Transient Response of Inductrack Systems for Maglev Transport: Part I—A New Transient Model

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang
Keyword(s):  
Transient Response ◽  
Degrees Of Freedom ◽  
Permanent Magnets ◽  
Magnetic Interaction ◽  
Response Analysis ◽  
Governing Equations ◽  
Interaction Forces ◽  
Transient Model ◽  
Two Degrees Of Freedom ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation, Inductrack systems with Halbach arrays of permanent magnets have been applied to Maglev trains and intensively researched in various projects. In an Inductrack system, the magnetic interaction forces are coupled with the motion of a moving vehicle carrying Halbach arrays, which in many situations results in complicated transient behaviors of the system. In this two-part paper, a new transient model of two degrees-of-freedom for Inductrack systems is proposed. The highlight of this work is that the transient model is developed based on the fundamental principle of physics, without the assumption of steady-state quantities and averaged magnetic forces and with the finite dimensions of Halbach arrays in consideration. In Part I, the transient model is derived through the establishment of a set of nonlinear integro-differential governing equations, and the magnetic interaction forces in the Inductrack system are determined in analytical form. In Part II, the solution of the governing equations, model validation with the previous results in the literature, and transient response analysis via numerical simulation is presented. Although only two degrees-of-freedom have been considered, the approach of modeling and analysis presented in this paper can be extended to general cases of multi-degrees-of-freedom.

DESIGN AND DEVELOPMENT OF AN EFFICIENT COMPUTER SIMULATION MODEL FOR RESPONSE ANALYSIS OF A MOORED SEMI-SUBMERSIBLE

2021 ◽  
Vol 161 (A1) ◽  
Author(s):  
V Domala ◽  
R Sharma
Keyword(s):  
Computer Simulation ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Experimental Results ◽  
Response Analysis ◽  
Computer Simulation Model ◽  
Governing Equations ◽  
Design And Development ◽  
Mooring Lines ◽  
Steel Wires

This paper presents the design and development of an efficient modular ‘Computer Simulation Model (CSM)’ for response analysis of a moored semi-submersible. The computer simulation model is designed in two split models (i.e. computational and experimental models) and each of these models consists of various modules. The modules are developed from basic governing equations related to motion and modules are integrated and we aim for a seamless integration. The moored semi-submersible is represented mathematically as six degrees of freedom dynamic system and the coupling effects between the structure and mooring lines are considered. The basic geometric configuration of semi- submersible is modelled and analyzed for stability computations in MS-Excel*TM and then the basic governing equations related to motion are modelled mathematically in a module and solved numerically with Ansys-AQWA**TM. The computational model is validated and verified with some available experimental results. The CSM is utilized to study the surge and sway responses with respect to the horizontal range of mooring lines and our results show good validation with the existing experimental results. Our presented results show that the fibre wires have minimum steady state response in surge and sway degrees of freedom as compared with the steel wires. However, they have large drift as compared with steel wires. Finally, we show that the computer simulation model can help in detailed analysis of responses and results can be utilized for design and development of new age semi-submersibles for optimum performances for a given set of parameters.

Transient Vibration and Feedback Control of an Inductrack Maglev System

2020 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang ◽  
Hao Gao
Keyword(s):  
Steady State ◽  
Feedback Control ◽  
Dynamic System ◽  
Permanent Magnets ◽  
Preliminary Investigation ◽  
Lookup Table ◽  
Lumped Mass ◽  
Transient Vibration ◽  
Transient Model ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation envisioned in 1990s, the Inductrack system with permanent magnets (PMs) aligned in Halbach arrays has been intensively studied and applied in many projects. Due to the nonlinear, time-varying electro-magneto-mechanical coupling in such a system, the dynamic behaviors are complicated with transient responses, which in most cases can hardly be predicted with fidelity by a steady-state Inductrack model. Presented in this paper is a benchmark 2-DOF transient Inductrack model, which is derived from the first laws of nature, without any assumed steady-state quantities. It is shown that the dynamic response of the Inductrack dynamic system is governed by a set of nonlinear integro-differential equations. As demonstrated in numerical simulations with the transient model, unstable vibrations in the levitation direction occur when the traveling speed of the vehicle exceeds a threshold. To resolve this instability issue, feedback control is implemented in the Inductrack system. In the development, an assembly of Halbach arrays and active coils that are wound on the PMs is proposed to achieve a controllable source magnetic field. In this preliminary investigation, the proposed control system design process takes two main steps. First, a PID controller is set and tuned based on a simple lumped-mass dynamic system. Second, the nonlinear force-current correlation is obtained from a lookup table that is pre-calculated by steady-state truncation of the full transient Inductrack model. With the implemented feedback control algorithms, numerical examples display that the motion of the vehicle in levitation direction can be effectively stabilized at different traveling speeds. Although only a 2-DOF transient model is used here, the modeling technique and the controller design approach developed in this work are potentially applicable to more complicated models of Inductrack Maglev systems.

Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation

1998 ◽  
Vol 65 (2) ◽  
pp. 479-484 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden
Keyword(s):  
Numerical Simulation ◽  
Momentum Transfer ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Slow Motion ◽  
Critical Values ◽  
Governing Equations ◽  
Two Degrees Of Freedom

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.

Transient Response of Inductrack Systems for Maglev Transport: Part II—Solution and Dynamic Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen Yang
Keyword(s):  
Steady State ◽  
Dynamic Analysis ◽  
Transient Response ◽  
Numerical Procedure ◽  
Steady State Response ◽  
Governing Equations ◽  
Transient Model ◽  
State Response ◽  
Proposed Model ◽  
Non Linear

Abstract In Part I of this two-part paper, a new benchmark transient model of Inductrack systems is developed. In this Part II, the proposed model, which is governed by a set of non-linear integro-differential governing equations, is used to predict the dynamic response of Inductrack systems. In the development, a state-space representation of the non-linear governing equations is established and a numerical procedure with a specific moving circuit window for transient solutions is designed. The dynamic analysis of Inductrack systems with the proposed model has two major tasks. First, the proposed model is validated through comparison with the noted steady-state results in the literature. Second, the transient response of an Inductrack system is simulated and analyzed in several typical dynamic scenarios. The steady-state response results predicted by the new model agree with those obtained in the previous studies. On the other hand, the transient response simulation results reveal that an ideal steady-state response can hardly exist in those investigated dynamic scenarios. It is believed that the newly developed transient model provides a useful tool for dynamic analysis of Inductrack systems and for in-depth understanding of the complicated electro-magneto-mechanical interactions in this type of dynamic systems.

scholarly journals ORTHODONTIC TREATMENT WITH Nd-Fe-B MAGNETS

2020 ◽  
Vol 3 ◽  
pp. 54-62
Author(s):  
Valerii Kutsevlyak ◽  
Vladyslav Starikov ◽  
Volodymyr Samofalov ◽  
Vadym Starikov
Keyword(s):  
Corrosion Resistance ◽  
Permanent Magnets ◽  
Mutual Influence ◽  
Electrochemical Corrosion ◽  
Magnetic Interaction ◽  
Original Method ◽  
Physiological Solution ◽  
Protective Oxide ◽  
Corrosion Properties ◽  
Interaction Forces

The aim. The development of methodology for experimental and theoretical assessment of interaction forces between magnets in an orthodontic apparatus, the test of corrosion resistance of protective oxide and nitride coatings deposited on Nd-Fe-B magnets surface. Materials and methods. The Nd-Fe-B permanent magnets with saturation magnetization Ms≈1100 G and bilayer ZrN / ZrO2 coatings were used. To experimental measure of interaction forces between magnets the device was assembled on the base of analytical balance. The distance between the magnets was varied using non-magnetic plates. The ZrO2 and ZrN coatings have been analyzed for their corrosion properties in 0.9 % NaCl quasi-physiological solution. Results. An original method was proposed for calculating of magnetic interaction forces for materials with high magnetic anisotropy, which has good agreement with experimental measurement of forces. The theoretical model takes into account the size of the magnets and the mutual influence of their opposite faces. An increase of corrosion resistance of magnetic materials can be provided by zirconium oxide or nitride compounds, which contribute to inhibition of electrochemical corrosion of Nd-Fe-B magnets. Conclusions. A method for calculating of interaction forces between permanent magnets, which are used for correction of malocclusion in orthodontic, has been developed. The passivation of the Nd-Fe-B permanent magnets surface can be achieved by applying of bilayer ZrN / ZrO2 coating.

Design and Development of an Efficient Computer Simulation Model for Response Analysis of a Moored Semi-Submersible

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Computer Simulation ◽  
Simulation Model ◽  
Degrees Of Freedom ◽  
Experimental Results ◽  
Response Analysis ◽  
Computer Simulation Model ◽  
Governing Equations ◽  
Design And Development ◽  
Mooring Lines ◽  
Steel Wires

This paper presents the design and development of an efficient modular ‘Computer Simulation Model (CSM)’ for response analysis of a moored semi-submersible. The computer simulation model is designed in two split models (i.e. computational and experimental models) and each of these models consists of various modules. The modules are developed from basic governing equations related to motion and modules are integrated and we aim for a seamless integration. The moored semi-submersible is represented mathematically as six degrees of freedom dynamic system and the coupling effects between the structure and mooring lines are considered. The basic geometric configuration of semisubmersible is modelled and analyzed for stability computations in MS-Excel*TM and then the basic governing equations related to motion are modelled mathematically in a module and solved numerically with Ansys-AQWA**TM. The computational model is validated and verified with some available experimental results. The CSM is utilized to study the surge and sway responses with respect to the horizontal range of mooring lines and our results show good validation with the existing experimental results. Our presented results show that the fibre wires have minimum steady state response in surge and sway degrees of freedom as compared with the steel wires. However, they have large drift as compared with steel wires. Finally, we show that the computer simulation model can help in detailed analysis of responses and results can be utilized for design and development of new age semi-submersibles for optimum performances for a given set of parameters.

