Flexible Guideway Research Articles

Dynamic analysis and vibration control for a maglev vehicle-guideway coupling system with experimental verification

Maglev trains are strongly nonlinear, open-loop unstable, and flexible track systems. Vehicle-guideway self-excited vibration, which occurs mainly due to the deflection of the flexible guideway, may take place when a train is levitated on the guideway, even if the train is stationary. In this research, maglev vehicle-guideway coupling vibration is studied by employing the Hopf bifurcation criterion. First, the nonlinear dynamic model is presented with consideration of the flexibility of the guideway. To avoid the massive computations required to solve all the eigenvalues when analyzing system stability, the stability criterion of the Hopf bifurcation for the maglev system is proposed and proven with strict mathematical analysis. Based on the proposed lemma, the bifurcation points of the maglev system are calculated, and the critical points of the coupling vibration are found. Next, the influence law of the parameters of the guideway on the vehicle-guideway coupling vibration is analyzed with theoretical and numerical simulation. Then the influence law and the system stability range of the control parameters are analyzed to suppress the coupled vibration. Finally, the effectiveness of the proposed theory is verified by experiments.

Improvement on Curve Negotiation Performance of Suspended Monorail Vehicle Considering Flexible Guideway

This work presents the investigation and improvement on curve negotiation performance of suspended monorail vehicle considering a flexible guideway. First, a spatial train–guideway interaction model of suspended monorail system (SMS) is established based on the secondary development of ANSYS software. Then, the dynamic analysis of the train over the flexible curved guideway is conducted, and the curve negotiation performance of the vehicle and the guideway vibration feature are revealed. Subsequently, several crucial design parameters that significantly influence the curve negotiation performance of the vehicle are found, and their influences on the train–guideway dynamic responses are systematically investigated. Finally, by comprehensively considering the dynamic indexes of the vehicle–guideway system, the optimal ranges of these crucial design parameters are obtained. Results show that decreasing the radial stiffness of guiding tyre can effectively reduce the lateral vibration levels of vehicle and guideway, but it would increase the lateral displacements of the bogie and hanging beam; and the radial stiffness is finally suggested to be around 1[Formula: see text]kN/mm by comprehensively considering all dynamic indexes. Increasing the initial compression displacement of guiding tyre can well limit the lateral displacements of the bogie and the hanging beam, thus enhancing the train running safety; however, it would intensify the vehicle-guideway lateral vibration level; especially, the optimal initial compression displacement of guiding tyre is related to its radial stiffness characteristics. To ensure a good curve negotiation performance of vehicle and guideway vibration level, the stiffness of the anti-roll torsion bar and the initial gradient angle of the installed trapezoid four-link suspended device are suggested to be 1.0[Formula: see text]MNm/rad and 65–[Formula: see text], respectively.

Nonlinear dynamic analysis of Maglev Vehicle Based on flexible guideway and random irregularity

Nonlinear dynamic analysis of Maglev Vehicle Based on flexible guideway and random irregularity

Nonlinear dynamic analysis on maglev train system with flexible guideway and double time-delay feedback control

In this paper, the dynamic behavior of time-delayed feedback control for maglev train system with double discrete time delays is considered with flexible guideway. Considering the maglev guideway as Beroulli-Euler beam, the mathematical model of maglev system with flexible guideway is constructed. The time delay of the two state feedback signals in the maglev system occurs simultaneously, and the values are different. The present treatment method only considers one single feedback delay, which are insufficiency. Thus, the Hopf bifurcation with double time-delay feedback of maglev train running on the flexible guideway is analyzed considering time-delayed position feedback signal τ1 and velocity feedback signal τ2. A novel method is presented to develop the double-parametric Hopf bifurcation diagram in relation to τ1 and τ2. Sufficient numerical simulations are provided to illustrate the complex dynamical behavior of the discrete delays τ1 and τ2 for maglev system and we verify the obtained theoretical analysis. Finally, the field experiments are carried out to validate the effectiveness of the Hopf bifurcation analytical method preliminarily.

