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CHAPTER 4. APPLICATION OF PERMANENT MAGNETS FOR FLYING MAGNETIC SYSTEMS
4.1 Amlev – A self-regulating version of Maglev 4.1-1 Magneto-dynamic suspension (MDS) for Amlev. An Amlev vehicle should fly at high speed (up to 150 m/s in the open air and up to 300 m/s in the tunnel with vacuum) separated from its a guideway by a tiny air gap (less than 0.01m.). The vehicle itself carries its magnetic field sources on board. Vehicular speed is determined by the shape of the track and the distribution of stop stations. At the high speed of the Amlev vehicle air resistance forces are measured in tons. To overcome these the vehicle is supplied with a propulsion motor, which must consume megawatts of power transferred through the air gap. In addition, a flying vehicle is affected by such external forces as gravity, lateral wind pressure and considerable centrifugal forces on curves. All these forces, except for gravity, may act unexpectedly and vary considerably in strength. To balance them the vehicle is supplied with a magnetic suspension capable of producing internal magnetic forces. At the same time the vehicle must strictly follow its projected trajectory and fly at an assigned speed. Deviation of a magnetically suspended vehicle from its track even by 0.01m leads to disaster. Under these super strenuous conditions control of vehicle speed and its deviations from the guideway pose the following main problems:
Self-regulation of both Magnetic suspension (MDS) and Propulsion motor (PMLM) would obviously be an optimal solution. Self-regulation for Maglev means that it should be capable of instant and faultless reaction to any deflection of the vehicle speed from its given value and any deviation from its position on a projected trajectory by producing internal magnetic stabilizing forces sufficient to eliminate such variations. A new type of Maglev – Amlev proposed here is based on permanent magnets and steel cores and utilizes the most intensive way of producing magnetic forces to directly perform all operational functions. The unique peculiarity of Amlev is its self-regulation. The Amlev vehicle like a living creature flies with alternating speed (20 ≤ Vv ≤ 150 m/s ) on a curly trajectory –guideway (that is preset by preliminary calculation) without a man or computer control. During its flight any deviation from the preset trajectory ( δ≥0.001m) or its sped Vv (x) from the given value (caused by external forces) instantly and flawlessly produce internal forces that return it back to the previous trajectory and its speed to the value that is preset by the stator winding turn length of the permanent magnet linear motor (PMLM). The Amlev vehicle flies suspended in the magnetic field produced by permanent magnets of its levitator. The air gap g between the levitator’s magnet poles and stator’s steel core does not exceed 0.01 m. Under these conditions it is impossible to control a vehicle manually. Regarding to an automatic control it is fraught with risk for passengers’ life though possibility of malfunctions. For the first time ever the peculiarities of physical processes and their interaction in MDS and PMLM are employed for Amlev self-regulation with the requirement that its vehicle moves with speed Vv >20 m/s . Lets outline them:
It is relevant to remind that “potential” energy is a part of energy of MDS magnetic field that can not be transformed unto kinetic one because of rigid constrains made separately between the levitator’s magnets and between stator’s magnetized cores. Figures 2.5, 2.9 and 2.10 show a structure of the levitator unit: four rows of permanent magnets Crumax 355 with alternating polarity are rigidly affixed to a long steel strip (steel insert). Together they form an assembly of quadrupoles from both sides of the insert with each turned by 180° with respect to an adjacent one. The length of the magnets is approximately 0.1m, thickness ≤ 0.03m, the width is 0.04 m, the distance between the adjacent magnets ≤ 0.01m. When the vehicle is immovable the qadrupoles’ magnets situated between laminated steel stator’s core magnetize them producing right and left magnetic fluxes - Ψ0R and Ψ0L respectively. The fluxes are closed through core backs and covering them aluminum screens forming right and left-hand circuit loops. In this case a considerable part of permanent magnetic flux – leakage flux Ψl escapes from the core backs through aluminum coating. Therefore core back saturation and magnetic reluctances are small. We will see absolutely different picture when the vehicle runs. Magnetic fluxes Ψ0R and Ψ0L become alternating. Moreover the bigger is the vehicular speed the bigger is frequency f of the fluxes . At the vehicular speed Vv =10m/s the traveling wave length gets the value λ =0.2 m , and frequency f = 50Hz. It is important to note that eddy-currents induced in the steel sheets of the laminated cores of thickness 3·10-4m made of electrical steel M5 are oriented contrarily and actually suppress the electrical part of electromagnetic wave (Fig.2.17) Conductivity of aluminum is known to be big enough σ= 3.7 ·107 [Ohm·m]. Then following Lentz Law of electromagnetic inertia of alternating leakage flux Ψl induces eddy-currents in aluminum screens with their own- counter magnetic flux −Ψl. This flux almost equals in value but is oriented oppositely to the leakage flux and therefore almost completely suppresses it thus creating electromagnet barrier. Knowing the value of the flux penetrating into core tips we can match the length and cross-section of the core backs, calculate magnetic flux density and determine specific magnetic reluctances ρ(B) employing the graph of Fig.2.7. The varying core back sizes, the length of hyperbola axes : α and b (Fig. 2.14) together with the air gap size we can select core back magnetic reluctances rfR and rfL in such manner to compensate changing the air gap magnetic reluctances rgR and rgL at the vehicle shift both to the left and to the right. In this case the difference between magnetic fluxes ΨwR – ΨwL =Fd / Cd and therefore the destabilizing force Fd = Fy (see expression 2-12) will reduce rapidly. In this case the condition of stability of MDS (2-6) is fulfilled. More than one hundred versions of the mathematical direct problem by varying values of the different parameters (see Paragraph 2.9) were calculated to solve this multi-parameters inverse problem assumed that (a) magnetic field in the air gap is plane-parallel and (b) the profile of the laminated core tips is hyperbolic. Such assumptions allow to apply analytical methods for calculation of stabilizing Fs and destabilizing Fd forces, to reduce significantly time and inaccuracy