Train Dynamic Model Research Articles

Semianalytical Calculation of Superconducting Electrodynamic Suspension Train Using Figure-Eight-Shaped Ground Coil

Superconducting electrodynamic suspension (EDS) train has the unique advantages of excellent levitation and guidance stabilities, large levitation gap, and so on. All of these merits make it a promising candidate for the future ultrahigh-speed transportations. In order to explore the dynamic characteristics of the EDS system with a figure-eight-shaped coil (ground coil), this article transforms the complex electromagnetic field coupling between the superconducting magnets and ground coils into a reduced circuit relationship based on the dynamic circuit theory. Meanwhile, the motion characteristics are introduced to establish the field-circuit-motion-coupled model. In this article, a faster and more convenient semianalytical method was proposed to solve mutual inductance. First, the dynamic circuit model of a single-sided figure-eight-shaped null-flux EDS system was established. The magnetic coupling calculation was carried out between the onboard superconducting magnets and ground coils by a semianalytical method. Furthermore, the time-step iteration method was utilized to solve the induced current governing equation of the ground coil under different operating conditions. The energy method was employed to find the transient solution of the levitation force, guidance force, and drag force. Second, the field-circuit-motion-coupled model was validated by the experimental data of MLX01 on the Japanese Yamanashi testline. To investigate the influence upon the suspension and guidance caused by the different connection types of figure-eight-shaped coil, a cross-connected EDS train dynamic circuit model was built. Finally, based on the field-circuit-motion-coupled model, the essential parameters affecting the stability of the system were explored, and the characteristics of the system when vertical or lateral displacement occurs were calculated and analyzed. The achievements of this article can provide a reference for the design of the EDS train for future even higher speed transportation.

Adaptive Fault-Tolerant Pseudo-PID Sliding-Mode Control for High-Speed Train With Integral Quadratic Constraints and Actuator Saturation

This paper investigates an adaptive fault-tolerant pseudo-proportional-integral-derivative sliding-mode control (pseudo-PID-SMC) scheme for a high-speed train (HST) subject to actuator faults, asymmetric nonlinear actuator saturation (ANAS), and integral quadratic constraints (IQCs). It is worth mentioning that a pseudo-PID-SMC surface is proposed in this paper and the scheme based on this surface does not require acceleration measurement. An adaptive saturation compensation system that makes no assumption, as in existing works where nonlinear functions are used to describe the unsaturated region of ANAS as known and strictly monotonous, is developed to attenuate the adverse effects of ANAS. For the saturation-free and ANAS cases, two adaptive fault-tolerant pseudo-PID-SMC schemes with no chattering, a simple structure, and inexpensive computation are developed to guarantee the exponential convergence of all signals in the closed-loop systems. Finally, simulation results based on a real train dynamic model are presented to show the proposed schemes’ effectiveness and feasibility.

Adaptive Control Design and Evaluation for Multibody High-Speed Train Dynamic Models

In this article, the adaptive tracking control problem is investigated for a multibody high-speed train dynamic model in the presence of unknown parameters, which is an open adaptive control problem. A four-car train unit model with input signals acting on the second and third cars and output signals being the speeds of the first and third cars is chosen as a benchmark model, in which the aerodynamic resistance force is also considered. To handle the nonlinear term, the feedback linearization method is employed to decompose the system into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is a Lyapunov stable and is also partially input-to-state stable under the condition that the speed error between the first and third cars is exponentially convergent (to be ensured by a nominal controller) or belongs to the L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> signal space (to be achieved by a properly designed adaptive controller). The system configuration leads to a relative degree 1 subsystem and a relative degree 2 subsystem, for which different feedback linearization-based adaptive controllers and their nominal versions are developed to ensure the needed stabilization condition, the desired closed-loop system signal boundedness, and asymptotic output speed tracking. Detailed closed-loop system stability and tracking performance analysis are given for the new control schemes. Simulation results from a realistic train dynamic model are presented to verify the desired adaptive control system performance.

