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Main >> Applications >> Sample problems

BLDC motor slots skewing - QuickField simulation example

Cogging torque and no-load back EMF of a BLDC motor with skewed stator slots, evaluating how slot skewing improves torque ripple and EMF waveform. Motor dimensions are taken from this paper [1].

Engineering question

How to calculate the effect of stator-slot skewing on cogging torque and back EMF in a BLDC motor?

Answer
Represent the skewed stator by angularly shifted 2D slices, then combine their torques and flux linkages to obtain the skewed-motor response.

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Typical applications
BLDC stator slot structures, skewed rotor-slot designs, brushless motor laminations

BLDC motor slots skewing

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Simulation problem

Problem Type
Plane-parallel problem of DC magnetics.

Geometry
Motor z-length is 40 mm.
BLDC slots skewing Тo reduce the cogging torque and improve the back EMF shape in the brushless permanent magnet motor the stator slots are skewed. We replace the 3D model with a set of 2D model-slices. S N Stator Rotor A+ A- B+ B- C+ C- 1 2 3 4 5 6 7 8 42 9 mm Ø 168 mm

Given
Rotational speed 170 rpm.
Number of turns per slot is 18.
Permanent magnet coercive force 979 kA/m, residual flux density 1.29 T.

Task
Calculate the cogging torque and back EMF in no-load mode.

Solution
We represent a skewed stator as a set of straight stators shifted by a fixed angle. Each section is modelled in a separate problem.
Slots skewing We represent a skewed stator as a set of straight stators shifted by a fixed angle 10 40 mm 2π / 42

In QuickField we simulate a series of problems with different rotor positions. Torque and the flux linkage are calculated. The flux linkage is calculated for each phase: ΨA+, ΨA-, ΨB+, ΨB-, ΨC+, ΨC-.
LabelMover parameterization tool is used to automate calculations. It automatically modifies the geometry model, solves the problems and extracts the result. We repeat the procedure for each of the straight-stator models.

Further steps are carried outside of QuickField:

  1. We sum up torques and the flux linkages of each straight-stator model. This gives us the torque and flux linkage of the skewed stator.
  2. We find the flux linkage of the coil by subtracting the slots' flux linkages: ΨA = ΨA+ - ΨA-
  3. We compute voltage by derivating flux vs. angle dependency: EMF = - dΨ dt = - dΨ d(angle) * d(angle) d(t) = - Δ Ψ Δ angle * rotational speed
    To measure the cogging harmonics accurately the Δ(angle) value should be small. We take it to be 1/60 of the stator tooth pitch angle.

Results

Magnetic flux density distribution in the brushless DC motor
Brushless DC motor slots skewing

Skewing allows to reduce cogging torque drastically. In the plot you can see torques from straight stators T1, T2, T3, T4 and a torque in a skewed stator (T1 + T2 + T3 + T4)

Flux linkage vs. angle dependency has a triangle shape that results in a trapezoidal shape of back EMF.

Reference:
[1] Jagiela, Mariusz & Mendrela, Ernest & Gottipati, P.. (2012). Investigation on a choice of stator slot skew angle in brushless PM machines. Electrical Engineering. 95. 10.1007/s00202-012-0252-8.

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