# problem background. - Edge

Mechanics

Nov 14, 2013 (4 years and 6 months ago)

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Project 11566:

ITT Magnetic Damper

Tom
Sciotto

Jacob Norris (ME)

Tiffany
Heyd

(ME)

Ben
Hensel

(ME)

Dampening satellite vibrations

Imagine a satellite in orbit

Rapid, jerky, but small motions (moving
camera parts) on satellite induce vibrations

But satellite is physically isolated; vibrations
can’t dissipate

So: need a dampener!

Satellite Design

Space Environment

Wide temperature range

-
40
°
C to 80
°
C

Too wide for hydraulic dampener

Rubber or solid
-
state dampener would harden

ITT decided: Electromagnetic dampening

Eddy Current Dampening

Used an induced
emf

to resist a magnet

Train brakes:

Lenz’s Law

“An induced current is always in such a
direction as to oppose the motion or change
causing it

Electromagnetic interpretation or result of
Newton’s Third Law

How Eddy Currents Work

Conductor
-
Magnet relative motion induces
current in conductor

Current creates magnetic field

Induced magnetic field opposes magnet;
strength proportional to flux, or relative speed

Dampening constant, c!

Eddy Currents in Action

Wheel (rotates)

Conductive Plate

Magnet

(but our application
is linear not angular)

Mathematical Model

Damped mass
-
spring system

Equation of Motion

𝑚
𝑥

+
𝑐
𝑥

+
𝑘𝑥
=
0

Mathematical Model

𝑚
𝑥

+
𝑐
𝑥

+
𝑘𝑥
=
0

𝑥

+
2𝜁
𝜔
0
𝑥

+
𝜔
0
2
𝑥
=
0

Where

𝜔
0
=
𝑘
𝑚
,
𝜁
=
𝑐
2𝑚
𝜔
0
=
𝑐
2
𝑚𝑘