energies Article Capsule Vehicle Dynamics Based on Levitation Coil Design Using Equivalent Model of a Sidewall Electrodynamic Suspension System Ranhee Yoon 1,2 , Birhan Abebaw Negash 1,2 , Wonhee You 2, * , Jungyoul Lim 2 , Jinho Lee 2 , Changyoung Lee 2 and Kwansup Lee 2   Citation: Yoon, R.; Negash, B.A.; You, W.; Lim, J.; Lee, J.; Lee, C.; Lee, K. Capsule Vehicle Dynamics Based on Levitation Coil Design Using Equivalent Model of a Sidewall Electrodynamic Suspension System. Energies 2021, 14, 4979. https:// doi.org/10.3390/en14164979 Academic Editor: Chunhua Liu Received: 9 July 2021 Accepted: 10 August 2021 Published: 13 August 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Transportation System Engineering, Korea Railroad Research Institute Campus, University of Science and Technology, Uiwang-si 16105, Gyeonggi-do, Korea; rhyoon3@krri.re.kr (R.Y.); birhanab@krri.re.kr (B.A.N.) 2 New Transportation Innovation Research Centre, Korea Railroad Research Institute, Uiwang-si 16105, Gyeonggi-do, Korea; jlim@krri.re.kr (J.L.); jinholee@krri.re.kr (J.L.); cylee@krri.re.kr (C.L.); kslee@krri.re.kr (K.L.) * Correspondence: whyou@krri.re.kr Abstract: A levitation system based on sidewall electrodynamic suspension (EDS) is considered for a capsule vehicle, which is a next-generation high-speed transportation system currently being studied. This levitation system does not require controlling of the gap between the guideway and the vehicle on which the superconducting electromagnet is mounted. However, when the vehicle is operated in a levitated state, the ride comfort is worse than that of the levitation system based on electromagnetic suspension (EMS), making it necessary to develop methods that can ensure good riding comfort. In addition, because the EDS system is complex and nonlinear with a combination of electromagnetics and mechanical dynamics, it is complicated to analyze the dynamic characteristics of the capsule vehicle, and the corresponding numerical analysis is time-consuming. Therefore, to easily understand the running dynamics of a capsule vehicle in the sidewall EMS system, the magnetic suspension characteristics corresponding to the primary suspension are simply modeled by considering the levitation stiffness in the vertical direction and the guidance stiffness in the lateral direction, similar to that in the case of the mechanical suspension. In this study, mathematical models of the levitation and guidance stiffnesses with respect to the speed and position of a vehicle body running at high speeds in a levitated state in the sidewall EDS system were derived for three design proposals of the levitation coil. The dynamic behavior of the vehicle based on the three design proposals was investigated by simulating a capsule vehicle model with 15 degrees of freedom. Keywords: capsule vehicle; electrodynamic suspension; levitation stiffness; guidance stiffness; vehicle dynamics 1. Introduction One of the recently developed transportation systems is the capsule train system [1–3]. This system has a capsule vehicle equipped with a superconducting magnet that enables it to move in a tube at an ultra-high speed of 1000 km/h. There are two types of magnetic levitation systems [4–6]: electromagnetic suspension (EMS) [7,8] and electrodynamic sus- pension (EDS) [9–11]. As shown in Figure 1a, in the case of EMS, the electromagnet of the vehicle is located under the magnetic material of the guideway and generates a levitation force through the attraction between the two. The guidance force is generated through the magnetic material and an electromagnet attached to the side of the guideway and the bogie. EDS is illustrated in Figure 1b; when the vehicle with electromagnets attached to the bottom or side drives along the guideway with a levitation coil installed over a certain speed, levitation force and guidance force are generated through the repulsive force. Unlike Energies 2021, 14, 4979. https://doi.org/10.3390/en14164979 https://www.mdpi.com/journal/energies