PatentDe  


Dokumentenidentifikation EP0921537 28.05.2003
EP-Veröffentlichungsnummer 0921537
Titel Magnetspulenanordnung
Anmelder Philips Medical Systems MR Technologies Finland Oy, Vantaa, FI
Erfinder Englund, Rurik, 06100 Porvoo, FI;
Kinanen, Ilmari V., 02210 Espoo, FI;
Lindholm, John-Erik M., 01120 Vasterkog, FI
Vertreter derzeit kein Vertreter bestellt
DE-Aktenzeichen 69813734
Vertragsstaaten DE, FR, NL
Sprache des Dokument EN
EP-Anmeldetag 04.12.1998
EP-Aktenzeichen 983099854
EP-Offenlegungsdatum 09.06.1999
EP date of grant 23.04.2003
Veröffentlichungstag im Patentblatt 28.05.2003
IPC-Hauptklasse H01F 7/20
IPC-Nebenklasse G01R 33/38   

Beschreibung[en]

The present invention relates to magnet coil assemblies, and more particularly to driver coils and cooling techniques for use in resistive electromagnets. The present invention finds particular application in the field of magnetic resonance imaging (MRI).

MRI is widely used for imaging anatomical and other structures. A commonly used type of magnet for MRI systems is the superconducting type, which is capable of generating field strengths in the range of 0.5-2 Tesla (T). Superconducting magnets are, however, relatively expensive to manufacture and operate.

At lower fields, for example in the range of 0.1 to 0.3 T, resistive magnets are commonly used to produce magnetic fields for MRI applications. Resistive magnets typically include one more magnet driver coils operating in cooperation with a suitable magnet structure, the magnetic field strength being generally proportional to the current through the coils. A limitation on magnet performance, however, is the heat generated in the resistance of the driver coils. As a result, cooling systems have been used to remove this excess heat.

To provide the necessary cooling, annular cooling flanges or discs fabricated from a material such as aluminium have been placed in thermal contact with the magnet coils (JP-A-01 276 707). Channels having a size and depth sufficient to accommodate and retain copper tubing having a round cross section have been included on one side of the cooling flange, which has had a thickness greater than that of the tubing. The channels and tubing are arranged in a bifilar wound pattern so that the inlet and outlet of the tubing are both accessible from the outer radius of the cooling flange. The cooling flanges have then been placed against the driver coils, with the tubing preferably on the side of the flange facing away from the magnet coil. In operation, a coolant such as water has been caused to flow through the tubing.

In practice, however, neither the surface of the driver coil nor surface of the cooling flange are perfectly flat. The resultant gaps degrade the thermal conductivity between the coil and flange. There have also been radial gaps between the channels and hence the turns of tubing, also reducing thermal efficiency. A cooling flange with a flat cooling surface has been proposed for cooling the windings of a transformer using a plate heat exchanger (WO-A-90/08390).

In magnet systems having two driver coils on each pole of the magnet it has been necessary to use three cooling flanges. The structure associated with each pole has thus included a first cooling flange, a driver coil having its first side electrically insulated from but in thermal contact with the first cooling flange, a second cooling flange located between the second side of the first driver coil and first side of a second driver coil (the second cooling flange being in thermal contact with but electrically insulated from the driver coils), the second driver coil, and a third cooling flange electrically insulated from but in thermal contact with the second side of the second driver coil.

Driver coils have also included many turns of a conductor such as aluminium arranged in a generally planar, disc-shaped coil. The conductor has had a rectangular cross-section, with the conductor wound or coiled from an inner to an outer radius in the form of an annulus or disc. To insulate between the multiple conductor turns, an anodized aluminium conductor has been used. A disadvantage of anodized aluminium, however, is its cost. A further disadvantage is that defects in the anodization may result in short circuits between coil turns, with a corresponding deleterious effect on magnet performance.

In accordance with a first aspect of the invention, a magnet coil assembly comprises a first generally planar driver coil having at least a first surface, heat being generated in the first driver coil in response to the flow of electrical current; and tubing for containing the flow of a coolant therethrough for removing heat generated in the first driver coil, the tubing including a flat exterior cross-section portion facing and in thermal communication with the first driver coil.

Improved thermal communication between the driver coil and the tubing for removing heat generated in the driver coil, is provided.