of the calculations. As a result we have managed to find the profile and size of the steel cores thus achieving considerable rigidness of the levitator stabilizing force that exceeds 3 ·107 N/m. After all the characteristics of any Maglev system is determined by its stability. It is known that stability of the system is produced and maintained by internal magnetic forces at levitator movement with speed 20 to 150 m/s.. Therefore it is necessary to know how to determine their values by calculations or measurements. To obtain internal forces is very complicated process because it suggests calculation of three-dimensioned magnetic field in inhomogeneous and non-linear medium with boundaries of figured profile. There is no analytical methods to find an exact solution for this problem. Numeric methods are not reliable because it may give an error 100% and more, i.e.., exceeded unknown quantity. To make precise measurements of the forces on flying model is very difficult because of hundreds of tests are required: at different speeds, at different gaps between levitator’s magnets and stator’s cores and also different shifts of the levitator from the set trajectory. That is why engineering design and experiments of Maglev (EDS and EMS) were carried out by “trial and error” methods. Development of their projects consumed dozens of years, required big collective bodies of designers, experiments required full-scale modeling of a vehicle and fragments of guideway .for accelerating and decelerating of the vehicle. It is no surprising that EDS and EMS projects were time consuming and very expensive. In Amlev we managed to calculate internal magnetic forces much more precisely. To prove this in addition we made an engineering design of unique stationary model were it is possible to make measurements of internal magnetic forces at different speeds, different gaps between levitator’s magnets and stator’s cores and different shifts of the levitator from the set trajectory. Its engineering assembly is presented in paragraph 2.3 and Fig.2.27. Model is made as a rotating motor. But its stator and rotor are unusual: Amlev guideway is rolled up into rotating ring made in the form aluminum wheel with .laminated steel similar to guideway stator cores. The wheel is rotated by DC motor. The steel non-rotating ring with permanent magnets situated on its internal surface, performs the functions of levitator. When the wheel is rotating the physical process occur inhere which are similar to those occurring in the real Amlev guideway stator and internal magnetic forces appear which are proportional those in MDS at a vehicle movement. The cost of such a model incommensurably lower than in full-scale models of EMS and EDS and accuracy of measurements is incommensurably higher since these are carried out on the immovable ring (levitator) and it is possible to measure accurately the forces at any rotation wheel speed of varying magnet’s lengths and shifts of the levitator. To transform rotation speed into traveling speed of the vehicle and calculate the speed acting on the whole vehicle is not expected to be difficult. Amlev consists of three parts essentially different from those of EMS and EDS:
The sources of magnetic field are rare-earth permanent magnets Crumax and steel cores. Amlev stator winding is powered by sinusoidal current of constant frequency. Let us consider each part separately. MDS must ensure stable equilibrium of two bodies only: a flying levitator and an immovable stator. The levitator magnets are fixed rigidly on a vehicle and together with it form a solid body of cylindrical shape. The solid body summarizes all forces applied to it in total equivalent force. Considering this peculiarity of a solid body when proving Lagrange‑Dirichlet theorem, a real‑conservative system comprising bodies of different configurations was substituted by system of mass points. With this approach real distribution of forces acting on each body was not considered but instead was substituted by an equivalent force. Therefore in order to apply Lagrange‑Dirichlet theorem for creating a stable suspension of a Maglev vehicle, the equivalent force must be expanded into components in such a way that they satisfy all necessary equations of the vehicle's equilibrium. In order to give the flying vehicle maximum stability the torques of these forces must be as big as possible. For this purpose the magnets on the vehicle must be fixed to its bottom and close to its walls along the entire body. Correspondingly, the stator cores must be located along the guideway, be parallel to flying magnets and within a small distance from them. It directly follows from the Lagrange-Dirichlet theorem [1] that a self-regulating stable MS can be built only from components capable of producing magnetic stabilizing forces F5 (δ) proportional to the shift δ of the vehicle and directed opposite to it. A mechanical analogue of such component is a bow with resilient string. As it was demonstrated above, strong dependence of steel permeability on magnetic flux density makes it possible to build such components. The MDS system is shown in Fig. 2.24. It consists of six identical interconnected magnetic units. Each of them, in turn, consists of two parts: one movable and the other stationary (Fig.2.12). The movable part contains four permanent magnets of rectangular cross-section assembled in a quadrupole with the help of a steel insert. The immovable part consists of two laminated steel cores of unlimited length with C-shaped cross-section. Each core has a long back and two thickened unsaturated tips. The core backs are covered by aluminum screens. The cores are located mirror-symmetrically to each other and extended along the whole guideway. There is a constant air gap between the thickened tips pertaining to the right- and left-hand cores. The quadrupole is inserted in this air gap and can move freely within it in all directions. The guideway consists of a concrete foundation (channel) with fixed MDS unit’s steel cores (and also a stator winding of a propulsion motor) It shown in Fig.1.3. It is expedient to remind here that the unit forms a two-contour magnetic circuit (Fig.2.9) with the sources of mmf (permanent magnets) and magnetic reluctances, both linear (the distance between the steel insert and core tips) and non-linear (saturated steel core backs). Magnetic fluxes penetrating core tips produce forces attracting the quadrupole to the cores. A specific force acting on a unitary surface of unsaturated steel (core tip) is oriented perpendicularly to the surface and proportional to the square of magnetic flux density. Proceeding from this basis, it has been proven that:
The mode of the unit action is similar to a bow. Tubes of magnetic flux closing through air are resilient. They are permanently coupled with their source – permanent magnet – and are held by the ends of the steel cores. If the magnet shifts up or down, the flux tubes bend and stretch, thus creating a force opposing the shift, which grows as the shift increases. The peculiarity of the unit is that a quadrupole shift produces not only a destabilizing force but also a stabilizing force. The values of the forces Fd and Fs are proportional to the difference of magnetic fluxes, penetrating correspondingly:
The fluxes in the unit follow Ohm’s law for magnetic circuit. If the quadrupole is shifted to the right by a small lateral shift Δy then the right-hand air gaps and their reluctance are reduced, and the flux increases (at the left side everything is reversed). In this case parity of the fluxes is violated and destabilizing force Fd appears, attracting the quadrupole to the right-hand core tips. In this direction the equilibrium of the quadrupole is unstable. At a small vertical shift Δz of the quadrupole in a symmetrical plane with respect to the cores, parity of the fluxes penetrating into the right- and left-hand is retained, but their parts entering the upper and bottom halves of the core tip surfaces are redistributed. In this case a stabilizing force Fs appears, which is perpendicular to Fd and counteracts the vertical shift. In this direction the equilibrium of the quadrupole is stable. Hence, in the immediate vicinity [d] of the equilibrium the internal forces Fd and Fs of the unit can be expanded in a Maclaurin series and expressed by the product of the shift value and their stiffness (which are the derivatives of the forces with respect to the shift coordinate). At a longitudinal shift of the quadrupole the fluxes will not change and forces are not produced. In this direction the quadrupole is in indifferent equilibrium. The MDS stator consists of a concrete channel (Fig 1.3) having indefinite length. Six pairs of steel cores are affixed to its floor and sides in such a way that their symmetrical planes are reciprocally perpendicular. Outside the vehicle six quadrupoles are installed along the vehicle’s entire length: four of them (supporting quadrupoles) affixed to the vehicle’s bottom, the other two (guiding quadrupoles) are affixed to the vehicle’s walls - one on each side. The guiding quadrupoles are furnished with a pull-out mechanism capable to draw them away during vehicle motion. When the vehicle moves along the channel, the quadrupoles get inserted in air gaps between core tips of the corresponding pair of cores. When the units are assembled in such a way stabilizing forces of the supporting units compensate for destabilizing forces of the guiding units, and vise versa. It has been proven (2-6) that if the stiffness of the stabilizing force exceeds the stiffness of the destabilizing force (the condition of stability) in every single unit, the MDS is stable and self-regulating. This means that any small shift of the vehicle as well as its small turn result in an instantly arising internal force or torque stabilizing the vehicle. It follows from the stability condition (2-6) that MDS should have such units where a lateral shift produces an internal destabilizing force as small as possible. Within the context of magnetic circuit, this means a slight dependence of the fluxes penetrating into the right- and left-hand core tip on the change of unit air gap reluctance at the lateral shift of the quadrupole. After all, a flux in a contour is determined by its total reluctance. Therefore, if non-linear magnetic reluctances (increasing with the growth of the flux) are included in the contour and connected in series with air gap reluctance, this stabilizes the total contour reluctance and reduces working flux dependence on the lateral shift (Fig. 2-15b). The steel core back included in the magnetic circuit (Fig.2.9) is a non-linear magnetic reluctance, which increases rapidly with the growth of its magnetic flux. However, there are no natural insulators for magnetic flux. When a steel core back becomes saturated its magnetic reluctance grows, forcing magnetic flux to flow out through its lateral surfaces. As a result the leakage flux reduces steel saturation level and its magnetic reluctance. This peculiarity of saturated steel makes it difficult to use it in magnetic circuits. Nevertheless, following the Lentz’s Law of electromagnetic inertia it possible to overcome this difficulty. If the long levitator magnets are cut into n equal parts, and each even part is turned by 180o (Fig.2.10), then during vehicle motion an alternating magnetic flux (including leakage flux) appears in the stator cores. Considering that the cores are made of thin laminated steel (Fig.2.17) eddy currents in each single sheet is oriented contrarily to each other and therefore compensate the electrical part of the traveling wave retaining only its magnetic part. Moreover, the lateral core surfaces are covered with an aluminum layer and the leakage flux induces eddy currents with the magnetic field that in accordance with the Lentz’s Law is oriented contrarily to the leakage flux. This means that an electromagnetic barrier appears, almost completely suppressing the leakage flux and maintaining core saturation at required level. In this case the stability condition is fulfilled. MDS is an example of a conservative system consisting of permanent magnets and steel cores covered by aluminum screens. Its potential energy has a local extremum (Fig.2.2). However, when the MDS levitator is at rest, its equilibrium is unstable because of in this case the screen does not work, leakage fluxes are not concentrated in the core back and Fd > Fs As a result, the extremum turns into a maximum. Fig.4.1 shows dependencies of stabilizing and destabilizing forces, their stiffness and also potential energy on the shift of the levitator: (a) when it is at rest (V=0), and (b) at its speed V>100m/s. As levitator speed increases, the energy maximum is depressed and then (at speed V>10 m/s) electro magnetic barrier arises on the core back surface and the extremum turns into a minimum (see Paragraph 2.8 for details). At vehicle speed >100 m/s the stiffness of the stabilizing force per vehicle length 20 m reaches 2·107 N/m. This essentially exceeds the stiffness of Maglev with EDS and means that at a lateral pressure of external force 3000 Kg on a vehicle, its shift does not exceed 2mm. The stabilizing force in Amlev is produced by interaction between surface currents on the permanent magnets lateral surfaces (mmf) and magnetization currents (of the same order) induced in the steel core tips.