Parallel co-simulation of locomotive wheel wear and rolling contact fatigue in a heavy haul train operational environment

Locomotive wheel wear and rolling contact fatigue simulations that consider both train dynamics and detailed traction control systems have not been reported. This paper developed a parallel co-simulation method to link an in-house longitudinal train dynamics simulator to a commercial software package named GENSYS. An advanced longitudinal train dynamics model, a traction control system model and a wheel–rail contact model were then incorporated into the simulation. Three wear calculation models (T-gamma model, USFD model and Archard model) and two rolling contact fatigue calculation models (T-gamma-based rolling contact fatigue model and shakedown-based rolling contact fatigue model) were implemented. A train with the configuration of 1 locomotive +54 wagons +1 locomotive +54 wagons was simulated. This paper shows that the simulation method is successful and can be used for such more detailed locomotive wheel wear and rolling contact fatigue calculations. Wear and rolling contact fatigue calculation results show that the wear numbers that were calculated using the T-gamma wear model and damage indexes that were calculated using the T-gamma-based rolling contact fatigue model were similar between the leading and remote locomotives. However, wear rates that were calculated using the USFD wear model, wear volumes that were calculated using the Archard model and fatigue indexes that were calculated using the shakedown-based rolling contact fatigue model have evident differences between the leading and remote locomotives. Maximum differences in these results were about 12, 18 and 34%, respectively.

Train energy simulation with locomotive adhesion model

Railway train energy simulation is an important and popular research topic. Locomotive traction force simulations are a fundamental part of such research. Conventional energy calculation models are not able to consider locomotive wheel–rail adhesions, traction adhesion control, and locomotive dynamics. This paper has developed two models to fill this research gap. The first model uses a 2D locomotive model with 27 degrees of freedom and a simplified wheel–rail contact model. The second model uses a 3D locomotive model with 54 degrees of freedom and a fully detailed wheel–rail contact model. Both models were integrated into a longitudinal train dynamics model with the consideration of locomotive adhesion control. Energy consumption simulations using a conventional model (1D model) and the two new models (2D and 3D models) were conducted and compared. The results show that, due to the consideration of wheel–rail adhesion model and traction control in the 3D model, it reports less energy consumption than the 1D model. The maximum difference in energy consumption rate between the 3D model and the 1D model was 12.5%. Due to the consideration of multiple wheel–rail contact points in the 3D model, it reports higher energy consumption than the 2D model. An 8.6% maximum difference in energy consumption rate between the 3D model and the 1D model was reported during curve negotiation.

Zero dynamics analysis and adaptive tracking control of underactuated multibody systems with flexible links

This paper studies the adaptive tracking control problem for underactuated multibody systems with flexible links in the presence of unknown parameters. A four-body system with input signals acting on the first and fourth bodies is chosen as a benchmark model, which can be decomposed into a control dynamics subsystem and a zero dynamics subsystem. A new and detailed stability analysis is conducted to show that such a zero dynamic system is Lyapunov stable and is partially input-to-state stable under the condition that the speeds of first and fourth bodies are synchronous. The physical meaning of such partial input-to-state stability is clarified. An adaptive controller is developed to ensure such a needed system stabilisation condition and thus the boundedness of the desired closed-loop system signal and asymptotic speed tracking of the control dynamics subsystem. Detailed closed-loop system stability and tracking performance analysis are given, in which the tracking errors satisfy the performance. Extensions to the other multibody systems with flexible links are derived. The developed adaptive controller is applied to a realistic train dynamic model, and simulation results verify the desired system performance.