According to another more limited aspect of the invention, the tubing is wound to define a plurality of generally planar turns. A layer of thermally insulating material having a thickness less than that of the tubing may be located between the turns.

According to yet another more limited aspect of the invention, the tubing is bifilar wound.

According to another more limited aspect, the driver coil and the and the tubing are separated by a layer of electrical insulation which defines a plurality of holes. According to a still more limited aspect, an epoxy is located between the insulation and the driver coil.

According to another aspect of the invention, a magnet for use in MRI includes two pole pieces in an opposed relationship which define an imaging region. A driver coil and tubing as defined above are associated with the first pole piece. The tubing has a flat exterior cross-section portion facing and in thermal communication with the driver coil. A driver coil and additional tubing are also associated with the second pole piece. The additional tubing has a flat exterior cross-section portion facing and in thermal communication with the driver coil associated with the second pole piece.

According to a more limited aspect of the invention, the driver coil associated with the first pole piece includes a conductor which has a generally rectangular cross section. An edge of the conductor which is adjacent to the material is beveled. According to a still more limited aspect, the conductor is wound to define a plurality of generally planar turns. The turns are separated by a layer of electrical insulation. According to a still more limited aspect, the electrical insulation does not extend past the edge of the conductor facing the material in thermal communication therewith.

According to another aspect of the invention, a magnet coil assembly for use in magnetic resonance imaging includes a first driver coil and tubing for containing the flow of a coolant therethrough, the tubing including a flat exterior cross-section portion which faces and is in thermal communication with the first surface of the first driver coil. A second surface of a second driver coil is adjacent the second surface of the first driver coil. Tubing for containing the flow of a coolant therethrough, the tubing including a flat exterior cross-section planar portion faces and is in thermal communication with the first surface of the first driver coil.

One way of carrying out the invention will now be described in greater detail, by way of example, with reference to the accompanying drawings, in which:

  • Figure 1 depicts an MRI apparatus according to the present invention;
  • Figure 2 is an exploded view of a magnet coil assembly;
  • Figure 3 is a top view of a cooling member;
  • Figure 4 is a top view of a perforated insulating layer, and
  • Figure 5 is a sectional view of a portion of the windings of a driver coil along line 5-5 of Figure 2.

With reference to Figure 1, an MRI apparatus which produces images of the anatomy of patient 1 includes a generally C-shaped magnet body 3. The patient 1 is placed in an imaging region located between the pole pieces 23. Current flowing in the driver coils contained in coil assemblies 2a, 2b generates a magnetic field Bo in the imaging region. Necks 4 connect the pole pieces 23 to the body 3 of the magnet, thereby providing a return path for the body of the magnet.

Gradient coils 6 generate time-varying gradient magnetic fields, preferably in three orthogonal directions (e.g., x, y, z). As known in the art, the MRI apparatus 100 also includes RF transmit and receive coils (not shown) for exciting magnetic resonance of materials within the imaging region and detecting signals excited thereby. As is also conventional in the art, associated signal processing and computer apparatus generates and displays images of the internal anatomy of the patient on a CRT or other suitable monitor.

Figure 2 depicts the various components of the lower magnet coil assembly 2b, it being understood that lower magnet coil assembly 2b is also representative of the upper magnet coil assembly 2a.

With reference to Figure 1, 2, and 3, the magnet coil assembly 2b includes a pair of cooling members 10, 12, a pair of magnet coils 14, 16, and electrical insulation layers 18, 20, 22. Each cooling member 10 is fabricated from tubing wound in a generally planar annular configuration. The tubing is preferably copper tubing having an 8 x 12 mm rectangular exterior cross section and is bifilar wound, with the 12 mm dimension of the tube running in the radial direction. Other materials and cross sections may also he used. provided that tubing is wound so that a substantially flat portion of the tubing cross section may be placed facing and in thermal contact with the magnet coil 14. Placed between each of the adjacent layers of tubing is thermal insulation such as PVC having a thickness of approximately 2 mm. Typical conductivity for a polymer such as PVC is approximately 0.3 w/mK. The tubing is wound so that adjacent turns of tubing are substantially adjacent, though separated by thermal insulation 28. The member has an inlet 24 through which a coolant such as water is introduced, and an outlet 26 from which the coolant exits after having flowed through the tubing. Mechanical spacers 29a, 29b arc placed in the inner layers of the winding to account for spaces caused by the bend of the bifilar wound tubing and thus maintain the circularity of the cooling member 10.