This approximate evaluation is supported by exact analytical calculation made by the methods published in [11,13.14,16]. Solid lines in Fig.4.1 show dependencies of the stabilizing force Fvs(δ) and its stiffness F's(δ) and also destabilizing force Fvd(δ) on the shifts d of a flying vehicle at its speed V>100m/s. As core backs is being saturated the magnetic flux is reducing there together with reducing destabilized force Fvd.
The dotted line shows stabilizing F0s(d) and destabilizing F0d(d) forces in a resting vehicle (V=0). Exploiting saturation of steel core backs we can reduce the value of destabilizing force by up to 17 times. In this case the stabilizing force Fs is reduced up to 1.69 times. Six levitator’s units are coupled stiffly: four of these (supporting and guiding units) form two pairs where the units located reciprocally perpendicularly to each other (Figs.2.8 and 2.13) The other two (supporting units) compensate the vehicle weight. Therefore, in each pair at any shift d of the levitator the value of destabilizing force Fd of one unit is subtracted from the value of the stabilizing force Fs of another one and vice versa. At the same time the differences of these forces are summarized geometrically. At the speed V=0 the above difference of forces is negative. With the growth of the speed it reduces to zero and then changes the sign “– “ for “+” and grows. When levitator shift d is changed the vector tips of above differences form the cone -shaped surfaces of forces in the coordinate space [y, z, F] ( see again Fig.4.1). Thus, integrating the above differences of forces over direction of shifts we obtain a paraboloid of potential energy –energy surface in the vicinity of the MDS levitator equilibrium. Figs.4.1 and 2.2 show paraboloids of potential energy: P0- when the vehicle is at rest (V=0) – local maximum (in the bottom), and P- when the vehicle flies with the speed V>100m/s – local minimum (at the top). As the speed is growing the maximum of energy is getting flatter and then turns into minimum. For comparison the stabilizing force FsE and its stiffness F¢sE in the EDS are shown by dot-and dashed line in the same scale.
4.1-2 Self-regulating motor based on permanent magnets with extending poles (PMLM) for Amlev and Power system. Self- regulation of MDS system and high stiffness of its stabilizing magnetic forces ensuring a stable flight of a vehicle it a small gap allows to create a specific design of self-regulating permanent magnet linear synchronous motor (PMLM) for vehicle propulsion in high speed ground transportation systems. In Fig. 3.1 showing the general design of Amlev the PMLM is situated in the middle of the bottom part. Its design and mode of operation in detail are presented in Chapter III. In this chapter we will consider how it works for Amlev. As was said above, PMLM consists of two basic parts:
One can see from Fig.3.1 that the stator winding together with MDS supporting and guiding units’ cores are affixed to a concrete channel. They form a stationary part of Amlev. The PMLM rotor together with the MDS units’ levitators are installed on a vehicle. They form a movable part of Amlev. Let us explain the essences of main peculiarities of the PMLM designed for Amlev system.
A synchronizing device assembly designed for stepped changing the rotor pole length during vehicle motion by switching on/off (displacing down/up respectively) the corresponding units. Each device of the assembly adjusts the length of the rotor magnets to the corresponding winding turn length when the vehicle passing the corresponding stator’s section (acceleration, slopes, curvatures and etc). A synchronizing mechanism designed for smoothly changing the rotor pole pitch during the vehicle motion by drawing apart or together the rotor front and rear halves. This mechanism performs adjustment of the pole-pitch to the center of a half of traveling wave thus increasing magnetic flux and propulsion force. The rotor comprises mirror-symmetrical halves of a steel yoke inserted into a longitudinal slit on the vehicle bottom (see Fig.3.1) which are capable of moving apart and coming together along the slit and are operated by the above mentioned synchronizing mechanism. Each half has cells containing permanent magnets capable of moving upward and downward within the cells, each being operated by a synchronizing device. All magnets are of rectangular form and have pole shoes. In different halves magnets have opposite polarities. The purpose of automatic joint work of the adjusting assembly is to ensure coincidence of the rotor’s magnet poles with central parts of the traveling wave halves where linear current density (and, consequently, the propulsion force) is the greatest. 4 A specific design of the stator propulsion winding scheme ( see Paragraph 3.3, Figs.3.2, 3.4; 3.6, 3.7, 3.8, 3.9, 3.10, 3.11) The theoretical analysis and calculations have been done to obtain the dependencies of all forces acting on the vehicle on its speed and then to find the distribution of the winding turn length and cross-section along the whole track ( see Paragraphs 3,4, 3.5, 3.6). As shown in Fig. 3.4 the stator has a common concrete beam with three toothed holders strengthening transverse segments of the turns of the three-phase winding along the whole stator length. When the propulsion winding is coupled to an electric generator, a traveling current wave is produced in the transverse segments of the winding turns. The PMLM stator winding is cut into fragments with each powered separately by a step-down transformer at the moment when a vehicle is passing it by. The peculiarity of the winding is that the current in the bus bars placed into the slots of even numbers of each phase is directed from the starting point of the winding fragment powered by a step-down feeding transformer towards its end. At the end of this fragment all four bus-bars are banded backwards and placed into the slots of odd numbers with current flowing back to the feeding transformer (Fig.3.11). As a result, in all eight transverse segments of the same phase (for example, phase “A” in Fig.3.8) the currents are summarized and produce a traveling current wave of velocity V. In the winding’s right- and left hand facing bars (Figs.3.4 and 3.6) the distribution of longitudinal currents travels with the same velocity but with phase shift equaled 90o. Their zero values coincide with the centers of the rotors poles. One can see from Fig. 3.11 that in spite of currents in two halves of stator winding flow in opposite direction their traveling wave directions are the same. Therefore magnetic flux in any yoke cross-section is zero that allows to eliminate armature reaction (Fig.3.6). In spite of that the profile of the traveling current wave is not sinusoidal and varies in shape ( see Paragraph 3.3 and Fig.3.10 a and b) the value of the total current in the traveling wave does not vary during the motion (the maximum oscillations the propulsion current are ≤ 0.5% ). One of the most important characteristics of the propulsion winding is it has no steel parts along the guideway. Steel C-shaped yokes are installed on the rotor only (see Figs. 3.1 and 3.2). The ferromagnetic yoke in the PMLM considerably increase magnetic field intensity in the rotor working gap. However, the PMLM does not have drawbacks caused by ferromagnetic cores distributed along the whole guideway that takes place in the other types of linear synchronous motors. As a result:
