation magnitude. Besides, there is the shortest response time and smallest parameters total changes after response when the cathode operating pressure is 15bar Moreover, when the inlet water temperature is 40 °C it has the characteristic of quick action time and small response magnitude. The model, analysis method, and findings in this paper provide an effective reference for the operational regulation of PEMEC's thermal and electrical parameters.

Design, dynamic modeling and testing of a novel MR damper for cable-stayed climbing robots under wind loads

To increase the adaptability of bridge construction equipment in high-altitude settings, this study examines a magnetorheological (MR) damper designed for cable-stayed climbing robots. Initially, a novel damper incorporating a spring-MR fluid combination and three magnetic circuit units is developed. A robot-cable-wind coupling dynamic model is subsequently formulated via Hamilton’s principle, based on force analysis. The simulation results indicate that the damper’s maximum output force is 204.60 N, with optimal working currents of 0.2 A (Force 4) and 0.4 A (Force 7). To verify the analysis, testing is conducted using an MR damper. The results reveal an average relative error of 4.60% for the actual output damping force. When mounted on the robot, the climbing speed range, average relative error, and maximum relative error are controlled within 0.66 mm/s, 0.78% and 2.5%, respectively. This approach allows for the rapid selection of suitable working currents and markedly enhances the climbing stability of the robot.

Dynamics modeling and simulation for satellites with optoelectronic tracking system

Abstract The optoelectronic tracking system has a strong coupling between the tracking platform and the satellite platform when rapidly capturing and precisely tracking targets. The high-precision coordinated pointing control between the two platforms is a key technology in the fields of space laser communication, debris monitoring, and astronomical observation. Firstly, a multi-level coupled dynamics model of spacecraft with two-dimensional (2D) motion platforms is derived based on the principles of momentum and angular momentum. Secondly, the coupling effects between the motion platform and the satellite platform are theoretically analyzed, highlighting the impact of platform orientation, configuration, mass properties, and motion characteristics on the coupling. Finally, a multi-level platform cooperative control strategy is proposed, and the model and control strategy are validated through mathematical simulations. The results show that the model is consistent with simulation results from ADAMS software, and the satellite attitude accuracy under the cooperative control strategy can be improved by 80%.

Cage Dynamic Analysis of Four-point Contact Ball Bearing for High-speed Railway Traction Motor

Abstract The cage, serving as a pivotal element in rolling bearings, possesses dynamic characteristics that have a direct bearing on the overall performance of the bearing. This paper caters to the requirements of dynamic and strength analysis of the four-point contact ball-bearing cage in high-speed railway traction motors. A rigid-flexible coupling dynamics model of the bearing is established on the ADAMS platform and its dynamic analysis was carried out under variable axial forces and with different guiding clearances. The results show that the variable axial force has little effect on the bearing cage stress, but has a great effect on the bearing cage motion. The guiding clearance has little effect on the stress of the cage, but it affects the displacement and speed of the cage obviously.

ANCF-based modelling of rigid-flexible coupling of helicopter flexible rotor blades

Abstract A high-precision rotor structure dynamic model applicable to a variety of helicopter blade hub structures is established considering rotor blade flexible deformation. The absolute nodal coordinate method is applied to the traditional rotor blade rigid-flexible coupling dynamics model, making the new model applicable to both fully articulated rotor blades and other advanced blade hub structures. No small-volume assumptions were made in the modelling process. Both Green’s strain expression under finite deformation and the geometrical relation of elastic deformation motion based on the absolute nodal coordinate method are used to derive the blade strain energy, kinetic energy, and the external load virtual work. The rotation angle at the articulation constraint at the root of the blade coupled with the elastic deformation degrees of freedom of the blade in three independent rigid body degrees of freedom, respectively. The rotor blade rigid-flexible coupling dynamics equations were established according to the Hamilton action principle. The time-domain simulation is carried out under a free single pendulum and fixed rotational speed/fixed torque for the established flexible blade model, which verifies the validity and high accuracy of the rigid-flexible coupling articulation model of the flexible rotor blade and the blade hub.

Design and modelling of a novel single-phase-driven piezoelectric actuator

Sandwich single-phase-driven piezoelectric actuators have attracted increasing interest owing to their simple control circuits, flexible designs, and high output forces. However, there are challenges in constructing a standing-wave driving mode for sandwich single-phase-driven rotary piezoelectric actuators and in achieving bidirectional driving as well as an integrated structural and functional design, which limit their applications. To address these issues and meet the demands of the joint drive, a novel sandwich single-phase-driven rotary piezoelectric actuator is proposed in this study. The actuator stator has a beam-ring configuration, with dual rotors effectively integrated with a preload adjustment mechanism to solve the contact-warping problem of the cantilever joint and achieve an integrated structural and functional design of the joint drive. The standing-wave rotation drive and steering functions are realized through the special design of modes and unique arrangement of the upper and lower driving teeth. To reveal the dynamic characteristics of the stator, a universal electromechanical coupling dynamic model for the torsional-bending composite vibration of sandwich piezoelectric actuators was developed for the first time using the transfer matrix method, and the correctness of the dynamic model was verified using a prototype of the proposed stator. Finally, the structural design feasibility of the proposed piezoelectric actuator was verified through performance evaluation experiments on the actuator prototype. The proposed sandwich single-phase-driven rotary piezoelectric actuator lays the technical and theoretical foundations for achieving simple, fast, efficient, and precise driving and control of robotic joints.