Nonlinear Feedback Control of the Inductrack System Based on a Transient Model

2021 ◽  
Author(s):  
Ruiyang Wang ◽  
Bingen (Ben) Yang ◽  
Hao Gao
Keyword(s):  
Feedback Control ◽  
Permanent Magnets ◽  
Control Method ◽  
Control Law ◽  
Operating Speed ◽  
Nonlinear Feedback ◽  
Transient Model ◽  
Mechanical Coupling ◽  
Wide Range ◽  
Halbach Arrays

Abstract As a new strategy for magnetic levitation envisioned in the 1990s, the Inductrack system with Halbach arrays of permanent magnets has been intensively researched. The previous investigations discovered that an uncontrolled Inductrack system may be unstable even if the vehicle travels well below its operating speed and that instability can be persistent near and beyond the operating speed. It is therefore necessary to stabilize the system for safety and reliability. With strong nonlinearities and complicated electro-magneto-mechanical coupling, however, the transient response of such a dynamic system is difficult to predict with fidelity. Because of this, model-based feedback control of Inductrack systems has not been well addressed. In this paper, by taking advantage of a recently available 2-DOF transient model, a new feedback control method for Inductrack systems is proposed. In the control system development, active Halbach arrays are used as an actuator, and a feedback control law, which combines a properly tuned PID controller and a nonlinear force-current mapping function, is created. The proposed control law is validated in numerical examples, where the transient motion of an Inductrack vehicle traveling at constant speed is considered. As shown in the simulation, the control law efficiently stabilizes the Inductrack system in a wide range of the operating speed, and in the meantime, it renders a smooth system output (real-time levitation gap) with fast convergence to any prescribed reference input (desired levitation gap).

Theoretical Laws for Rear Steering in Four-Wheel Steering Vehicles, Seen from the Tire's Point of View

1989 ◽  
Vol 17 (1) ◽  
pp. 52-65
Author(s):  
P. Salerno
Keyword(s):  
Linear Model ◽  
Transient Response ◽  
Degrees Of Freedom ◽  
Rear Wheel ◽  
Point Of View ◽  
Relaxation Length ◽  
Two Degrees Of Freedom

Abstract Theoretical laws governing rear-wheel steering of a vehicle are developed from a linear model having two degrees of freedom. Such laws can aid in improving vehicle transient response. Examples are given of their use to show that the same handling behavior can be obtained in rear-steering vehicles that are equipped with variant tires as with front-steering vehicles equipped with standard tires. Tire variants studied were cornering stiffness and relaxation length. The laws also suggest ways to nullify lags in steering actuation.

Response Analysis of a Circular Cylinder Undergoing Vortex Induced Vibrations Along Two Degrees of Freedom in the Presence of Noise

2017 ◽  
Author(s):  
M. S. Aswathy ◽  
Sunetra Sarkar
Keyword(s):  
Circular Cylinder ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical System ◽  
Real Life ◽  
Stochastic Modelling ◽  
Response Analysis ◽  
Mean Flow ◽  
Time Step ◽  
Two Degrees Of Freedom ◽  
Vortex Induced Vibrations

In this study, we perform uncertainty quantification of a nonlinear dynamical system consisting of a circular cylinder undergoing free vibrations with two degrees-of-freedom in the presence of a fluctuating flow-field. Most of the studies in Vortex Induced Vibrations till now are conducted in a deterministic environment. Real life situations involving VIV are subjected to high amount of uncertainties, with the main culprit being the randomness in the incoming flow. Studies involving modelling of the flow with a prescribed set of parameters, represents only an idealistic situation and hence is not sufficient for a complete understanding of the associated dynamics. In this context, we make an attempt to characterise the flow by doing a stochastic modelling on the same. In the current study, we have mathematically modelled the noise through a uniform distribution. These fluctuations are superimposed on a mean flow at every time step. We use a Duffing Van der Pol combined system to model the structure and flow oscillators. It is observed that stochastic modelling brings noticeable changes in the structural responses both quantitatively and qualitatively. The influence of the fluctuations on both the transverse and inline oscillations have been studied. One of the most important changes in the response of the structure is in its amplitude. Noise amplifies the maximum amplitude attained both for transverse and inline oscillations. Further, additional qualitative types of responses are visible in the presence of noise which were absent in the deterministic environment. One such behaviour the ‘intermittent’ response which occurs during the transition from higher to lower amplitudes in the lock-in region. Intermittency is observed both for transverse and inline oscillations. It has been seen that the system undergoes stochastic Phenomenological bifurcations, which have been characterised by the probability density functions of both the transverse and inline responses.

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