Calculation And Stiffness Of A Radial Magnetic Force Of Permanent Magnet Bearings

Magnetic bearings can support rotating shaft without physical contact, and therefore have many advantages such as no frication, no wear, no lubricant equipment and long service life. Long considered a promising advancement, they are now moving beyond promise into actual service in such applications as aircraft, electric power generation, high speed and high precision machine tool, petroleum refining and robots. Magnetic bearings with permanent magnet to provide levitation force have lower power consumption, smaller volume, more compact structure and larger load capacity than electromagnetic ones, and thus attract the interest of many bearing researchers.Focused on the radial permanent magnetic bearing (the mated permanent magnetic rings) used in a magnetic bearing system, by the magnetic charge theory, this paper establishes the mutual magnetic force models while their axes are parallel or intersectant. Based on those models, a fast numerical integration method is founded from the angle of the integral's physical meaning. Then the author uses the VC++6.0 to compile a computer program and realizes the corresponding numerical method. Later, a calculation example is illustrated by using the parameters of the mated magnetic rings that will be used in future bearing experiment device. Finally, the stiffness characteristics are deeply analyzed. The results demonstrate while the same two axial even magnetized permanent magnetic rings are arranged along the same magnetization direction:1) When their axes are parallel and the radial distance between the two axes is little, they can automatically make their axes overlap, and the radial magnetic force linearly increases as the radial distance becomes larger. While the axial distance between the two magnetic rings becomes larger, the radial load capacity will decrease.2) When their axes are intersectant and the angle is small, the direction of the radial magnetic force acting on the levitated magnetic ring will always point to the axis of the fixed magnetic ring, but the magnetic moment on the levitated magnetic ring can be positive or negative when the point ofthe intersection moves along the axis of the fixed magnetic ring. If the magnetic moment is positive, the two rings still can automatically make their axes overlap. However, if the magnetic moment is negative, the levitated ring will further circumrotate.3) The stiffness characteristics analysis shows that the levitated ring is unstable in the axial direction, but it is self-steady in the radial direction. However, its stability in the directions around X-axis or Y-axis is closely related to the distance between the point of intersection and the levitated ring's lower side. And the analysis also shows that the variation of the radial displacement or the angle displacement around X-axis or Y-axis will change the axial magnetism. Therefore, besides an axial displacement sensor, radial displacement sensors are necessary so as to realize the precise position control on the shaft. The signals from radial displacement sensors should be put into a controller that can control the axial magnetic force.In the last part of this paper, an experiment is given to test the validity of the numerical calculation. The result shows that the calculation is correct.