Eddy Current Damping
Jayson Jochim Kembu Makino Lihao Wang
Physics 202: Summer 2004
Professor: Richard Muirhead, Ph.D, M.D.
North Seattle Community College
Contents
- Introduction
- Purpose
- Procedure
- Materials
- Setup
- Experiment
- Data Transfer
- Data
- Analysis
- Maple Prediction:
- Mathematica
- Discussion
- Power Law Damping
- Error
- Conclusion
Abstract
The purpose of this experiment was to demonstrate the effects of the motion of a conductor in a an magnetic field. The resulting induced current was found to effect pendulant oscillation amplitude by power law damping. This paper outlines such results.
Introduction:
Eddy Currents are induced when nearby currents change their strength thereby producing a changing magnetic field. The Lenz Law requires that the eddy currents flow so as to induce currents opposing the change of the original currents and fields. As we will see a bulk piece of metal or metal plate produces such eddy currents in the presence of a magnetic field. Specifically, “as the plate enters the field the changing magnetic flux induces a emf in the plate, which in turn causes the free electrons in the plate to move, producing the swirling eddy currents.“(Serway p.987) Again these eddy currents are directed in such a manner as to oppose the changing magnetic field and therefore the motion of the plate.
Figure 1 a.) As the conducting plate enters the field, the eddy currents are counterclockwise. As the plate leave the field the currents are clockwise.
Eddy currents are currently used in several commercial operations. Braking systems for trains and subways utilize electromagnetic induction and eddy currents to bring cars to a stop. Also some power tools use eddy currents to stop dangerous moving parts.
Eddy currents change mechanical energy into internal energy in the form of heat and electricity. For this reason is often desired to minimize the resistance of eddy current paths.
Purpose:
The purpose of this experiment is to observe the effect of eddy currents and realize some scale of the behavior of such currents in reduced fields by varying the distance from a magnetic source. By digitizing this effect and direct comparison to an undamped pendulum oscillation we will make some conclusions as to the nature of the retarding effect that eddy current impose of a conductor in a magnetic field.
Procedure:
Tools:
- non-ferrous conducting metal plate
- large U magnet
- digital camera
- ring stand
- pendulum with frictionless baring system
- back drop for image enhancement
- logger pro analysis software
- meter stick
Setup:
We constructed a pendulum from a disk of non-ferrous conducting metal suspended from a .3 meter plastic insulating rod. The pivot we constructed from a 6 baring wheel assembly clamped to a horizontal bar mounted to a 1 meter ring-stand. A large U magnet was placed at the base of the ring-stand such that the arc of the pendulum’s motion swung between the poles. A black backdrop was positioned behind the pendulum parallel to the plane of motion to enhance image resolution. The digital camera was setup normal to the back drop approximately 1 meter from the pendulum.
Experiment:
The first set of videos were taken with the conducting metal passing through poles of the U magnet and the release from an small initial angle. The second set were taken from the same height but a larger initial angle.
Additional runs were repeated at a height above the magnetic poles and with the removal of the magnets altogether.
Data:
Data Transfer:
The Venier product Logger Pro™ allows us to digitize and analyze digital videos of AVI format. We used a USB to Firewire cable to transmit the DV video from the Digital Video Recorder to a Laptop with Logger Pro installed. An intermediate program Cannon Software Zoom™ was used to convert the DV video to AVI format.
Data:
The video data imported to Venier’s Logger Pro software cananalyzed to produce x and y coordinates as a function of time.
Figure 2 Screen shot of digitization.
We programmed a subsequent calculated column transforming the position of x(t) and y(t) to the angle the pendulum makes with the vertical with respect to time (Fig:
Figure 3 : At height 0 ( inside maximum magnetic field) Theta vs Time “Full Damped”
Figure 4 At height 1 ( outside magnetic field) Theta vs Time “Partial Damped”
Figure 5 At height 0 without magnet. Theta vs. Time “Not damped”
Figure 6 Comparison of Undamped and Damped vs. Time
Although the amplitude and time of oscillations was greatly effected by the position of the magnetic field the frequency remained constant at 1hz. (Fig.5-7)
Figure 7 Frequency of height 0 in Magnetic Field. “Full Damped”
Figure 8 Height 1 Above magnetic field. “Partially Damped”
Figure 9 Height 0. Without Magnet. “ No Damping”
Analysis:
We used Mathematica software to import the calculated data sets from the Venier software Logger Pro™ and provide the best non-linear fit for the data of each of the experiments. The best fit was of the form:
Note the power law damping effect. One might assume exponential damping as with viscous fluid models: ( See Maple Supliment)
Figure 10 Plot of Damped data Set 1 in Black. Best fit in Red.
For fully damped pendulum:
*Note t to the order of 2.39914.
Figure 11 Patially Damped data set 1 in Black. Best fit in Red.
For partially damped pendulum:
*Note t to the order of 0.164151.
For undamped pendulum:
*Note t to the order of 0.012893.
Discussion:
The damping effect of the eddy current increases with proximity to the concentration of the magnetic field. We see evidence of this in the examples of the pendulum passing through the area between the poles as the power damping is of the order –2.4. Where when raised to a position above the poles the power damping is of the order -.16. This is due to the strength of the magnetic field and the amount of cross-sectional area of the conducting portion of the pendulum passing through the field. Readings taken without the magnet showed a damping effect of -.024 this may be attributed to air resistance and friction in the pivot mechanism.
One might have expected to see a more traditional model of exponential decay however the data fits perfectly power law decay. This is an interesting finding. Research in regards to power law damping leaves questions unanswered. What does this mean? What does it say about the nature of our system? We know power law functions are fractal in nature and are with out scaling. Of interesting note natural occurring rock fractures are of power law scaling across 3.4 – 4.9 orders of magnitude, regardless of rock type. Consequently, data representing a limited range of fracture sizes may be used to characterize a much broader spectrum of fracture sizes. (Geology: Vol. 27, No. 9, pp. 799–802).This can then lead us to believe that our model of eddy current damping behaves in a similar manor.
Of similar nature I have read several articles regarding mapping strategies and their relationship as a power law. The accuracy of the mapped area of a intricate surface increases as a power law function of the length of the measuring device. Additionally this technology has been applied to internet topology to similar consequence.
The potential energy stored in the system by raising the pendulum arm is converted to kinetic energy as the pendulum accelerates toward earth after release. In the fully damped experiment this kinetic energy is transferred in another form within seconds of release. The kinetic energy must be transferred into electrical energy in the form of moving electrons. Which in turn is transferred to surrounding molecules by heat. An more accurate experiment may include the measurement of the current produced by moving a conducting plate in a magnetic field or the heat dissipated.
Error:
Our calculations do not take air resistance into account. However the cross-sectional area perpendicular to the plane of motion is very small for our object of interest so this effect over the time intervals in which we are interested is essentially zero. Also frictional contact in the pivot mechanism was not accounted for , however the mechanism was a 6 baring wheel designed specifically to produce insignificant friction and therefore over a small time interval may essentially be considered to be zero. Also our pendulum was tethered using a metal lock bracket which increased the mass of the pivot arm. This off centers the moment of inertia for the pendulum and may have effected the motion of the pendulum.
Conclusion:
We have demonstrated the damped effect of the amplitude of pendulant oscillation of a conductor in a magnetic field. The results of this experiment indicate power law scaling functionary decay of amplitude. As well as the location dependence of the intensity of the magnetic field between poles and the relative effective damping at locations outside of such a location.