5. The PMLM is self-regulating. (see Paragraph 3.1) The current wave traveling in the stator winding coheres with magnetic field produced by the rotor magnets and propels a vehicle (the maximum value of the propulsion force is determined by Lorenz force). The propulsion force should overcome the forces hindering the vehicle flight – resisting forces, such as: inertia on its acceleration parts, gravity on slopes, air resistance along the whole track. Resilience of flux pipes (lines of force) lays in the ground of self-regulation. During vehicular motion the resistance force (Fig.3.5) brakes the rotor and shifts its magnets back away from the current wave. But current of the traveling wave does not allow middle parts of the magnetic pipes to be displaced backwards together with the magnets, stretching and bending them. Summarized, the stretching forces produce the propulsion force proportional to displacement. The balance of the forces is restored and the rotor continues its motion with velocity V of the current wave. If the force resisting vehicle movement changes, the PMLM changes propulsion force, automatically maintaining rotor speed equal to the velocity of the traveling current wave. Consequently, the PMLM is self-regulating. It never falls out of synchronism. Eventually self-regulation in PMLM has two components. The main one is regulation of the speed and amplitude of the running current wave. It is provided by analytically calculated distribution of the length and cross-section of the winding turns at each track segment between two nearest stop stations. Additional component is self- regulation of the propulsion force that is secured by resilience of magnetic field lines within the working gap of the rotor. The Power System of Amlev is a three-phased system of constant frequency f=25Hz. A high voltage line extending along the Amlev track supplies power to step-down transformers feeding each part of the stator’s propulsion winding. A vehicle passing a certain part of the track switches on or off the next winding part. Now we will consider how a vehicle departs from a stop station and how to return a suspended vehicle to the nearest stop station in case of emergency. A vehicle is supplied with special side- wall pullout wheels supporting it during its motion on the start section (when it begins departure from a stop station) until its velocity reaches the value V0= 25 m/s, sufficient to achieve stability. The vehicle can be accelerated by induction motors (with pullout contacts) rotating the pullout supporting wheels. To power the induction motors three-phased contact bars are laid along the guideway walls. In addition special rails made of plastic or stiff rubber are fixed along the guideway walls where the pullout wheels may roll. The Amlev vehicles may start from stop station with interval 3 to 5 minutes. It opens possibility for reducing their dimensions and passenger capacity that may, in turn, reduce considerably expenses for their development and maintenance. In case of power outage the propulsion force vanishes and the vehicle decelerates its flight. When the speed approaches 40 m/sec the starting wheels pull out fixing the vehicle to the track.. Simultaneously the pull-out mechanism draws out the guiding quadrupoles from the guiding units. As a result the vehicle suspends on supporting units and stops. To deliver the suspended vehicle to a nearest stop station power will be delivered to the mentioned contact bars, the induction motors start rotating the supporting wheels and move the vehicle to a nearest stop station. It is important to emphasize in conclusion the original features of Amlev:
4.2 Simplified variant of Amlev: S-Amlev 4.2-1 Horizontal Wheels Assembly for Magnetic Levitation of S-Amlev Unlike MDS presented in the previous paragraph the Magnetic Levitation system with Horizontal Wheels Assembly is designed in such a way that it is supplied by pairs of horizontal wheels substituting for MDS guiding units. This variant exploits the same Permanent Magnet Linear Motor The main peculiarity of the wheel assembly is that wheels of each pair roll both on a side wall of the guiding channel in special paths.
For high speed ground transportation with speed not exceeding 150 m/s (540 km/h) it is expedient to employ a simplified version of levitation based on permanent magnets and steel cores that contains only supporting units together with guiding horizontal wheels performing function of guiding units (Fig.4.4). Constant distance Wc between concrete walls of the guideway and big curvature radius of the vehicle trajectory (Rg >1000 m) make it possible to ensure reliable lateral stabilization of the vehicle with the help of the horizontal wheels rolling freely in separate narrow guiding paths affixed to guideway walls. Wheel shafts are affixed rigidly to the vehicle metallic floor. The wheels are set down on the shafts with the help of rolling bearings. The shaft centers of each pair should lay on the same line perpendicular to the vehicle track. Diameters of all wheels are less than a half distance between their paths D = Wc /2 (Fig.4.3) .
The wheels are situated by two pairs ahead and behind of permanent magnet linear propulsion motor. There is a slot in the vehicle walls close to its floor for each wheel letting its rim to touch the guiding path. As a result the horizontal wheels compensate lateral forces acting on the flying vehicle (including the destabilizing force of the supporting units) by reaction of guideway channel concrete walls.