3차원 다물체동역학 시뮬레이션 기반 자기부상열차와 3경간 연속교 동적상호작용 해석

This study aims to investigate dynamic interaction characteristics between Maglev train and 3 span continuous guideway. The integrated model including a 3D full vehicle model based on multibody dynamics, flexible guideway by a modal superposition method, and levitation electromagnets with the feedback controller is proposed. The proposed model was applied to the Incheon Airport Maglev Railway to analyze the dynamic response of the vehicle and guideway from the numerical simulation. Using field test data of air gap and guideway deflections, obtained from the Incheon Airport Maglev Railway, the analysis method is verified. From the results, it is confirmed that Maglev railway system are designed and constructed safely according to the design criteria.

Design of an Electromagnet with Low Detent Force and its Control for a Maglev Super-speed Vehicle

The vibration and noise caused by the dynamic interaction between electromagnetic suspension and the linear synchronous motor stator beneath a flexible guideway remain problems in designing attractive Maglev trains. One possible method to reduce the sources of vibration is to minimize the detent force in the linear synchronous motor that creates variations in both lift force and thrust. This paper proposes lowering detent force by using separated core instead of single united core. The magnet is designed to adapt to the deflected guideway at a speed of 550km/h. This study will analyze the electromagnetic field and control performance, and how they relate to lift forces and dynamic responses.

가이드웨이 유연성이 고려된 자기부상열차 부상제어 시뮬레이션

In magnetic levitation vehicles, the clearance between the magnet and track should be maintained within an allowable range through a feedback control loop. The flexibility of the guideway would introduce additional modes in the overall suspension system, resulting in dynamic interaction between the guideway vibration and the electromagnetic suspension control system. This dynamic interaction can be a serious problem, particularly at very low speeds or standstill, and may cause airgap instability. To optimize the overall system dynamics, an integrated dynamic model including mechanical and electrical parts and a flexible guideway as well as a control loop was developed. With the proposed model, airgap simulations at standstill were performed while varying the control gains, specifically with the aim of understanding the effects of gains of the PID controller on the airgap variation. The findings may be used to achieve a stable levitation controller design.

Coupled vibration analysis of Maglev vehicle-guideway while standing still or moving at low speeds

Dynamic instability, that is, resonance, may occur on an electromagnetic suspension-type Maglev that runs over the elevated guideway, particularly at very low speeds, due to the flexibility of the guideway. An analysis of the dynamic interaction between the vehicle and guideway is required at the design stage to investigate such instability, setting slender guideway in design direction for reducing construction costs. In addition, it is essential to design an effective control algorithm to solve the problem of instability. In this article, a more detailed model for the dynamic interaction of vehicle/guideway is proposed. The proposed model incorporates a 3D full vehicle model based on virtual prototyping, flexible guideway by a modal superposition method and levitation electromagnets including feedback controller into an integrated model. By applying the proposed model to an urban Maglev vehicle newly developed for commercial application, an analysis of the instability phenomenon and an investigation of air gap control performance are carried out through a simulation.

자기부상열차/가이드웨이 동적상호작용 해석

This study aims to investigate the dynamic interaction characteristics between Maglev vehicles and an elevated guideway. A more detailed model for the dynamic interaction of the vehicle/guideway is proposed. The proposed model incorporates a 3D full vehicle model based on prototyping, flexible guideway by a modal superposition method, and levitation electromagnets including the feedback controller into an integrated model. The proposed model was applied to an urban transit Maglev developed for a commercial application to analyze the dynamic response of the vehicle and guideway, and the effect of the surface roughness of the rail, mid-span guideway deflections, and air gap variations are then investigated from the numerical simulation.

