SECTION II
It is known that electromagnetic suspension produces contrarily directed attraction forces of the levitator’s magnets to right- and left-side stator’s rails. At the lateral shift the difference of these forces produces a destabilizing force tending to attract the vehicle to a core. Because of the great mass of the vehicle a servo control system manages to change periodically the values of currents in the right- and left-side electromagnets thus maintaining oscillating conditions of the vehicle in the air gap between cores. However, at any malfunction of the servo control system the vehicle will be attracted to a core which will lead to a disaster. This is an incurable disadvantage of the electromagnetic suspension.
Superconductive magnets moving along conductive plates are capable of producing stabilizing forces. This was the reason for their being recommended for electrodynamic suspension despite of the fact that other their characteristics are not compatible with the requirements for public transportation. Later it was found out stiffness of the stabilizing forces turned out to be far less than necessary: 3.5×107 N/m. To obtain an internal stabilizing force of sufficient stiffness, superconductive magnets with mmf at least an order higher than in those currently employed should be utilized. But utilization of such strong magnets in a transportation system causes virtually non- resolvable problems arising from insufficient magnet durability, and an unacceptably intense magnetic field penetrating the passenger salon.
Magneto-dynamic suspension which employs permanent magnets is a conservative system, i.e. the one that preserves its magnetic energy [1]. Its peculiarity is that two of its parts - the stator and the levitator - are separated in space, interacting with each other through magnetic field.
The internal forces in a conservative system are derivatives of potential energy with respect to coordinates of the shift between its parts. In the absence of external forces, the parts of the conservative system tend to reach a mutual position in which the system potential energy is reduced. Therefore, if both the levitator the vehicle are in a state of stable equilibrium (i.e. all internal forces turn into zero) without touching the guideway surface, it can be said that the magnetic suspension represents a stable conservative system with its potential energy having a local minimum (not coinciding with the guideway surfaces). In this case, any shift of the vehicle from the equilibrium position under pressure of an external force instantly produces an internal force tending to bring the vehicle back to equilibrium, since in the vicinity of the minimum of potential energy its derivatives (i.e., internal forces) along any direction are negative. Hence, ensuring stable equilibrium of a flying vehicle along the whole length of its track is sufficient for achieving self-regulation.
Self-regulating permanent magnet linear motor with extended poles
The vehicle speed should be lowered on curves in order to reduce a centrifugal force to a permissible value, then increased again and so on. Simultaneously, the propulsion force should vary in accordance with the speed: increase during vehicle acceleration and guideway ascents and reduce during vehicle deceleration and guideway descents. A Propulsion motor should also respond to air resistance which grows proportionally to the square of the vehicle speed. In other words, the Propulsion Motor has to work according to a precise program. It is different for each guideway part and is the same for each next vehicle passing the same guideway point.
Maglev vehicles will consume energy from a stationary source powering a propulsion motor’s stator winding.
The three-phase sinusoidal current produces a current wave in transverse segments of the winding turns. The current wave travels along the winding with a velocity proportional to the current frequency and the length of the winding turns. The magnetic field of the traveling wave coheres with rotor’s magnet field and propels the vehicle.
Rotation speed in an ordinary synchronous motor’s rotor can be regulated by changing the frequency of powering current. In addition, the unfolded winding of a linear motor makes it possible to regulate the traveling wave velocity by changing the length of winding turns. Consequently, at constant frequency it is possible to compose a strict program for regulation of the current traveling wave velocity by means of non-uniform distribution of the stator’s winding turn length along the assigned track .
The propulsion force of the propulsion motor is proportional to the product of the magnetic flux of the rotor’s poles and the current in the winding turns. The design of unfolded rotor poles allows changing the magnets’ length proportionate to the stator’s winding turns length during the vehicle is passing by at the moment. As the result, the propulsion force will grow proportionally to vehicle speed.
Forces resisting the vehicle’s motion grow as its speed grows. If their sum exceeds the propelling force then the rotor will fall out synchronism and PM switches off. Thus, the distribution of the speed along the guideway should be executed in such a fashion that the propulsion force always exceeds the total sum of the resistance forces along the whole guideway. This is a necessary condition for the stable functioning of the propulsion motor.
Forces acting on the vehicle depend on values of its speed and acceleration. Expressing all forces (including the propulsion force) in terms of lengths of the winding turns (i.e., vehicle speed) and equating them ,according to the third Newton’s law, to zero, we obtain a differential equation with respect to the winding turn lengths. Solving this equation we find the distribution of the stator’s winding turn lengths and cross-sections, and also the distribution of propulsion forces. Then we can find the capacities of all substations corresponding to the propulsion forces.
Embodying these ideas in the design of propulsion motor makes self-regulation of the vehicle speed and propulsion force of the motor possible with stability condition fulfilled in every point of the track at minimal power of the installed equipment.
In the propulsion motors of the existing Maglev the propulsion forces as well as speed are regulated by the frequency and value of current. The stator winding is powered according to a scheme that employs the following components:
- a high voltage transmission line of commercial frequency;
- step-down transformer substations installed along the stator winding parts;
- electronic alternative-to-direct-current converters;
- electronic inverters of direct current in three-phase alternating current of regulated frequency, capacity, and voltage;
- servo control systems to monitor each vehicle along the whole its track and controlling electronic converters and inverters by means of radio transmission.
The last three points of the above scheme are responsible for performing the motor’s working function of speed regulation for each vehicle along the entire guideway. This leads totremendous complication of power system and lowering its reliability.