An electrical insulation layer 18 is located between the cooling member 10 and the driver coil 14. The insulation layer 18 should provide a desired degree of electrical isolation consistent with good thermal communication between the cooling spiral 10 and the driver coil 14. With reference to Figure 4, the insulation layer 18 is of an annular shape and contains a plurality of perforations or holes . A uniform layer of epoxy adhesive is used to fasten the cooling member 10 to the driver coil 14. The epoxy preferably provides a high degree of thermal conductivity, which in practice means a high filler content, and a desired degree of electrical isolation. Because the insulation layer 18 contains numerous perforations, the epoxy layer joins the cooling member 10 and the driver coil 14 over a substantial portion of their surface. The epoxy preferably has a minimum of voids so as to maximize thermal communication between the cooling member 10 and the driver coil 14. To improve electrical isolation, the cooling member 10 may also be coated with a layer of lacquer.

With reference to Figures 2 and 5, a generally planar driver coil 14 contains a plurality of turns of a spiral-wound electrical conductor 30 such as aluminium. An electrical connection is made at one end of the conductor 30 at the inside of the spiral and at the other end at the outside of the spiral. A cross section of a portion of the driver coil 14 showing a representative portion of the coil windings is shown in Figure 5. While gaps are shown between the windings for ease of illustration, it will be appreciated that in practice the windings are substantially adjacent.

The conductor 30 is characterized by a generally rectangular cross section having beveled edges 32a and 32b. An electrical insulation layer 34 such as Mylar is placed between the turns of the conductor 30, thus preventing the turns from making electrical contact. The beveled surfaces prevent electrical contact near the upper and lower edges of the conductor 30 in the event that the vertical dimensions of the insulating layer 34 or conductor 30 should vary or if the insulating layer 34 is not precisely positioned. In practice, the nominal dimensions of the bevels 32a, 32b and the height of the insulating layer 34 are chosen so that electrical insulation between the conductor 30 turns is achieved despite variations in the material and assembly techniques while preventing or minimizing protrusion of the insulating layer 34 beyond the vertical extent or edges of the conductor 30. This in turn facilitates thermal communication between the conductor and adjacent layers or structures such as the cooling member 10. In an arrangement where the conductor has a nominal height of 100 mm and a nominal thickness of 0.5 mm, satisfactory results have been achieved with bevels 32a, 32b having a height of 1 mm and a depth of 0.02 mm and an insulation layer 34 having a height of 100 mm.

An electrical insulation layer 20 is placed between the driver coils 14, 16. The insulation layer 18 is selected to provide a desired degree of electrical isolation between the driver coils 14, 16. The coils 14, 16 are bonded to the insulation layer using an epoxy. Of course, other arrangements, such as those described above in regard to insulation layer 18, may be used if improved thermal communication between driver coils 14, 16 is desired.

While the foregoing description has been directed primarily to cooling member 10, insulating layer 18, and driver coil 14, it will be appreciated that it applies equally to driver coil 16, insulating layer 22, and cooling member 12. After assembly, the entire structure is hermetically sealed using epoxy, a glass fibre laminate, or like technique.

In operation, a current source provides an electrical current to the magnet assemblies 2a, 2b so that a desired magnetic field Bo is generated, and coolant such as water is caused to flow through passages defined by the material of the cooling members 10, 12. Being relatively flexible, the cooling members may be placed in good thermal contact with the driver coils 14, 16 during the manufacturing process, for example by applying pressure during assembly. Thus, the system is relatively tolerant of variations in the surfaces of the cooling member and driver coils. Because protrusions of the relatively thermally insulating Mylar beyond the surface of the driver coils are minimized, thermal communication between the cooling members and the driver coils 14, 16 is further enhanced.

Although the cooling member has been described in terms of bifilar wound tubing, other configurations are possible. Thus, for example, coolant may be introduced to the cooling members through headers or manifolds, each feeding a plurality of cooling passages. In one embodiment, each cooling member includes a first inlet manifold and first exit manifold which are associated with a first plurality of cooling passages, and a second inlet manifold and second exit manifold which are associated with a second plurality of passages. The first and second passages are interleaved, with the direction of coolant flow in opposite directions.