DYNAMIC ANALYSES OF A FLEXIBLE VEHICLE MOVING ALONG A FLEXIBLE GUIDEWAY CONSIDERING THE TIP-OFF EFFECT

A semi-analytical solution for the tip-off response of a vehicle moving along a guideway is obtained, considering the dynamic interaction between the two subsystems. The guideway is modeled as an inclined simply-supported uniform flexible beam, and the vehicle as a flexible free-free beam under a pre-specified thrust force. The equations of motion for the vehicle and guideway are developed using the Lagrangian approach and the assumed mode method based on the Euler–Bernoulli hypothesis. In the form of nonlinear differential equations, they are solved by the Petzold-Gear backward differentiation formula (BDF) method. The solutions obtained are validated by comparing them with the published results for the models with a rigid vehicle running over a rigid guideway or a flexible guideway. Comparisons of the present solutions with the existing ones for the vehicle and guideway reveal the advantages of the approach proposed herein. Other effects on the tip-off responses of the vehicle that are investigated include the length of the guideway, distance between the shoes of the vehicle, and mass and rigidity ratios of the vehicle to the guideway. The results presented herein provide valuable information for the design of the vehicle launch system.

Dynamic response and robust control of coupled maglev vehicle and guideway system

This study develops a computational model of the dynamic characteristics of the actively controlled, magnetically levitated (maglev) system moving on a flexible guideway. The 5-dof (degree-of-freedom) vehicle model, the modeling of the EMS (electromagnetic suspension ), guideway, and guideway irregularity are described, respectively. In this sense, the dynamic response of a coupled vehicle and guideway system is investigated with different vehicle speeds and masses. Furthermore, the formulation of SMC (sliding mode control) based on the Kalman filter is addressed for the control of the dynamic response of the maglev system for various prescribed running speeds. For numerical simulation, the Runge–Kutta method is used to solve the state-space equation, which includes information about the vehicle, guideway and controller. The results reveal that both the air gap fluctuation and the cabin CG (center of gravity) vertical acceleration are strongly affected by the vehicle speed and guideway irregularity, but only slightly affected by the vehicle mass. Moreover, SMC based on the Kalman filter considerably reduces the air gap fluctuation and cabin CG vertical acceleration responses, and the efficiency of the adopted control methodology is demonstrated even at higher critical speed conditions.

Response of a Maglev Vehicle Moving on a Two-Span Flexible Guideway

AbstractThis paper is intended to present a preliminary framework for dynamic interaction analysis of a maglev (magnetically levitated) vehicle running on a two-span guideway using a comprehensive iterative approach. A maglev vehicle with electrodynamic suspension (EDS) system is simplified as a two degrees-of-freedom (2-DOF) maglev oscillator tuned by a PID (Proportional-Integral-Derivative) controller. The guideway is modeled as a two-span continuous beam with uniform section. Two sets of equations of motion are written, with the first set for the guideway and the second set for the maglev oscillator traveling on the guideway through a motion-dependent magnetic force. To achieve the stable levitation gap for a maglev vehicle moving on a flexible guideway, Ziegler-Nicholas (Z-N) tuning rules are used to determine the tuning parameters of the PID controller. Numerical simulations demonstrate that the levitation gap affects the dynamic response of the maglev vehicle while little influence on the guideway response since the inertial force of the moving maglev vehicle is much lower than its static load.

Dynamic Interaction of a Distributed Supported Guideway and a Asymmetrical Multimagnet Suspension Vehicle with Unbalanced Mass

AbstractThis study investigates the steady state dynamic interactions between a vehicle and guideway of a high-speed ground transportation system based on magnetically levitated (Maglev) vehicles. The guideway is assumed to be made up of identical simply supported beams with single spans and rigid supports. The vehicle is considered two-dimensional, with numerous degrees of freedom representing the passenger cabin and primary and secondary suspensions of the vehicle with lumped masses, linear springs and dampings. The Bernoulli-Euler beam equation is utilized to model the characteristics of a flexible guideway, and the guideway synthesis is based on a modal analysis method. The dynamic behaviors of both vehicle and guideway are then simulated to investigate how the locations of the passenger cabin mass of center and asymmetric suspension characteristics of the vehicle suspensions influence high speed vehicle-guideway interaction. Finally, simulation results are compared. Results of this study provide basic design guidelines for Maglev vehicle-guideway systems.

