Abstract
Mathematical model of radial passive magnetic bearingIn the article a mathematical model of radial passive magnetic bearings applicable to ocean engineering units has been presented. The application of the bearings in ship thrusters should increase durability of propulsion systems and give lower maintenance costs. The rotor of thruster's electric motor is suspended in magnetic field generated by radial passive magnetic bearings. However the maintaining of axial direction of the rotor must be controlled with electromagnets equipped with a high-dynamic controller. The risk of application of the magnetic bearings results from very low stiffness of the unit in comparison with rolling bearings. Also construction of the bearing should be different due to gyroscope effect and high forces generated during ship manoeuvring. The physical model performs correctly if electromagnets are controlled properly; and, technological problem with sealing system seems more significant than power supply to electromagnets winding. The equations presented in the article are necessary to build algorithms of a digital controller intended for on-line controlling magnetic bearing in axial direction.
Highlights
Possible application of magnetic bearings to ocean engineering units has been considered and tested for several years
- The elaborated mathematical model makes it possible to assess magnetic force value and direction. Such model is necessary for determination of maximum magnetic force generated by radial passive magnetic bearing
- The software based on the finite elements method (FEM), commonly used for solving static magnetic fields and magnetic forces do not make it possible to perform a comprehensive dynamic analysis of radial passive magnetic bearing
Summary
Possible application of magnetic bearings to ocean engineering units has been considered and tested for several years. In compliance with Lorentz principle [2] the magnetic interaction force depends on the vector product of the surface constrained current and the vector of magnetic induction which penetrates the moving magnet:. The vector product of the surface current flowing through the left wall of moving magnet and the magnetic induction in the point of the coordinates (x, y, z), is equal to:. The coordinates of the vector for the left wall are equal to: and, for the right wall, as follows: where: x,y,z – coordinates of the point for which value of magnetic induction has to be determined. For the radially magnetized ring vector the magnetization vector amounts to: The values of surface current in the motionless magnet left and right walls are the following, respectively: The vector product of the surface current and the vector is equal to: (15). By taking into (17) account the relations (13), (14), (15) and (16) the following magnetic induction value can be obtained: where: By solving the above given integrals and accounting for magnetic induction values in Lorentz force it is possible to determine lifting force of the bearing
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