The wheels should be durable and light at the same time. Therefore they are made of duralumin that has tension strength σ0≥ 44 to 49 Kg/mm2. For flawless work of such suspension it is necessary to make distance Wc constant along the entire guideway with accuracy not exceeding ± 1.0 mm. Both wheels are identical of radius rr< Wc /2, rim thickness is hr = 0.05 m, rim width is qr = 0.1m, and rim cross-section is Sr= hr∙ qr=50 cm2. Duralumin specific gravity is dα=2.79 kG /dm3. If Wc= 3m, then rr<0.75m. When vehicle speed is maximum V=150m/s each wheel rim rolls with the same speed. Then centrifugal force Fc appears striving to tear the wheel rim into two equal halves along two its cross-sections along its diameter. Let us find the centrifugal force assuming Wc= 3 m:
where
Assuming V=150m/s and substituting all the values in formula (4.2-1) we obtain Fc(150) ≈57∙1502/0.7 ≈ 183.22∙104N ≈ 186.8 t Mechanical tension σ in each rim cross-section is determined as
because breaking the rim is possible in diametrically opposite cross-sections, At V≤ 150 m/s σ= 18.7 kG / mm2 < σ0 =44 to 49, where σ0 is permissible tension for duralumin. Consequently the horizontal wheel are capable to ensure safe work of magnetic suspension at vehicle speed V≤ 150 m/s = 540 km/h. The horizontal wheels limit the value of lateral shift δh of a vehicle by permissible value of guideway width margin Wc= 3m ± 1mm , thus reducing maximal admissible value of the destabilizing force of the supporting units Fdm ≤F’d ·103 m. In addition the fact that levitator’s magnets may shift just in one direction (downwards), makes it possible to increase the stabilizing (levitation) force of the units by varying profile of their core tip cross-section. If we make the lower part of the surface of each core tip horizontally flat then we change the orientation of the forces attracting the levitator’s magnets to this parts of the core tips (Fig.4.5). In this case the lines of force become vertically oriented and thus penetrate into the flat parts bottom-up and consequently the value of the destabilizing forces will reduce considerably.
4.2-2 Supporting Units for S-Amlev. A supporting unit with core tips that have the best profile for S-Amlev are shown in Fig. 4.5. The top section of the core tip has a hyperbolic profile, and the bottom section is flat. The flat side of the core tips produces a vertical levitating (stabilizing) force. The horizontal destabilizing force decreases. Considering that saturation of the core backs can reduce the destabilizing force by an order of magnitude, the resulting destabilizing force can be negligibly small.
4.2-3 Start of a vehicle from a stop station and its return to a nearest one in case of emergency. Start of a vehicle from a stop station can be performed by a motor rotating the horizontal wheels. The energy required for accelerating a vehicle of weight 20t to speed V0 =10m/s for 20 seconds is
Hence power of the motor is
Consequently it is sufficient to install one motor of power 15 kW per each pair of the horizontal wheels. In case of power outage of high voltage these motors can be utilized for returning the vehicle to the nearest stop station. . In this case contact wires of low voltage should be extended in the guideway channel between stop stations.
4.2-4 Conclusions. Simplified Amlev is much less expensive that Amlev itself because it does not have guiding units and construction of its supporting units is much simpler than those of Amlev. In addition, the technology of manufacturing aluminum screens is much simpler and cheaper. S. Amlev also has indisputable advantages over high speed railway transportation. Let us describe them. The high speed rail transportation can achieve a speed of up to 400 km/h. The speed limit is dictated by the reliability of contact devices powering the vehicle and also the wear on its wheels. In contrast, the power supply in S. Amlev is contactless. Its powering is performed by Lorentz force via air gap. In addition its horizontal wheels do not carry the weight of the vehicle. They only compensate the horizontal destabilizing force that can be reduced by 8 to 10 times less than vehicle’s weight. (See 4.2-2). Therefore the horizontal wheels are much lighter than those in high speed rail transportation. The evaluation presented in 4.1-1 shows that S. Amlev can achieve a speed of up to 540 km/h. The proposed design of Amlev and S. Amlev vehicles and the linear synchronous motor PMLM adjusted to the these systems was considered for 100 passengers per vehicle and the weight of loaded vehicle at approximately 25t at frequency of AC powering current of 25hz. It is possible to build the vehicle of less size and weight, for instance for 50 passengers per vehicle. In that case, if the air resistance was reduced by improving the vehicle shape, then it would be possible to considerably reduce the maximum propulsion force of the PMLM, the length of the traveling wave λ of the propelling current, and thus to increase the current frequency up to standard hertz frequency of 50 – 60 Hz.
