Magnetic levitation (maglev) is used to suspend and propel trains without contact with a rail, and...

Transcribed Image Text:

Magnetic levitation (maglev) is used to suspend and propel trains without contact with a rail, and many cases, used to support rotating bearings for high-performance machines in order to eliminate friction and the need for lubrication. In the magnetic levitation system shown, the current-carrying coil produces an electromagnet that pro- vides an attraction force Fem on the metal ball: ein (1) Fem where K is a "force constant" (units of N-m/A) that depends on the number of coil wraps, material properties of the electromagnetic core, and geometry of the electro- magnet. Position of the ball is measured upward from a fixed at-rest position and distance d is a constant equal to the nominal air-gap distance from the electromagnet tip and the ball for a nominal coil current. R www KEI (d- x) Nominal air gap, d sa I (for x = 0) Metal ball, m Electromagnet Coil, L Derive the complete mathematical model of the magnetic levitation system where voltage source ein (t) is the input variable. Magnetic levitation (maglev) is used to suspend and propel trains without contact with a rail, and many cases, used to support rotating bearings for high-performance machines in order to eliminate friction and the need for lubrication. In the magnetic levitation system shown, the current-carrying coil produces an electromagnet that pro- vides an attraction force Fem on the metal ball: ein (1) Fem where K is a "force constant" (units of N-m/A) that depends on the number of coil wraps, material properties of the electromagnetic core, and geometry of the electro- magnet. Position of the ball is measured upward from a fixed at-rest position and distance d is a constant equal to the nominal air-gap distance from the electromagnet tip and the ball for a nominal coil current. R www KEI (d- x) Nominal air gap, d sa I (for x = 0) Metal ball, m Electromagnet Coil, L Derive the complete mathematical model of the magnetic levitation system where voltage source ein (t) is the input variable.