2(8), 2017

Kim K. I., Kim K. K.
Emperor Alexander I Petersburg State Transport
University(St. Petersburg, Russia)


This paper is devoted to the development of the suspensionsystem for the high-speed transport of a type hyper loop. This systemconsists of a continuous longitudinal non-magnetic electroconductivestrip (μ and σ are the strip permeability and conductivity(μ = μ0 = 4π×10-7 H/m)), which are placed in the lower part of the pipe,and the vehicle superconducting solenoids. It is possible to use astructure of permanent magnets instead of superconducting solenoids(2a×2b are the solenoid dimensions).
These systems have a large efficiency, high economicalefficiency and the better weight characteristics. This paper deals with
the problem of the optimization of geometrical parameters for thesuspension system and gives some recommendations for the choiceand definition of these parameters.
The configuration of a superconducting solenoid can bedifferent, however, the better form of the solenoid is a rectangular onefor the fixed width of a strip (where c and d are the strip thickness andthe width).
In the case of the high-speed tube transport the strip must benarrow with a rectangular cross-section.
The calculations showed:
1. The end effects caused by the limitation of the strip widthlead to the change of the electromagnetic drag and suspension forces.When the strip width is less than c1 (c1 depends on the clearance) theelectromagnetic forces are smaller than the corresponding forces ofthe infinitely wide strip. When the strip width is more than c1 thesituation is opposite. At c ≥2a<1+5a(a+h)> the strip width doesntinfluence on the electromagnetic forces. h is the suspension heightabove the strip.
2. The change of the suspension and drag forces withchanging the strip thickness occurs in the opposite direction. In
comparison with the case of an infinitely thick strip the suspensionforce decreases but the drag force increases. For solenoids with a high levitation quality more than 60 at the speeds more than 50 m/s thedepth of the field penetration is equal to 0.05 m.
3. With the increasing of the solenoid displacement ε (ε isthe solenoid displacement from the strip axis) until its value remainsmoderate (ε*= 2ε/c-2a <0.8), the suspension and drag forces changebut a little while the lateral force grows rapidly. In this area the lateralforce changes with the displacement due to the law which is close tothe rectilinear law.
4. The problem of the choice of the strip thickness may bepresented as the extremal problem of this kind:
Levitation force → max, Drag force → min, v=v0
(v0 is the cruising speed).

The problem of the choice of the strip width is reduced to theevaluation of this parameter at the given values of εmax and (T/L)max.
5. The magnetic interaction of solenoids leads to the changeof the suspension and drag forces. The levitation system is in the betterconditions than the traction one, the interaction between solenoids canbe used to decrease the drag force in comparison with the case ofmagnetically isolated solenoids. It is possible to provide if thesolenoid currents circulate in the same direction.
6. At the given suspension force the minimum drag force isachieved when the solenoid has an elongated rectangular form. Atachieving the same suspension force with the help of magneticallyinteracting solenoids (in case when the solenoids are not far from eachother) the drag force can be reduced to the value corresponding to thedrag force which is peculiar for a single solenoid. The replacing of asingle solenoid by a solenoid system with effective using theirmagnetic interaction to decrease the drag force we can consider as amethod to improve the reliability without energy losses.
7. We can assume that the levitation system of a vehicle ofHyper Loop will be consisted of four solenoid groups. Each group willbe consisted of two or three solenoids. To reduce the drag force thecurrents in these coils must flow in the same direction and the distancebetween the adjacent solenoids should be minimal.

Information of authors:
Konstantin Ivanovich Kim, kimkk@inbox.ru
Konstantin Konstantinovich Kim, kimkk@inbox.ru