Finite Element Analysis of
the Electromagnetic Field of
a Motor Rotor Slot
MANE 6960 – ADVANCED TOPICS IN FINITE ELEMENT
ANALYSIS
THOMAS PROVENCHER
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Introduction:
The electromagnetic fields within an electric motor provide the motive force needed to make a
motor spin and are therefore critical to the motor’s performance. The many designs of motor
armatures can yield vastly different results ranging from a motor that can spin extrememly fast to
one that can provide massive amounts of torque at low speeds. This report and the included
Finite Element Analysis (FEA) model of a small portion of a motor armature, the rotor slot, will
provide some insight into the general electromagnetic field strengths and shapes of a theoretical
motor. Figure 1 shows an armature and several of the rotor slots where the electrical wire wraps
around the core.
Figure 1: Electric motor armature
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Formulation and Solution:
The model created for this analysis will simulate the electromagnetic field flow lines through an
electric motor rotor slot using a purely theoretical mathematical Coefficient form PDE model
within COMSOL Multiphysics. The shape of the model can be seen below in Figure 2. Both the
top, horizontal, and the lower, vertical rectangles were combined to one shape and had a zero
source term coefficient condition assigned. All of the circles were assigned a 1000 source term
coefficient condition to simulate the wires within the motor. All of the outer borders except for
the upper right edge were assigned a zero flux term to prevent the electromagnetic fields from
escaping as well as to simulate symmetry. The upper right edge of the model was given a
Dirichlet boundary condition which simulates a place for the fields to exit and create their motive
force.
Figure 2: Flow path and obstructions
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Three different meshes were chosen for this analysis; all were derived from COMSOL’s physics
based mesh creator and were constructed of Lagrange quadratic elements. Coarser, Normal,
Finer, and Extra Fine meshes were chosen, the Finer mesh can be seen in Figure 3.
Figure 3: Finer mesh density of the flow model
The variational formulation is shown below:
(𝑢′ , 𝜐′) = (𝑓, 𝜐)
The COMSOl model was run four times, once for each mesh density to verify the mesh was
sufficiently dense. Figure 4 shows the contour plot of the electromagnetic potential and Figure 5
shows the values of the potential on the left and right hand vertical sides of the model.
general flow direction and relative velocities of the fluid and Figures 5 and 6 show the velocity
potential and fluid pressure contour curves, respectively, of the fluid flow as it traveled around
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the objects on the normal mesh model. Table 1 shows the maximum values provided by contour
curves for all three mesh densities.
Figure 4: Finer mesh contour plot representation of the electromagnetic potential
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Figure 5: Finer mesh line plot of electromagnetic potential values of left (blue) and right (green) vertical edges
Table 1: Velocity potential and fluid pressure maximum values
Mesh Density
Coarser
Normal
Finer
Extra Fine
Maximum velocity potential and fluid pressure values
Maximum
Percent
Minimum
Electromagnetic
change to
Electromagnetic
Potential
lesser density
Potential
567.87
N/A
5.736
583.77
2.723675
5.8966
585.45
0.286959
5.9136
573.79
2.032102
5.9153
Percent
change to
lesser density
N/A
2.723603
0.287473
0.028739
The data provided in Table 1 shows that quadratic Lagrage elements are able to provide accurate
results when the mesh density is at set to finer. The percent change between the normal and finer
mesh densities was small, at less than a third of a percent. However, as the mesh density
increased to extra fine, the maximum electromagnetic potential decreased significantly while the
minimum was extremely close to that of the finer mesh. This indicates that this mesh density is
too dense and has resulted in an inaccurate model.
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Conclusions:
This model was able to approximate the electromagnetic fields of a motor rotor. It contained
areas where the electromagnetic potential was created, similar to the wiring in a motor, and a
place for it to disperse its energy and transform it into rotational motive force . It was shown that
both the normal and finer mesh densities provided by COMSOL Multiphysics yielded very
similar results indicating that the model’s analysis results had converged. Further increasing the
mesh resulted in an inaccurate approximation due to calculation irregularities.
References:
"Motor Rotor." Turtle Consulting. Web. 29 June 2015.
<http://www.turtleconsulting.com/blog/wp-content/uploads/2010/11/MotorRotor_610x300.jpg>.
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