Long Short-Term Memory Neural Network Applied to Train Dynamic Model and Speed Prediction

The automatic train operation system is a significant component of the intelligent railway transportation. As a fundamental problem, the construction of the train dynamic model has been extensively researched using parametric approaches. The parametric based models may have poor performances due to unrealistic assumptions and changeable environments. In this paper, a long short-term memory network is carefully developed to build the train dynamic model in a nonparametric way. By optimizing the hyperparameters of the proposed model, more accurate outputs can be obtained with the same inputs of the parametric approaches. The proposed model was compared with two parametric methods using actual data. Experimental results suggest that the model performance is better than those of traditional models due to the strong learning ability. By exploring a detailed feature engineering process, the proposed long short-term memory network based algorithm was extended to predict train speed for multiple steps ahead.

Research on speed control of high-speed train based on multi-point model

The traditional train speed control research regards the train as a particle, ignoring the length of the train and the interaction force between carriages. Although this method is simple, the control error is large for high-speed trains with the characteristics of power dispersion. Moreover, in the control process, if the length of the train is not considered, when the train passes the slope point or the curvature point, the speed will jump due to the change of the line, causing a large control error and reducing comfort. In order to improve the accuracy of high-speed train speed control and solve the problem of speed jump when the train runs through variable slope and curvature, the paper takes CRH3 EMU data as an example to establish the corresponding multi-point train dynamics model. In the control method, the speed control of high-speed train needs to meet the fast requirement. Comparing the merits and demerits of classical PID control, fuzzy control and fuzzy adaptive PID control in tracking the ideal running curve of high-speed train, this paper chooses the fuzzy adaptive PID control with fast response. Considering that predictive control can predict future output, a predictive fuzzy adaptive PID controller is designed, which is suitable for high-speed train model based on multi-point. The simulation results show that the multi-point model of the high-speed train can solve the speed jump problem of the train when passing through the special lines, and the predictive fuzzy adaptive PID controller can control the speed of the train with multi-point model, so that the train can run at the desired speed, meeting the requirements of fast response and high control accuracy.

Adaptive Fault-Tolerant Sliding-Mode Control for High-Speed Trains With Actuator Faults and Uncertainties

In this paper, a novel adaptive fault-tolerant sliding-mode control scheme is proposed for high-speed trains, where the longitudinal dynamical model is focused, and the disturbances and actuator faults are considered. Considering the disturbances in traction force generated by the traction system, a dynamic model with actuator uncertainties modeled as input distribution matrix uncertainty is established. Then, a new sliding-mode controller with design conditions is proposed for the healthy train system, which can drive the tracking error dynamical system to a predesigned sliding surface in finite time and maintain the sliding motion on it thereafter. In order to deal with the actuator uncertainties and unknown faults simultaneously, the adaptive technique is combined with the fault-tolerant sliding-mode control design together to guarantee that the asymptotical convergence of the tracking errors is achieved. Furthermore, the proposed adaptive fault-tolerant sliding-mode control scheme is extended to the cases of the actuator uncertainties with unknown bounds and the unparameterized actuator faults. Finally, the case studies on a real train dynamic model are presented to explain the developed fault-tolerant control scheme. The simulation results show the effectiveness and feasibility of the proposed method.

Dynamic performance analysis of heavy-haul locomotives running through turnout branches with electric brake

This paper develops a dynamic model of heavy-haul train to investigate the dynamic behaviour of heavy-haul locomotives passing through turnout branch lines with electric brakes. A heavy-haul train dynamic model including 2 HX-type locomotives and 4 sets of coupler and buffer systems has been built up by SIMPACK software. The developed coupler-tail arc surface contact friction element, improved nonlinear hysteretic buffer element and flattened pin rotation stop element are all taken into consideration in the coupler and buffer subsystem. The turnout branch line is simplified as an S-shape curve without considering the profile change of turnout switch and frog rails. This dynamic model is validated by comparing its calculation results with those of the real turnout model and test data respectively. On this basis, the simulations of heavy-haul locomotives passing through Chinese 12# turnout branch lines with electric brakes have been carried out, and the influences of electric brake forces, locomotive and coupler structural parameters have been investigated deeply. Results indicate that both the locomotive electric brake force and the coupler-tail friction coefficient have significant influences, and the locomotive secondary lateral stop also has a great effect. Controlling the locomotive electric brake force and optimising these locomotive and coupler structural parameters could improve the dynamic performance of heavy-haul locomotives passing through turnout branches with electric brakes.