As will be appreciated, coolant entering the inlet side 24 of the cooling member is cooler than that exiting through the outlet 26. A particular advantage of the bifilar winding of the cooling member is that variation in temperature of the cooling member in the radial direction are minimized. This in turn minimizes variation in temperature of the driver coils 14, 16 in the radial direction. Effective thermal insulation between the individual turns in the cooling member also improves the thermal efficiency of the cooling member.

The invention has been described in relation to a C-shaped magnet apparatus. It will be appreciated that the invention can be used with other magnet configurations, such as the so-called four-poster type, the so-called H-form, or other configurations which provide a return path for the magnet flux.

A first advantage of the described embodiment is that improved thermal performance in a magnet system is provided while minimizing cost and complexity, including that of the cooling system. Another advantage is that improved thermal communication between the cooling member and the driver coil is provided. Not only can absolute temperature of the magnet coils be reduced, but also temperature gradients within the coils themselves can be minimized. Yet another advantage is that a separate cooling flange may be eliminated. Another advantage is that the turns of the magnet coil are insulated using a technique which avoids the disadvantages of the anodized approach but which does not degrade the performance of the cooling system.

The invention has been described with reference to the preferred embodiment. Obviously, modifications and alterations will occur to others upon reading and understanding the preceding description. It is intended that the invention be construed as including all such modifications an alterations insofar as they come within the scope of the appended claims.