Aerodynamic vibrations of a maglev vehicle running on flexible guideways under oncoming wind actions

This paper intends to present a computational framework of aerodynamic analysis for a maglev (magnetically levitated) vehicle traveling over flexible guideways under oncoming wind loads. The guideway unit is simulated as a series of simple beams with identical span and the maglev vehicle as a rigid car body supported by levitation forces. To carry out the interaction dynamics of maglev vehicle/guideway system, this study adopts an onboard PID (proportional-integral-derivative) controller based on Ziegler–Nicholas (Z–N) method to control the levitation forces. Interaction of wind with high-speed train is a complicated situation arising from unsteady airflow around the train. In this study, the oncoming wind loads acting on the running maglev vehicle are generated in temporal/spatial domain using digital simulation techniques that can account for the moving effect of vehicle's speed and the spatial correlation of stochastic airflow velocity field. Considering the motion-dependent nature of levitation forces and the non-conservative characteristics of turbulent airflows, an iterative approach is used to compute the interaction response of the maglev vehicle/guideway coupling system under wind actions. For the purpose of numerical simulation, this paper employs Galerkin's method to convert the governing equations containing a maglev vehicle into a set of differential equations in generalized systems, and then solve the two sets of differential equations using an iterative approach with the Newmark method. From the present investigation, the aerodynamic forces may result in a significant amplification on acceleration amplitude of the running maglev vehicle at higher speeds. For this problem, a PID+LQR (linear quadratic regulator) controller is proposed to reduce the vehicle's acceleration response for the ride comfort of passengers.

A parametric study on the dynamics of urban transit maglev vehicle running on flexible guideway bridges

The purpose of this study is to develop a numerical model for a dynamic interaction analysis of an actively controlled maglev vehicle and flexible guideway structure. In addition, an investigation is performed of the effect of vehicle and guideway characteristics on dynamic responses of low and medium speed maglev systems. Dynamic governing equations are derived by combining the 5-dof maglev vehicle model, the modal properties of guideway structures and a LQG controller for electromagnetic suspension. An investigation is then carried out on the effect of vehicle models, vehicle speed, irregularity, guideway deflection ratio, span length, span continuity and damping ratio on dynamic responses of the relatively low speed maglev vehicle and guideway structures. From the numerical simulation, it is found that the air gap of the vehicle is strongly affected by vehicle speed, tract roughness and guideway deflection ratio. In particular, the guideway deflection ratio is the most influential parameter which governs the air gap. Continuous span girders are found to be effective in reducing the air gap because of its smooth curvature and small deflection slope near the support. However, the span length and damping ratio of the guideway structure do not affect the air gap. The overall dynamic magnification factor of the guideway girder is not severe compared to the traditional wheel type vehicle.

Effects of the guideway's vibrational characteristics on the dynamics of a Maglev vehicle

The levitation control system in an electromagnetically levitated vehicle controls the voltage in its winding to maintain the air gap, which is the clearance between the electromagnet and the guideway, within an allowable range of variation, while strongly interacting with the flexible guideway. Thus, the vibrational characteristics of the guideway play an important role in the dynamics of Maglev (magnetically levitated) vehicles that utilise an active electromagnetic suspension system. In this study, the effects of the guideway's vibrational characteristics, such as natural frequency and damping, on the dynamics of the Maglev vehicle UTM-02 are numerically and experimentally analysed. From these analyses, the coupled equations of motion of the simplified vehicle–guideway model with three degrees of freedom are derived. Eigenvalues are calculated and frequency response analysis is also performed, in order to obtain a clear understanding of the dynamic characteristics resulting from the guideway's vibrational characteristics. To verify the numerical results, air gap tests of the urban Maglev vehicle UTM-02 are also carried out. These results lead us to recommend that the natural frequency of the guideway be decreased by increasing mass density rather than by decreasing rigidity, and that its damping ratio be increased in the Maglev vehicle UTM-02 employing a five-state feedback control law as a levitation control law.