Train distance and speed estimation using multi sensor data fusion

The accurate distance and speed estimates of train and individual coaches are necessary for the safe operation of the high-speed train system. Often, the train system does not rely on a single sensor for its distance and speed measurements as the sensors are susceptible to diverse operating conditions such as snow, rain, fog, tunnel, hilly region, slip, slide, etc. Hence, the information from a combination of sensors which can complement each other under certain operating conditions is required for the correct estimation. For distance measurements, Global Navigation Satellite System (GNSS) and balise are generally used. For speed sensing, the combination of wheel sensor, radar and GNSS are chosen. The diversity of sensors in terms of sampling rate and noise characteristics, etc. greatly affect the overall estimation accuracy and reliability if the measurements are used directly. Hence, this work presents a probabilistic weighted fusion algorithm which is based on the nonlinear longitudinal train dynamic model. The fusion algorithm combines the state estimates from distributed and sensor-specific extended Kalman filters. The effectiveness of the proposed fusion algorithm is demonstrated on the simulated sensor measurements along with a wide range of noises, spurious measurements, train operating conditions and track environmental disturbances.

Motor car–track spatial coupled dynamics model of a high-speed train with traction transmission systems

As an important component of a high-speed train motor car, the traction transmission system, which directly affects the dynamic performance and the running safety of the vehicle. The present paper establishes a comprehensive spatial coupled dynamics model of the motor car–track system. The model is based on classical vehicle–track coupled dynamics and gear dynamics theory. The coupling effects between the traction transmission subsystem and the vehicle–track system are captured by the suspension system, gear mesh, and wheel–rail interactions. Some nonlinear factors, such as the nonlinear damping characteristics, the gear time-varying mesh stiffness, and the wheel–rail contact relationship, are considered. The results of the proposed dynamics model are compared with those of experimental field tests for validation, which reveals the dynamics performance of the whole system, particularly the dynamics of the traction transmission system in vehicle-coupling vibration environments. The traction transmission exerted non-negligible effects on the wheelset vibrations and the wheel–rail interface, especially in the low-speed range. Furthermore, this dynamics model can assess the vibrational characteristics of the coupled system under the complex excitations that occur during service, such as gear cracking, wheel defects and rail local defects, particularly during the acceleration process.

Low frequency vibration control of railway vehicles based on a high static low dynamic stiffness dynamic vibration absorber

In order to control the low frequency vibration of railway vehicles, a vertical two degrees of freedom (2DOF) low frequency dynamic vibration absorber (DVA) based on acceleration is proposed. Parameters of the dynamic vibration absorber are put forth to control the low frequency vibration of car body bouncing and pitching. Next, the acceleration power spectrum density (PSD) and ride quality of the car body are calculated based on the pseudo excitation method (PEM) and covariance algorithm, respectively. According to the requirement of 2DOF low frequency DVA, the isolators with high static low dynamic stiffness (HSLDS) are designed. A high-speed train dynamic model containing HSLDS isolators is established to validate the effects on the car body vibration. The results reveal that the 2D low frequency DVA can significantly reduce the vibration of the car body bouncing and pitching. Thus, the ride quality of the vehicle is increased, and passenger comfort is improved.

