A simplified motor is shown below. The circular rotor is made of a non-magnetic material, but...

  

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A simplified motor is shown below. The circular rotor is made of a non-magnetic material, but inside the rotor, a magnetic material "insert" with the shape shown in the diagram below is positioned. At the 0° position shown, the length of the magnetic material insert "a" is 10 cm, the width of the material "b" is 8 cm, the same as the width of the stator (as labelled in diagram), and the depth of the insert material is the same as the depth of the stator. All magnetic materials have a relative permeability of 5000. Number of turns-250 Path length 50 cm Flex dendry (T) 28 26 24 2.2 20 1.8 16 14 a. If a current of 10 A flows through the winding, what is the resulting flux density in the airgap? Ignore any fringe effects. b. If the rotor is rotated 90°, estimate the resulting flux density in the airgap. Ignore fringe effects. c. What is the inductance of the winding at the 0° position? d. Estimate the inductance of the winding at the 90° position. e. Sketch the qualitative inductance variation as the rotor rotates from the 0° position to the 90° position. f. If the relative permeability of the magnetic materials is not a constant as given before, but provided by the plot below, calculate the amount of current needed through the winding, in order to get the same airgap flux density as in (a) and (b). 12 1.0 0.8 04 04 02 0 10 Cross sectional area-20 cm 20 30 40 30 Non magnetic rotor diameter 12 cm Airgap- Imm 200 300 500 1000 Magingny, A 2000 Non magnetic rotor viewed from the side, with the magnetic material insert 5000 A simplified motor is shown below. The circular rotor is made of a non-magnetic material, but inside the rotor, a magnetic material "insert" with the shape shown in the diagram below is positioned. At the 0° position shown, the length of the magnetic material insert "a" is 10 cm, the width of the material "b" is 8 cm, the same as the width of the stator (as labelled in diagram), and the depth of the insert material is the same as the depth of the stator. All magnetic materials have a relative permeability of 5000. Number of turns-250 Path length 50 cm Flex dendry (T) 28 26 24 2.2 20 1.8 16 14 a. If a current of 10 A flows through the winding, what is the resulting flux density in the airgap? Ignore any fringe effects. b. If the rotor is rotated 90°, estimate the resulting flux density in the airgap. Ignore fringe effects. c. What is the inductance of the winding at the 0° position? d. Estimate the inductance of the winding at the 90° position. e. Sketch the qualitative inductance variation as the rotor rotates from the 0° position to the 90° position. f. If the relative permeability of the magnetic materials is not a constant as given before, but provided by the plot below, calculate the amount of current needed through the winding, in order to get the same airgap flux density as in (a) and (b). 12 1.0 0.8 04 04 02 0 10 Cross sectional area-20 cm 20 30 40 30 Non magnetic rotor diameter 12 cm Airgap- Imm 200 300 500 1000 Magingny, A 2000 Non magnetic rotor viewed from the side, with the magnetic material insert 5000

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