QQuiz Lab
← Back to questions
Question #176single-choiceverified

A very simplified model for a brushless DC surface permanent magnet motor is presented in the figure. Its equivalent magnetic circuit has also been included. Calculate the flux density (Bg) in the airgap, assuming the cross-sectional area of the airgap is the same cross-sectional area as for the ferromagnetic material and the permanent magnet (1cmx1cm). The length of the two ferromagnetic material sections (Lc1, Lc2) and the airgap length (g) are presented in the figure. Also, the permeability of the ferromagnetic material is presented (μ) and assume the permeability of the airgap is the permeability of free space (μ0). The reluctance of the permanent magnet (Rm) and its remanent flux (Φr) are also provided. When you have calculated the airgap flux density (Bg) use the equation provided below to calculate an estimation of the electromagnetic motor torque (Τ) using the parameters in the table and the calculated airgap flux density value (Bg). Τ=2Nm NBg Lst Rro I where Nm represents the number of magnets, N represents the number of conductors per stator slot, Bg represents the airgap flux density, Lst is the stator motor length, Rro is the airgap radius and I is the stator DC phase current. Number of magnets: 4 Number of conductors per stator slot: 14 Stator motor length: 124 mm Airgap radius: 60 mm Stator DC phase current: 300 A

Left: U-shaped ferromagnetic core surrounding a vertical permanent magnet marked N at the top and S at the bottom, with a right-side air gap g = 0.5 mm between upper and lower pole faces. Flux arrow φ points downward in the upper limb. Both core portions are marked μ = 2000 μ₀ and Lc1 = Lc2 = 5.25 cm; the limb cross-section is annotated 1 cm by 1 cm. Right: a single-loop equivalent magnetic circuit with a source F = φr Rm and series reluctances Rm, Rc1, Rg, Rc2, with flux φ directed clockwise. Given φr = 0.00157 Wb and Rm = 300000 A·turns/Wb. Legend identifies Rc1/Rc2 as iron core reluctances, Rg as airgap reluctance, Rm as magnet reluctance, μ as iron core permeability and μ₀ as free-space permeability.
AI image description

Left: U-shaped ferromagnetic core surrounding a vertical permanent magnet marked N at the top and S at the bottom, with a right-side air gap g = 0.5 mm between upper and lower pole faces. Flux arrow φ points downward in the upper limb. Both core portions are marked μ = 2000 μ₀ and Lc1 = Lc2 = 5.25 cm; the limb cross-section is annotated 1 cm by 1 cm. Right: a single-loop equivalent magnetic circuit with a source F = φr Rm and series reluctances Rm, Rc1, Rg, Rc2, with flux φ directed clockwise. Given φr = 0.00157 Wb and Rm = 300000 A·turns/Wb. Legend identifies Rc1/Rc2 as iron core reluctances, Rg as airgap reluctance, Rm as magnet reluctance, μ as iron core permeability and μ₀ as free-space permeability.

  1. Airgap Flux Density (Bg) = 1.2T, Torque = 300 Nm
  2. Airgap Flux Density (Bg) = 1.4T, Torque = 350 Nm
  3. Airgap Flux Density (Bg) = 1T, Torque = 250 NmCorrect
  4. Airgap Flux Density (Bg) = 0,8T, Torque = 200 Nm

Official answer

Airgap Flux Density (Bg) = 1T, Torque = 250 Nm

Departments

Not tagged yet.

Occurrences

  • FSS 2020 · ev · quiz 17