Analysis of the influence of magnetic stiffness on running stability in a high-speed train propelled by a superconducting linear synchronous motor

There are two major obstacles that prevent a conventional train from achieving high speed: the limitation of wheel–rail adhesion and the increase of instability in the wheel–rail running dynamics. To overcome these problems, a new hybrid train model is introduced in this study. This train utilizes a superconducting linear synchronous motor (SC-LSM), instead of a traction motor, for propulsion; therefore, this train does not have the limitation of adhesion between the wheel and the rail. Using an SC-LSM also improves the stability of the train during high-speed operations. The magnetic stiffness between the train and the guideway is additionally generated by using the SC-LSM, which is favorable for the running stability at a high speed. This study focuses on the magnetic stiffness and its effect on the running stability in the proposed hybrid train model. First, the magnetic stiffness in the SC-LSM is investigated both theoretically and experimentally. Then, a train dynamic model including the magnetic stiffness is developed and the effect of magnetic stiffness on the running stability is analyzed through various simulations.

D-Type ILC Based Dynamic Modeling and Norm Optimal ILC for High-Speed Trains

Differential-type (D-type) iterative learning control (ILC) is a typical control method for repetitive operating nonlinear systems and has been used for speed tracking of high-speed train (HST). However, the derived $\lambda $ -norm convergence property of the D-type ILC may lead to unsafe operation of the HST since huge overshoot phenomenon of tracking errors in the iteration axis may occur. To address this problem, this paper presents a novel dynamic modeling and norm optimal iterative learning control (Dynamic modeling based NOILC) approach. By making full use of the valuable information data generated after each repetitive operation of the HST, a modified iterative learning recursive least squares algorithm is proposed to identify the unknown and time-varying even fast time-varying aerodynamical coefficients in the nonlinear train dynamic model. Then, based on this identified nonlinear train model, a norm optimal iterative learning control with consideration of security, punctuality, and traveling comfort will be designed. Through theoretical analysis, reliable 2-norm convergence of both the model identification error and the tracking control error can be guaranteed. Simulation and experimental studies further verify that the proposed approach achieves a significant improvement in tracking control precision and meanwhile obeys safety requirement.

Longitudinal train dynamics model for a rail transit simulation system

The paper develops a longitudinal train dynamics model in support of microscopic railway transportation simulation. The model can be calibrated without any mechanical data making it ideal for implementation in transportation simulators. The calibration and validation work is based on data collected from the Portland light rail train fleet. The calibration procedure is mathematically formulated as a constrained non-linear optimization problem. The validity of the model is assessed by comparing instantaneous model predictions against field observations, and also evaluated in the domains of acceleration/deceleration versus speed and acceleration/deceleration versus distance. A test is conducted to investigate the adequacy of the model in simulation implementation. The results demonstrate that the proposed model can adequately capture instantaneous train dynamics, and provides good performance in the simulation test. The model provides a simple theoretical foundation for microscopic simulators and will significantly support the planning, management and control of railway transportation systems.

Resonance characteristics analysis of the power reflux hydraulic transmission system

The power reflux hydraulic transmission system (PRHTS), which is a new continuously variable transmission system, is put forward to enhance the efficiency of the torque converter. This study shows that the basic structure and operating principle of the PRHTS. Because the six-cylindered diesel engine’s operation range is between 40 Hz and 150 Hz, resonance point of the PRHTS should not exist in resonance region of engine. In order to study the resonance characteristics of the PRHTS, the dynamic model of the PRHTS is established by merging the planetary gear train dynamic model and torque converter dynamic model. This study also researches the amplitude-frequency characteristic curves of the PRHTS with different speed ratio and the effect of the torsional stiffness and damping coefficient to the amplitude-frequency characteristic of the PRHTS. The simulation result shows that the resonance frequency of the PRHTS could be excluded from engine’s operation range and the amplitude will decrease by changing the torsional stiffness and damping coefficient of the coupling.

Research on Integrated Optimization Design Method for Diesel Engine Valve Train

In order to have a good performance of gas exchange in working process, a function of six order polynomial dynamic cam was established in this paper. The influence of the maximum ample factor to valve including the maximum positive and negative accelerations and the minimum curvature radius was analyzed by NLPQL. On this basis, multi-body dynamic analysis for diesel engine valve train was done, valve train dynamic model was established by ADAMS, multidisciplinary optimization process of cam profile and its model was put forward, and ISIGHT software was used to optimization and calculation. Finally, a set of different cam parameters and corresponding valve performance parameters was established, multipart integrated design and multidisciplinary optimization for diesel engine valve cam was realized. This paper provides a new method for the multicomponent integration design and multidisciplinary integration optimization for diesel engine valve train.