4.3 Gas-Gun Accelerator based on passive magneto-dynamic suspension 4.3-1 Description of Gas-Gun Accelerator design. In recent years space flight organization are researching possibilities for using passive levitation systems combined with combustive gases for acceleration and repeated launching of heavy objects into outer space. We propose to use Magneto-dynamic suspension system – MDS for this purpose. The object is stably suspended in magnetic field and flies inside a lunch tube with acceleration not touching the tube’s walls that is without friction. (Fig.4.13). The launching tube should be built along the west side of a mountain with angle of declination 45° or more (Fig.4.14). The length of the track is 3 miles or more. It is known that the best condition for lunching is when the lunching assembly is located as close to the equator as possible. Magneto-dynamic suspension system in detail is presented in Chapter II. In this Paragraph we will just remind about some of its essentials. Magnetic suspension utilizes permanent magnets, steel cores and rigid constrains. It is a conservative system, i.e. one that conserves its potential magnetic energy. Two of its parts - the stator and the levitator - are separated in space, interacting with one another through the magnetic field. Internal forces in a conservative system are derivatives of potential magnetic energy with respect to coordinates of the shift between its parts. In MDS the levitator's magnets are affixed rigidly to an object and together with it form a free solid body. As distinguished from any regular function that has a minimum just in one point, in our case the potential energy of MS has a minimum in the whole volume of the levitator body. Because of rigid constrains a shift of any point of a solid body leads to the same shifts of the rest of the points with the stabilizing force as a function of the shift having the same value and direction in all the points. Therefore the levitator-object assembly may be substituted by a massive point Q coinciding with equilibrium (as if we have compressed the real body in a point). With this approach function of potential energy in the vicinity of Q looks like regular function of two variables (y, z) (See Paragraph 2.1)
Speaking of Gas Gun Acceleration system we must ensure stable equilibrium of two bodies only: an immovable stator (tube) and a flying object with a levitator. To attain this it is necessary to situate levitator magnets and stator cores in a specific manner. Interaction between the levitator magnets and stator steel cores produces stabilizing forces. To give the flying vehicle maximum stability the torques of these forces must be as big as possible. Because the torque of the couple of forces is proportional to a distance between these forces the magnets on the cylindrical object must be attached to it on both sides of its diameter along the entire body (Fig. 4.13) Correspondingly, the stator cores must be located along the launching tube and be parallel to flying magnets within a small distance from them. The stator cores together with two sets of magnets located in series on the object make up three magnetic devices intended to produce stabilizing forces. In this case the object has one degree of freedom directed along the Axis OX. The other shifts and turns should produce stabilizing forces and torques. The shapes of both MDS magnets and cores must be cylindrical with their generatrices parallel to the Axis OX of the launching tube. The equilibrium of the levitator flying along the Axis OX supposes that the shape of levitator and stator parts are symmetrical with respect to the plane XOZ. The levitator together with the object are in homogenous gravity. Therefore in addition MDS should compensate its weight.
Fig.4.7 Gas-Gun Accelerator – Lateral view of a launching tube segment
It is shown Paragraph 2.2 how to build a stable MDS. The design of an MDS unit and its whole assemble is shown in Paragraph 2.3 ( See Figs. 2.12 and 2.13). In order to compensate the object weight it is necessary to add one more supporting unit to each pair of devices (Fig. 4.8).
4.3-2 Gas-Gun operation. Like in an ordinary cannon, a heavy cylindrical object here is moved and accelerated along the launch tube by gas under high pressure. The latest developments in Gas Gun design employ the use of continuous injection of combustive gas through multiple ports along thе tube as the object passes and burn gas in the space behind the object. This reduces initial high pressure requirements, lowers peak acceleration values for the object and maintains a more constant base pressure. Human-piloted object requirement for modest acceleration (<3g) can be satisfied by building a long acceleration tubs of large diameter.
To protect the magnets of quadrupoles from overheating by burning gases, the MDS stator is made of two lateral cameras (Fig.4.6) of the same length as the launch tube. Three pairs of steel cores are attached to each camera in such a way that their symmetrical planes are reciprocally perpendicular. Accordingly outside the object three holders with quadrupoles are installed on both its sides along its entire length (Fig.4.8) . Each holder has support and guide quadrupoles affixed to it. The launch tube itself is cut into two halves, upper and lower, by two opposite slits. Both parts are joined on each side by the cameras. When the object moves in the launch tube the holders with levitator magnets move inside the cameras through the slits between the two parts of the tube.
Heavy object launching begins on a start segment before entering the launch tube. This segment has only stator cores of support units and rails for an electric locomotive that pushes a platform with the object. The function of guiding units is performed by a platform with horizontal wheels rolling along side rails fixed on the ground. The electric locomotive accelerates the object to the speed of V ≥ 40m/sec and stops with the platform at the entrance to the tube. Inertia pushes the object into the tube where its flight quickly stabilized due to the impact of the cores of the guiding units. At this point the entrance into the tube is locked airtight behind the object, and a combustive mix of gases is injected into the tube across the tube wall through sprayers. Its burning creates excessive pressure DP that accelerates the object. Moving forward the object turns on the sprayers it passes by. Productivity of the sprayers has to increase proportionally to increase of object speed so that the pressure behind it would be maintained constant. When the object reaches its defined speed Vt its rocket engine starts, the object is released from the levitator and flies out into the sky. Then it extends its side wings and increasing the angle between its trajectory and horizon it moves into the outer space. In order to reduce penetration of combustive gases into the gap between the object surface and internal surface of the lunch tube a series of circular slots are supposed to be cut on the tail part of cylindrical surface of the object (Fig.4.16) similar to that usually made on high pressure steam turbine’s shafts.
4.3-3 Evaluation of Gas-Gun Accelerator’s parameters To show the advantages of MDS levitation system applied for launching heavy objects we will evaluate parameters and capabilities of a Gas -Gun Accelerator. Let the object mass M = 105 kg = 100 t, its outer surface radius Rp = 2.0 m, its length lp= 40 m, the angle between the launch tube and horizon q = 45°, sin q = 0. 7071. Let’s assume that constant excessive pressure DP = 200 atm ≈ 200 kg/cm2 is behind the object. Assuming that speed of the object coming out of the launch tube Vt = 1500 m/sec, we can determine tube length, its material and weight. Propulsion force Fp = pRp2 × DP » 25,132.7 t should overcome the inertia of the object Fi =M∙a (a is acceleration) and the force of gravity Fg =M∙ g∙sinq = 693.665t (g » 9.81m/s2). The propulsion force can be determined as Fp = M∙a + M∙g∙ sin q . From this expression we will find a = Fp /M – g∙ sin q = 244.383 m/s2. Hence the time of acceleration of the object inside the tube is tt = Vt /a » 6.1379 s. The length of the launch tube is Lt = a ∙t2 / 2 » 4,600 m And therefore the height of the mountain is hm= Lt / √2 = 3,255m.