Study on meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification

Due to errors and tooth surface wear of herringbone gear is inevitable. And tooth surface modification is the key technology to improve gear performance. Therefore, this paper studies the influence of tooth surface uneven wear and modification on herringbone gear pair's meshing and dynamic characteristics with errors. Firstly, herringbone gear pair meshing characteristic analysis model based on discrete tooth surface is established. Secondly, herringbone gear pair bending-torsion coupling dynamic characteristic analysis model considering friction is established, and the dynamic frictional force analysis process is given. Thirdly, combined with Archard's wear theory, the tooth surface uneven wear amount is obtained. The tooth surface uneven wear amount is substituted into meshing matrix as a tooth surface deviation. Finally, the meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification are studied by using the established analysis model of meshing characteristics and dynamic characteristics. The calculation results show that without tooth surface modification, tooth surface wear will deteriorate the meshing and dynamic characteristics rapidly. However, reasonable tooth surface modification can effectively improve meshing and dynamic characteristics of gear pair, so that the gear pair can still maintain stable transmission under wear condition.

Dynamic wheel-rail interaction of a train crossing a turnout under traction/braking behaviour and research on rail wear of the turnout

In order to study the dynamic behaviour of a vehicle passing through turnouts under traction and braking conditions, as well as its influence on the wear of turnout rails, a high-speed vehicle-turnout rigid-flexible coupling dynamic model is established based on the coupling dynamic theory of vehicle and turnout, using China’s No. 18 high-speed turnout and CRH380 high-speed EMU as prototypes. The model is used to analyse wheel-rail creep characteristics, wheel-rail contact mechanics, and wheel-rail wear under traction and braking conditions. The results indicate that when a high-speed train passes through a turnout under traction or braking conditions, the longitudinal creepage of the wheel-rail will change due to the rotative speed difference generated by traction or braking. Furthermore, due to the existence of the lead curve, the longitudinal creep rate of the wheel-rail becomes even more complex when passing through the turnout in the diverging route. The calculations reveal that the traction behaviour of the train leads to a significant increase in wear at the front of the switch rail and nose rail, while the wear number of the switch rail in the heel of the frog after 6m increases significantly under braking conditions. The different impact characteristics of vehicle traction and braking conditions on turnout rail wear obtained in this study can provide guidance for optimizing and grinding the profiles of turnout rails at the throat of railway stations.

Comparative analysis of ride comfort evaluation indices of high-speed vehicles based on a vehicle-seat-human body coupled dynamics model

As high-speed vehicles become increasingly lightweight, the influence of passengers on the vehicle vibration system cannot be overlooked. In this paper, a 3D vehicle-seat-human body coupled dynamics model is established to comprehensively evaluate the ride comfort of high-speed vehicles. The model combines the passenger biomechanics with the carbody flexibility. This is often neglected in previous studies and only the carbody vibrations are considered. Applying the validated model, four types of ride comfort evaluation indices are calculated and compared at 250–400 km/h. Results show that the ride comfort of high-speed vehicles at different speeds is excellent when the carbody acceleration and Sperling indices are used. While the results are significantly different when the total equivalent weighted acceleration and annoyance rate indices based on human body vibrations are used. At full load and speed of 400 km/h, the passengers sitting near the windows at both ends of the carbody felt ‘slightly uncomfortable’ or ‘less comfortable’ with an annoyance rate of about 30%, which indicates that up to 30% of the passengers might find the vibrations intolerable. This study underscores the necessity of integrating human body vibrations and passenger subjective psychology into ride comfort assessments, which can provide theory references for the selection and optimization of evaluation indices for high-speed lightweight vehicles.