Towards eco‐aware timetabling: evolutionary approach and cascading initialisation strategy for the bi‐objective optimisation of train running times

In railway planning, the timetabling step needs, as input, the train running times, which are calculated from a train dynamic model. Usually, this model determines the most energy-efficient train trajectory for a predefined time. However, this time may not correspond to the timetable-makers’ needs. They should have the choice among a set of solutions, more or less energy-consuming. This study proposes a method capable of producing a set of alternative running times with the associated mechanical energy required. To this end, the authors’ contribution is to set up an efficient evolutionary multi-objective algorithm builds a set of well-spread and diversified solutions which approximate a Pareto front. The solutions are all compromises between running time and energy-consumption, the two minimisation objectives concurrently optimised. Given that an evolutionary algorithm is strongly dependent on the initialisation phase, the efficiency of the algorithm is improved through a specific and original mechanism connecting multiple initialisations in cascade in order to accelerate the convergence towards the best solutions. A set of results obtained on randomly-generated instances is analysed and discussed.

자기부상열차의 부상안정성을 고려한 3방향 분기기의 설계 파라미터 연구

분기기 거더 경량화는 제작비 감소 및 제작의 용이함을 위해 필수적이다. 자기부상열차용 3방향 분기기 경량화를 위한 설계변수는 부상안정성과 관련 있기 때문에 신중히 결정되어야 한다. 도시형 자기부상열차는 대차가 레일을 감싸는 구조로 되어 있기 때문에 거더 높이 변경을 통해서 경량화가 가능하다. 실제 테스트베드에서 반복 주행시험을 통해 안정성을 확보해야 하지만 공간적, 비용적 제한에 의해 여러 거더 높이의 테스트베드 제작은 불가능하며 이를 보완하기 위한 설계 파라미터 연구는 필수적이다. 본 논문에서는 자기부상열차 주행 시 3방향 분기기 경량화에 따른 부상안정성을 고려한 설계 파라미터 연구에 그 목적이 있다. 이를 위해 분기기 거더 높이 변경을 통해 경량화하였고 모달 중첩법을 이용하여 유연체로 모델링 하였다. 유연체 분기기와 자기부상열차 동역학 모델과의 연동해석을 통해 차량의 통과속도, 횡 공극, 부상 공극을 비교하고 부상안정성에 미치는 영향을 분석하였다. 이를 통해 거더높이와 부상안정성과의 상관관계에 대해 분석하였다. 본 논문의 연구 결과는 자기부상열차용 분기기 설계에 활용 가능할 것이다. It is essential to lighten the weight of switch girders in order to reduce their costs of manufacturing and make it easier to use them in construction. Lightening the weight of switch is also important to the Maglev 3-way switches system, however, the design variables should be considered very carefully if lightening is to be applied to the system, because these variables are vitally related to the levitation stability. Because Urban Maglev trains have a structure in which train bogie wraps around the guiderail, the adjustment of a girder's height is a possible way to reduce the weight. The safety of the application of this concept is ensured by repeated experiments in a test bed, however, due to a lack of space and budget limits, the design parametric study for the system model can substitute for actual application. The purpose of this paper is to study the design parameters that are concerned with levitation stability while a Maglev train is running on the Maglev 3-way system depending on the weight of the switch girders. In this study, switch girder weight is reduced by adjustment of girder height and girders are and modeled as a flexible body. The effect of the adjustment of girder height on the levitation stability can be analyzed by comparing the velocity of the train when it passes the switch girders, with the lateral gap, and the levitation gap which are obtained from the co-simulation of the Maglev train's dynamics model and flexible switching system. The results of this research will be used to design a Maglev switch.