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Halbach array generator voltage

QuickField simulation example

The excitation of the magnetic system on the rotor side is due to the Halbach assembly. The Halbach array is a special arrangement of permanent magnets that increases the magnetic field on one side of the assembly while cancelling it to near zero on the other side.

Engineering question
How to find generator voltage with Halbach rotor?

Engineering answer
Set up a plane-parallel QuickField DC Magnetics problem for a Halbach rotor generator and evaluate generated voltage from computed field results.

Typical applications
Halbach rotor generators, permanent magnet generators, synchronous generator rotors

Problem Type
Plane-parallel problem of DC magnetics.

Geometry
Axial length is 50 mm.
Halbach array generator voltage The Halbach array is a special arrangement of permanent magnets that increases the magnetic field on one side of the assembly while cancelling it to near zero on the other side. A c B a C b Stator Rotor Shaft Ø 120 mm Ø 74 mm Ø 68 mm Ø 20 mm

Given
Stator phase coil number of turns w = 90,
Coercive force of permanent magnets 730 kA/m,
Rotor poles 2p = 4,
Synchronous rotation speed n = 750 rpm.

Task
Calculate the idle generator electromotive force (EMF).

Solution
In no-load there is no electric current in the winding, the output voltage is equal to the induced electromotive force.
First in QuickField we measure the flux linkage with half-coils Φ_A, Φ_a, Φ_B, Φ_b, Φ_C, Φ_c as a function of rotor angular position. We get this dependency automatically using the LabelMover parametric calculation utility. Then the phase winding flux linkage is calculated: Φ_Aa = Φ_A-Φ_a, Φ_Bb = Φ_B-Φ_b, Φ_Cc = Φ_C-Φ_c.
The electromotive force is calculated as the ratio of the flux linkage increment ΔΦ to the angle increment Δφ:
EMF = -w * dΦ/dt = -w * ΔΦ / (Δt), where time increment is related to the angle increment Δφ as: Δt = (Δφ/360) / (n/60).

Result
In LabelMover we set the angle increment to be Δφ = 1 degree. The time required to rotate the rotor by 1 degree is Δt = (1/360) / (750/60) = 2/9 ms.
Phase coil flux linkage vs. rotor angular position

The caculated EMF is non-sinusoidal. Amplitude of the fundamental harmonic was computed with a harmonic analyzer tool: U1 = 19 V.

Magnetic flux density distribution in the permanent-magnet generator
Magnetic flux density distribution in the permanent-magnet generator