Anspruch[de]
  1. Magnetspulenanordnung, die Folgendes umfasst: eine erste, im Allgemeinen planare Treiberspule (14, 16) mit mindestens einer ersten Oberfläche, wobei infolge des elektrischen Stromflusses Wärme in der ersten Treiberspule erzeugt wird; und Rohrleitungen (10, 12) fiir das Kühlmittel, das hierdurch fließt, um die in der ersten Treiberspule erzeugte Wärme abzuführen, wobei die Rohrleitung einen Bereich mit flachen Außenquerschnitt hat, der zu der ersten Treiberspule hingewandt ist und in thermischem Kontakt mit dieser steht.
  2. Spulenanordnung nach Anspruch 1, wobei die Rohrleitung einen rechtwinkligen Außenquerschnitt hat.
  3. Spulenanordnung nach Anspruch 1 oder 2, wobei die Rohrleitung so gewunden ist, dass eine Vielzahl von im Allgemeinen planaren Windungen entsteht.
  4. Spulenanordnung nach Anspruch 3, mit einer Schicht aus thermisch isolierendem Material (28) zwischen den Windungen.
  5. Spulenanordnung nach Anspruch 4, wobei die Dicke des thermisch isolierenden Materials (28) geringer ist als die der Rohrleitung.
  6. Spulenanordnung nach einem der Ansprüche 1 bis 5, wobei die Rohrleitung bifilar (zweigängig) gewunden ist.
  7. Spulenanordnung nach einem der Ansprüche 1 bis 6, wobei die erste Treiberspule (14, 16) und die Rohrleitung (10, 12) durch eine elektrische Isolierschicht (18, 22) getrennt sind und die elektrische Isolierschicht eine Vielzahl von Löchern aufweist.
  8. Spulenanordnung nach Anspruch 7, mit einem Kleber zwischen der elektrischen Isolierschicht (18, 22) und der ersten Treiberspule (14, 16).
  9. Spulenanordnung nach Anspruch 8, wobei der Kleber ein Epoxid mit hoher thermischer Leitfähigkeit ist.
  10. Spulenanordnung nach einem der Ansprüche 1 bis 9, wobei das Kühlmittel Wasser umfasst.
  11. Spulenanordnung nach einem der Ansprüche 1 bis 10, wobei die erste Treiberspule (14, 16) einen Leiter (30) mit einem im Allgemeinen rechtwinkligen Querschnitt umfasst, wobei eine Kante des Leiters, die an die Rohrleitung angrenzt, abgeschrägt ist (32a, 32b).
  12. Spulenanordnung nach Anspruch 11, wobei der Leiter (30) so gewunden ist, dass eine Vielzahl von im Allgemeinen planaren Windungen entsteht und die Windungen durch eine elektrische Isolierschicht (34) voneinander getrennt sind.
  13. Spulenanordnung nach einem der Ansprüche 1 bis 12, wobei die Rohrleitung (10, 12), die der ersten Oberfläche der ersten Treiberspule gegenüberliegt und in thermischer Verbindung zu ihr steht, eine Vielzahl von Durchgängen (24, 26) definiert.
  14. Spulenanordnung nach einem der Ansprüche 1 bis 13, die weiterhin Folgendes umfasst: eine zweite im Allgemeinen planare Treiberspule (14, 16) mit mindestens einer ersten Oberfläche, wobei infolge des elektrischen Stromflusses Wärme in der zweiten Treiberspule erzeugt wird; und zusätzliche Rohrleitungen (10, 12) für das Kühlmittel, das hierdurch fließt, um die in der Magnetspule erzeugte Wärme abzuführen, wobei die zusätzliche Rohrleitung einen Bereich mit flachen Außenquerschnitt hat, der zu der zweiten Treiberspule hingewandt ist und in thermischem Kontakt mit dieser steht, wobei die erste Treiberspule zu einem ersten Polschuh (23) gehört und die zweite Treiberspule zu einem zweiten Polschuh (23) gehört, wobei der erste und der zweite Polschuh in entgegengesetzter Beziehung zueinander stehen und eine Bildgebungsregion für die Magnetresonanz-Bildgebung zwischen ihnen definieren .
  15. Magnet zur Verwendung für die Magnetresonanz-Bildgebung mit zwei Polschuhen in entgegengesetzter Beziehung, die eine Bildgebungsregion definieren, wobei die Magnetspulenanordnung nach einem der Ansprüche 1 bis 13 zu mindestens einem der Polschuhe gehört.
Anspruch[en]
  1. A magnet coil assembly comprising: a first generally planar driver coil (14, 16) having at least a first surface, heat being generated in the first driver coil in response to the flow of electrical current; and tubing (10, 12) for containing the flow of a coolant therethrough for removing heat generated in the first driver coil, the tubing including a flat exterior cross-section portion facing and in thermal communication with the first driver coil.
  2. A coil assembly as claimed in claim 1, wherein the tubing has a rectangular exterior cross section.
  3. A coil assembly as claimed in claim 1 or claim 2, wherein the tubing is wound to define a plurality of generally planar turns.
  4. A coil assembly as claimed in claim 3, including a layer of thermally insulating material (28) between the turns.
  5. A coil assembly as claimed in claim 5, wherein the thermally insulating material (28) has a thickness less than that of the tubing.
  6. A coil assembly as claimed in any one of claims 1 to 5, wherein the tubing is bifilar wound.
  7. A coil assembly as claimed in any one of claims 1 to 6, wherein the first driver coil (14, 16) and the tubing (10, 12) are separated by a layer of electrical insulation (18, 22), the layer of electrical insulation having a plurality of holes.
  8. A coil assembly as claimed in claim 7, comprising adhesive between the layer of electrical insulation (18, 22) and the first driver coil (14, 16).
  9. A coil assembly as claimed in claim 8, wherein the adhesive is an epoxy having a high thermal conductivity.
  10. A coil assembly as claimed in any one of claims 1 to 9, wherein the coolant comprises water.
  11. A coil assembly as claimed in any one of claims 1 to 10, wherein the first driver coil (14, 16) comprises a conductor (30) having a generally rectangular cross section, an edge of the conductor adjacent the tubing having a bevel (32a, 32b).
