# display ```Modeling Process
Part 1: COMSOL Multiphysics 4.0
 Modeled one magnet pair with copper conductor moving through it
 Input different neodymium magnet sizes and shapes found on magnet
vendor website to find the strongest magnetic field
 The magnet with the largest magnetic field that also had a diameter less
than or equal to 0.75 inches was chosen for the damper
 Induced a variety of velocities to the conductor (0.5 in/sec, 1 in/sec &amp; 100
in/sec)
 Outputs:
o Magnetic field distribution and strength
o Eddy current distribution at specified velocity
o Opposing force applied to the conductor as it travels through the
magnetic field (Damping Force)
 Model Layout:
 Theoretical Magnetic Field created (velocity of conductor = 0.5 in/sec):
 Theoretical Eddy Current Induced in system (velocity of conductor = 0.5
in/sec):
 Theoretical Damping Force applied to conductor (velocity of conductor =
0.5 in/sec):
o Error occurred when trying to solve. Cause found due to “0” value
input for electric conductivity of air surrounding model. Fixed by
changing to extremely small value (1E-7 S/m)
update.
o Eddy current saturation. This was found only to occur at larger
velocities, which should not be seen in the damper’s environment.
Part 2: Microsoft Excel
 Governing equation of motion
𝐹 = 𝑚𝑥̈ + 𝑐𝑥̇ + 𝑘𝑥
or in the frequency domain
𝐹 = 𝑥̈ + 2𝜁𝜔𝑛 𝑥̇ + 𝜔𝑛2 𝑥
where
𝜔𝑛 = √𝑘⁄𝑚
𝑎𝑛𝑑 𝜁 =
𝑐
𝑘
2√𝑚
 Spring constant, k, is the flexure spring constant and the mass, m, is the
 “c” (damping constant) is found from dividing the damping force
(COMSOL output) by the velocity input into the model
 Values multiplied by twelve to get final values because damper contains
12 magnet pairs
Part 3: Experimental Input
 Re-modeled in COMSOL and excel using actual/experimental values found
after prototype was built
o Spring constant of the flexure
o Magnetic field strength produced by the magnets
o Mass of the payload used during test
 New damping force was found and new zeta value calculated
 Experimental Magnetic Field created (velocity of conductor = 0.5 in/sec):
 Experimental Eddy Current Induced in system (velocity of conductor = 0.5
in/sec):
 Experimental Damping Force applied to conductor (velocity of conductor
= 0.5 in/sec):
Part 4: Comparison of Theoretical and Experimental Results
Magnetic
Damping
Field
Force
Strength (T) (lbf)
Mass of
m (kg)
Spring
Damping
Constant, Coefficient, c
k (lbf/in) (lbf-s/in)
Zeta
(%)
Theoretical
1.48
1.812
10
20.87
3.624
13.83
Experimental
0.8867
0.6528
1.19
82.87
1.306
7.25
```