Vibration control of maglev vehicles traveling over a flexible guideway

As a series of maglev (magnetically levitated) vehicles travel over a flexible guideway with constant speeds, their acceleration amplitudes will be amplified significantly at resonant or higher speeds. This paper intends to develop a neuro-PI (proportional-integral) controller to control the dynamic response of the maglev vehicles around an allowable prescribed acceleration. The maglev vehicle is simplified as a two-degree-of-freedom (two-dof) moving oscillator controlled by an on-board PI controller and the guideway is modeled as a simply supported beam. Considering the motion-dependent nature of electromagnetic forces working in a maglev system, this study presents an iterative approach to compute the dynamic response of a maglev-oscillator/guideway coupling system based on the Newmark method. The proposed neuro-PI controller is trained using back-propagation neural network in such a way that its PI gains are correlated to the generated data set of moving speeds, mid-span acceleration amplitude of the guideway, and maximum vertical accelerations of maglev oscillators. Numerical simulations demonstrate that a trained neuro-PI controller has the ability to control the acceleration amplitude for running maglev vehicles within an allowable region of prescribed acceleration.

Sup-Resonant Response of a Nonautonomous Maglev System With Delayed Acceleration Feedback Control

A Maglev system with delayed acceleration feedback control is disturbed by the deflection of flexible guideway, and resonant response may take place. We have investigated sup-resonant response of the Maglev system by employing center manifold reduction and the method of multiple scales. We present the dynamic model and expand it to a third-order Taylor series. Taking time delay as its bifurcation parameter, we discuss the condition for the occurring of Hopf bifurcation. We apply center manifold reduction to get the Poincare normal form of the nonlinear system and employ the perturbation technique to study sup-resonant response of the system. This yields the sup-resonant periodic solution of the normal form. We analyze the stability condition of the free oscillation in the solution and discuss the relationship between guideway excitation and periodic solution. Finally, numerical results show how time delay, control, and excitation parameters affect the system response. With the proper system parameter, the free oscillation may vanish and only the periodic solution plays a part. Time delay can control amplitude of the forced oscillation. The appearance of the chaos phenomenon can also be governed by regulating time delay. And judiciously selecting a control parameter makes it possible to suppress the response.

가이드웨이 진동 특성이 자기부상열차 동특성에 미치는 영향

The electromagnet in Maglev vehicles controls the voltage in its winding to maintain the air gap, a clearance between the electromagnet and guideway, within an allowable deviation, with strongly interacting with the flexible guideway. Thus, the vibration characteristics of guideway plays important role in dynamics of Maglev vehicles using electromagnet as an active suspension system. The effects of the guideway`s vibrational characteristics on dynamics of the Maglev vehicle UTM-01 are analyzed. The coupled equations of motion of the vehicle/guideway with 3 DOFs are derived. Eigenvalues are calculated and frequency response analysis is also performed for a clear understanding of the dynamic characteristics due to guideway vibration characteristics. To verify the results, tests of the urban Mgalev vehicle UTM-02 are carried out. It is recommended that the natural frequency of the guideway be minimized and its damping ratio in the Maglev vehicle with a 5-states feedback control law as a levitation control law.

Non-resonant response, bifurcation and oscillation suppression of a non-autonomous system with delayed position feedback control

The maglev system with delayed position feedback control is excitated by the deflection of flexible guideway and resonant response may take place. This paper concerns the non-resonant response of the system by employing centre manifold reduction and method of multiple time scales. The dynamical model is presented and expanded to the third-order Taylor series. Taking time delay as its bifurcation parameter, the condition with which the Hopf bifurcation may occur is investigated. Centre manifold reduction is applied to get the Poincare normal form of the nonlinear system so that we can study the relationship between periodic solution and system parameter. At first, the non-resonant periodic solution of the normal form is calculated based on the method of multiple time scales. Then the bifurcation condition of the free oscillation in the solution is analyzed, and we get the conditions with which the free oscillation has maximum and minimum values. The relationship between external excitation and the periodic solution is also discussed in this paper. Finally, numerical simulation results show how system and excitation parameters affect the system response. It is shown that the existence of the free oscillation and the amplitude of the forced oscillation can be determined by time delay and control parameters. So felicitously selecting them can suppress the oscillation effectively.