  12. A coil assembly as claimed in claim 11, wherein the conductor (30) is wound so as to define a plurality of generally planar turns and the turns are separated by a layer of electrical insulation (34).
  13. A coil assembly as claimed in any one of claims 1 to 12, wherein the tubing (10, 12) facing and in thermal communication with the first surface of the first driver coil defines a plurality of passages (24, 26).
  14. A coil assembly as claimed in any one of claims 1 to 13, further including a second generally planar driver coil (14, 16) having at least a first surface, heat being generated in the second driver coil in response to the flow of electrical current; and additional tubing (10, 12) for containing the flow of a coolant therethrough for removing heat generated in the magnet coil, the additional tubing including a flat exterior cross-section portion facing and in thermal communication with the second driver coil, wherein the first driver coil is associated with a first pole piece (23) and the second driver coil is associated with a second pole piece (23), the first and second pole pieces in an opposed relationship and defining an image region therebetween for use in magnetic resonance imaging.
  15. A magnet for use in magnetic resonance imaging includes two pole pieces in an opposed relationship which define an imaging region, a magnet coil assembly as claimed in any one of claims 1 to 13 being associated with at least one of the pole pieces.
Anspruch[fr]
  1. Ensemble de bobines d'électro-aimant comprenant: une première bobine excitatrice (14, 16) du type généralement planar ayant au moins une première surface, de la chaleur étant générée dans la première bobine excitatrice en réaction au flux de courant électrique; et des tubes (10, 12) pour contenir le flux d'un fluide de refroidissement à travers ceux-ci pour enlever de la chaleur qui est générée dans la première bobine excitatrice, les tubes comprenant une portion de coupe transversale extérieure plate qui se situe vis-à-vis de la première bobine excitatrice et qui est en communication thermique avec celle-ci.
  2. Ensemble de bobines selon la revendication 1, dans lequel les tubes présentent une coupe transversale extérieure rectangulaire.
  3. Ensemble de bobines selon la revendication 1 ou selon la revendication 2, dans lequel les tubes sont enroulés de manière à définir une pluralité de spires du type généralement planar.
  4. Ensemble de bobines selon la revendication 3, comprenant entre les spires une couche en matériau thermiquement isolant (28).
  5. Ensemble de bobines selon la revendication 5, dans lequel le matériau thermiquement isolant (28) présente une épaisseur qui est inférieure à celle des tubes.
  6. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 5, dans lequel les tubes sont enroulés de manière bifilaire.
  7. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 6, dans lequel la première bobine excitatrice (14, 16) et les tubes (10, 12) sont séparés par une couche d'isolation électrique (18, 22), la couche d'isolation électrique ayant une pluralité de trous.
  8. Ensemble de bobines selon la revendication 7, comprenant un adhésif entre la couche d'isolation électrique (18, 22) et la première bobine excitatrice (14, 16).
  9. Ensemble de bobines selon la revendication 8, dans lequel l'adhésif est un époxyde ayant une conductivité thermique élevée.
  10. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 9, dans lequel le fluide de refroidissement comprend de l'eau.
  11. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 10, dans lequel la première bobine excitatrice (14, 16) comprend un conducteur (30) ayant une coupe transversale généralement rectangulaire, un bord du conducteur étant adjacent aux tubes ayant un biseau (32a, 32b).
  12. Ensemble de bobines selon la revendication 11, dans lequel le conducteur (30) est bobiné de manière à définir une pluralité de spires du type généralement planar et les spires sont séparées par une couche d'isolation électrique (34).
  13. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 12, dans lequel les tubes (10, 12) qui se situent vis-à-vis de et qui sont en communication thermique avec la première surface de la première bobine excitatrice définissent une pluralité de passage (24, 26).
  14. Ensemble de bobines selon l'une quelconque des revendications précédentes 1 à 13, comprenant encore une deuxième bobine excitatrice (14, 16) du type généralement planar ayant au moins une première surface, de la chaleur étant générée dans la deuxième bobine excitatrice en réaction au flux de courant électrique; des tubes additionnels (10, 12) pour contenir le flux d'un fluide de refroidissement à travers ceux-ci pour enlever de la chaleur qui est générée dans la bobine d'électro-aimant, les tubes additionnels comprenant une portion de coupe transversale extérieure plate qui se situe vis-à-vis de la deuxième bobine excitatrice et qui est en communication thermique avec celle-ci, où la première bobine excitatrice est associée à une première pièce polaire (23) et la deuxième bobine excitatrice est associée à une deuxième pièce polaire (23), les première et deuxième pièces polaires étant en relation opposée et définissant une région d'image entre elles pour être utilisée dans l'imagerie par résonance magnétique.
  15. Aimant pour être utilisé dans l'imagerie par résonance magnétique comprenant deux pièces polaires en relation opposée qui définissent une région d'imagerie, un ensemble de bobines d'électro-aimant selon l'une quelconque des revendications précédentes 1 à 13 étant associé à au moins une des pièces polaires.






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