Multi-Scale Evaluation and Simulation of Livelihood Efficiency in Post-Poverty Mountainous Areas

Promoting the coordination of livelihoods at the county and farmers’ scales is essential for achieving balanced regional development and rural revitalization in post-poverty mountainous areas. Existing studies predominantly focus on farmers’ or regional livelihood capital and livelihood efficiency at a single scale, lacking research on cross-scale coordination between farmers’ and county livelihoods. Consequently, these studies fail to reveal the interactions and synergistic enhancement pathways between the two scales. This study, using the Qinba mountains in southern Shaanxi as a case, employs system dynamics to construct a coupled system dynamics model of farmers’ livelihood efficiency and county livelihood efficiency. From the perspective of livelihood capital, five regulatory modes, comprising a total of 17 scenarios, were designed and simulated. The results indicate the following data: (1) The coupling coordination degree between farmers’ livelihood efficiency and county livelihood efficiency in the Qinba mountains is 0.623, indicating a moderate level of coordination overall. However, the coupling coordination relationship requires further optimization and adjustment. Specifically, Foping exhibits a severe imbalance, while the coupling coordination degree of Shiquan, Zhashui, Baihe, Pingli, and Lan’gao is in a state of basic coordination. Additionally, 19 other counties, including Lueyang, Ningqiang, Yang, and others, exhibit moderate coordination. (2) Enhancing social or financial capital through various means typically promotes the coordinated development of farmers’ and county livelihood efficiency. On average, social capital and financial capital regulation models can increase the coupling coordination degree by 0.08 and 0.17, respectively. Additionally, strategies such as increasing fixed asset investment and regulating other capital types, including reducing arable land, also effectively improve the coupling coordination degree of farmers’ and county livelihood efficiency. This study provides a decision-making basis for improving the coordination of farmers’ and county livelihoods in post-poverty mountainous areas, thereby promoting economic development and intensive resource utilization. It assists in formulating more precise policy measures and offers a reference for sustainable development and rural revitalization in similar regions.

Dynamic characteristics and damage identification with interface damage of slabs in movable point crossing

As the operating density of China’s high-speed railway increases, the phenomenon of interlayer debonding in movable point crossing (MPC) is becoming more prevalent, which can lead to failure of the frog’s slab track. Meanwhile, vehicle impacts and interlayer debonding can exacerbate abnormal vibration of the vehicle and even lead to derailment. Therefore, based on the theory of rigid-flexible coupling dynamics, a vehicle-turnout-slab coupling dynamics model is established for the first time. In this model, the crossing rails with variable cross sections is considered and the interlayer debonding between turnout slabs is modelled by nonlinear springs. Then, the characteristics of the debonding is identified by applying a wavelet transform to the dynamic response of the vehicle. Finally, different types and sizes of debonding between the layers are considered. The results show that different debonding can lead to two types of contact, partial contact and complete voiding, which can further lead to detrimental effects on vehicle safety. And the limit of the defect size that causes the track slab to void is 1 mm. On this basis, it was found that when MPC’s slab tracks were voided, longer debonding can cause high frequency vibration acceleration of approximately 700 Hz in the vehicle axle box. The new insights obtained by this study could provide guidance for the maintenance period and avoid the development of the damage. This study not only obtained a mechanism for the effect of interlayer debonding on the dynamic response of the vehicle-track system, but also provides a theoretical basis of detecting interlayer debonding for future study.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

Multi-Scenario Simulation of Land Use and Assessment of Carbon Stocks in Terrestrial Ecosystems Based on SD-PLUS-InVEST Coupled Modeling in Nanjing City

In the context of achieving the goal of carbon neutrality, exploring the changes in land demand and ecological carbon stocks under future scenarios at the urban level is important for optimizing regional ecosystem services and developing a land-use structure consistent with sustainable development strategies. We propose a framework of a coupled system dynamics (SD) model, patch generation land-use simulation (PLUS) model, and integrated valuation of ecosystem services and trade-offs (InVEST) model to dynamically simulate the spatial and temporal changes of land use and land-cover change (LUCC) and ecosystem carbon stocks under the NDS (natural development scenario), EPS (ecological protection scenario), RES (rapid expansion scenario), and HDS (high-quality development scenario) in Nanjing from 2020 to 2040. From 2005 to 2020, the expansion rate of construction land in Nanjing reached 50.76%, a large amount of ecological land shifted to construction land, and the ecological carbon stock declined dramatically. Compared with 2020, the ecosystem carbon stocks of the EPS and HDS increased by 2.4 × 106 t and 1.5 × 106 t, respectively, with a sizable ecological effect. It has been calculated that forest and cultivated land are the two largest carbon pools in Nanjing, and the conservation of both is decisive for the future carbon stock. It is necessary to focus on enhancing the carbon stock of forest ecosystems while designating differentiated carbon sink enhancement plans based on the characteristics of other land types. Fully realizing the carbon sink potential of each ecological functional area will help Nanjing achieve its carbon neutrality goal. The results of the study not only reveal the challenges of ecological conservation in Nanjing but also provide useful guidance for enhancing the carbon stock of urban terrestrial ecosystems and formulating land-use planning in line with sustainable development strategies.