Now we will determine the force Fz trying to break a ring-shaped segment of the tube of length ΔL = 1 cm into two equal parts. Fz = ΔP ∙ΔL ∙2R1
∙ one side of the ring is affected by Fz /2 = 40,600 kg. Let us assume that thickness of the tube wall Δ = 4cm = 40 mm. Then the cross-section of the ring is Sr = ΔL. Δ= 400 mm2. Then tensile strength of the ring σ = Fz /2 / Sr = 40,600/400 =101.5 kg/mm2< 140 kg/mm2 , where 140 kg/mm2 is permissible specific tensile strength for alloyed steel (for example, chromo-cilico - mangenic). Hence the tensile strength is approximately one third lower than permissible limit and the launch tube can be made of rolled alloyed steel with thickness 40 mm. Steel specific gravity d = 7.8 g/стз, therefore the weight of the tube is W1 ≈ 2π∙R1 ∙Δ∙ d∙ Lt ≈ 18,321 t. the height of a mountain on the side where launching tube is placed h ≥ 3255 m.
4.3-4 Conclusions. The proposed project of Gas-Gun Accelerator is distinguished from the existing ones by that the heavy object flies inside a lunch tube without touching the tube’s internal walls that means without friction and so without its burning that is inevitable at such big speed and object’s mass. An assembly of Gas-Gun with MDS would allow repeated launching of heavy objects into space. It would also considerably reduce the cost of planned cosmic programs since in this case the energy of combustive gases are spent only for acceleration of the object’s mass that is dozen times less than the cost of rocket stages carrying fuel. All of the above allows concluding that choosing MDS has many advantages vs. EDS when considered for use in development of Gas Gun Accelerator for repeated launching of spacecrafts.
O1eg V. Tozoni, "New stable magnetodynamic suspension system", IEЕЕ Transactions on Magnetics., vol. 35, no 2 pp . 1047-1054, Marсh 1999. O1eg V. Tozoni, "Designing a Magnetodynamic Stab a Suspension System", IEEE Transactions on Magnetics, vol.35, No.5, pp. 42684274 , September. 1999. A.M. Lyapunоv, "Lectures in Theoretical Mechanics", Ukraine, Kiev, Naukova Durnka, 1982 , р.376-384. O1еg V. Tozoni "AMLEV — a self-regulating version of Maglev", IEЕЕ Transactions on Magnetics., vol. 37, no 6 рр . 3925-3933, November 2001. Oleg V. Tozoni, "Magnetodynamic levitation and stabilizing self-regulating system",U.S.Patent No 5,652,472, Jul. 1997. O.V. Tozoni "Method of secondary sources in electrical engineering", pp.8-14, Energy, Moscow, USSR, 1975 (Russian). Smirnov "Advanced mathematics course", vol.4, SPTTL, Moscow, 1953 (Russian) O.V. Tozoni "Mathematical Models for the evaluation of Electric and Magnetic Fields", Gordon and Breach Science Publishers, New York, 1969, p. 34 A.I. Knyaz "Information systems electrodynamics", pp. 346,361 (4.3), Radio and communication, Moscow, 1994 (Russian). Oleg V. Tozoni, "Self-regulating Permanent Magnet Linear Motor", IEEE Transactions on Magnetics., vol. 35, no 4, pp. 2137-2145 July, 1999. Oleg V. Tozoni, "Linear synchronous motor with screening permanent magnet rotor with extendible poles", U.S. Patent No 5,717,261, Feb. 1998. S.Earnshaw, Trans.Cambrudge Philosophical, vol. 7, pp.97-112, 1839. W. Braunbek, "Freischwebende korper in elektishen und magnetishen feld", Z.Phisik, vol. 112, pp.753-763, 1939. K. J. Binns, P. J. Lawrenson, "Analysis and computation of electric and magnetic field problems", Nauka, p.33, Moscow, 1970. G. A. Korn, T. M. Korn, “Mathematical handbook for scientists and engineers", McGraw-Hill Book Company, Inc., New York, Toronto, London, 1961. A. E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans, "Electric machinery", p.16, McGraw-Hill Book Company, Inc., New York, 1983. K.M. Polivanov, “Electrodynamic of moving bodies, p.112, Energoizdat, Moscow, 1982. K.M. Polivanov, “Electrodynamic of moving bodies, pp. 90-92, Energoizdat, Moscow, 1982. O1eg V. Tozoni, "Gas gun accelerator based on passive magnetodynamic suspension", IEЕЕ Transactions on Magnetics., vol. 40, no 3, May 2004. |
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is saturation
factor of core backs (see formula (2-17)). At the same time destabilizing
force
decreases as saturation of core backs grows and the resulting force
forms a cone of
stabilizing forces shown by a solid line in the upper part of the graph.
, (4.2-1)
is
rim mass, dα =2.79 Kg/dm3 is aluminum
specific gravity; rr =0.7m=7.0 dm is a
rim’s radius ; hr=0.5 dm is rim’s thickness; qr
=1
dm is rim’s width; Sr = hr∙qr
=0.5dm2= 5·103mm2 is
cross-section of the wheel rim. Consequently mr= 2
=18.7kG/mm2 (4.2-2)
[Joules],
d
