Structure analysis of levitation chassis of medium-to-low speed maglev vehicles based on left-right decoupling

Fang LIU 0 1 Jinwen DONG 1 Yongzhi JING 1 0 School of Mechanical Engineering, Southwest Jiaotong University , Chengdu 610031, China 1 Key Laboratory of Magnetic Levitation Technologies and Maglev Trains (Ministry of Education of China), School of Electrical Engineering, Southwest Jiaotong University , Chengdu 610031, China Levitation chassis, as an extremely important component of maglev vehicles, provides functions of transmitting levitation force and steering force, and directly affects the safety performance of the vehicle. Based on the vertical dynamics model of the levitation chassis, kinetic equations of the model are established, and a simulation program is designed to analyze the structural decoupling function of the chassis, especially under the influence of elastic constraints between the left and right modules, which are exclusively owned by maglev vehicles. A finite element model of the levitation chassis based on left-right decoupling is constructed. Analysis results of the model show that the mechanical properties of the chassis tailored for the vehicle meet the design requirements, and the stiffness and strength is adequate to bear the weight of the whole vehicle. - L are a new kind of rail transit system, which feaong-stator medium-to-low speed maglev vehicles tures low noise, small vibration, moderate transport volume, safety, and economy, and is more suitable to be the citys dominant means of rail transportation over trams, light rails, and subways [1]. Levitation chassis, as well as the chassis of the whole maglev vehicle, is an extremely important component of the vehicle that provides functions of transmitting levitation force and steering force [2], and also has a direct impact on safety performance of the vehicle. Therefore, it is quite necessary to analyze the structural strength and stiffness of the levitation chassis. In addition, because of the comparatively complicated structure of the maglev, finite element method (FEM) is an effective method for calculation of structural strength and stiffness of the levitation chassis. Current research on structure strength analysis of the levitation chassis only considers one side of the module instead of both sides in left-right decoupling. Jiang et al. [3] presented some suggestions for structure design and improvements of anti-rolling sills after analyzing of the relationship between anti-rolling sills and curve negotiation of maglev vehicles. Luo and Zhang [4] offered credible data for optimized design of anti-rolling sills of maglev bogie after electromagnetisms calculation of U-shaped levitation electromagnet. Simulation of structural decoupling functions of right and left levitation modules is rarely reported. Therefore, it has great theoretical values to conduct an FEM analysis on the levitation chassis based on the left-right decoupling. This paper establishes a vertical dynamics model of a levitation chassis, and analyzes the influence of elastic constraints between the left and right modules of the maglev vehicle. An FEM model of the levitation chassis is built with consideration of the left-right decoupling. Stress and deformation data under different conditions are obtained from the model by ANSYS to test whether the vehicle meets the requirements. They may provide a reference for the structural improvements of levitation chassis. 2. Vertical dynamics of levitation chassis 2.1. Vertical dynamics model This paper only considers a common levitation chassis unit running on a single-span flexible track with a simple support. The elastic structure deformation of levitation chassis itself is ignored, and then levitation chassis can be simplified to a vibration system consisting of two rigid bodies interconnected by elastic damping elements (Kb,Cb). Each rigid body has three degrees of freedom: plunging, nodding, and rolling motion. The vehicle body is installed above the levitation chassis through an air spring and the force acted on the air spring is F. When the maglev vehicle is in steady-state suspension, the magnetic gap has a small-scale change only near the steady-state point. Thus, the magnet/rail relationship can be regarded as linear [5-7]; that is, the interaction effect between levitation chassis and track (magnet/rail relationship) is equivalent to the springdamper suspension (Kp,Cp). The vertical dynamics model of levitation chassis is established, as shown in Fig. 1. Fig. 1 Vertical dynamics model of levitation chassis 2.2. Kinetic equation and solution 2.2.1. External disturbances The vertical irregularity of the track, caused by processing, installation error, thermal stress, and static deflection under the influence of vehicles and other loads, can be described by the cosine function excitation model [8]: where 2 v / L , L is the irregularity wavelength; a is the irregularity wave depth; and v is the vehicle speed. 2.2.2. Vibration equation of levitation chassis The general forms of vibration equations of left and right levitation chassis modules are given below. Equation of plunging motion: Equation of nodding motion: Equation of rolling motion: In Eqs. (2)(4), Zt , t , and t represent the plunging displacement, nodding angle, and rolling angle, respectively; Kp , K , Cp , and C represent the vertical stiffness, rolling angle stiffness, vertical damping, and rolling angle damping, respectively; Kb and Cb are the spring stiffness and damping of anti-rolling sills, respectively. The rest are shown in Fig. 1. In actual calculation for the left and right modules, the subscript t should be replaced by the corresponding tl or tr. Besides, subscripts 1 should be replaced by 1l or 1r, and 2 by 2l or 2r. Symbol in Eq. (3) is decided by the rule: for the left module, + for the right module. According to Eqs. (2)(4), the vibration dynamics equation of levitation chassis can be written in the following unified form: where, X , X , and X are the generalized displacement, velocity, and acceleration, respectively; M , C , and K are the system mass, damping, and stiffness matrices, respectively; P is the generalized load matrix. Expansion of Eq. (5) is shown as follows: We can solve Eq. (6) using a new rapid display integration method introduced by Zhai [9] without solving the high-order algebraic equations in the integration process. The method proves to be fast, and accurate, and is especially suitable for solving large-scale engineering dynamics problems. 3. Left-right decoupling simulation of levitation chassis Anti-roll constraint parameters of levitation chassis ( Kb , Cb ) are unique and important suspension parameters of maglev systems, the value of which is crucial in the right-left decoupling of the chassis because too large or small parameters will cause an unstable rolling motion. Left-right decoupling requires that anti-roll constraints have damping effects when the levitation chassis module on one side is subjected to an external disturbance, and that the v (...truncated)