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2d Magnetostatic Analysis of the Permanent Magnet Unbalanced Flux Gate Design
© Terrence Staton
Sunday, June 13, 2004
I have been working on a new gate design that I call the unbalanced flux gate. The design incorporates ideas from the minatowheel Yahoo group. I have been running many magnetostatic FEA magnetostatic parametric simulations to explore these ideas. I feel it might still be too soon to post this idea as I don’t want to lead anyone down a path that will prove to be fruitless. On the other hand I might be missing something very critical in this research if I don’t share it with others. In the interest of speeding the progress of this research this document will detail the research I have done thus far on this gate design. You may not distribute this document or information contained in this document without prior permission from me.
I will present a quick overview of the concepts that are employed in this gate design.
• Permanent magnet gate designs are best constructed using configurations where the magnets are primarily repelling each other. Using attractive forces is very problematic due to energy required to pull attracted objects apart. For attractive configurations the equilibrium state is to remain as close as possible to the object of attraction. For repelling configurations the equilibrium state is to remain as far from the repelling object. Another force such as friction eventually counter balances the repelling force and then the magnets will remain at rest.
• Materials with a relative permeability greater than 1, ex. steel and iron, can reduce the measured B of a permanent magnet when placed between the point of measurement and a permanent magnet. The B takes the path of least resistance by traveling through the steel versus the air.
• Materials with high relative permeability can also cause two permanent magnets that would normally repel each other move toward each other when placed in between the repelling magnets.
• Materials with high relative permeability often have non-linear B-H curves. Due to their non-linear nature they reach a point where they become “saturated” with magnetic fields (B). The concept of saturation refers to the fact that that little to no new magnetic domains can be created in the material.
These are the most crucial ideas employed for the design tested in this document, but there are many other concepts which I will not mention here that make permanent magnet gate designs possible.
Simulation and Analysis Procedure
All of the simulations in this document are conducted using 2d magnetostatic analysis. The permanent magnets are simulated with Grade 40 NdFeB material. Parametric analysis is done by moving the rotor through the gate by creating 16 solutions per inch of movment. The results of the parametric solving are then exported for analysis using Matlab. In Matlab area plots as well as 2d comparison plots are created to analyze the difference of varied parameters from each gate design. The trapezoidal integral is also calculated for each area plot to produce the total area under the entire force curve.
Initial Goals of the Project
My initial goal was to increase my understanding of how relative permeability materials greater that 1 interacted with magnetic flux from permanent magnets. Several people in the minatowheel group including myself felt using a material like steel with magnets configured to repel might prove to be useful in a permanent magnet motor design. The problem is how to use it and in what configuration should the magnets be configured. My first step was to tackle the permanent magnet configuration without using steel. I needed a configuration where a permanent rotor magnet could pass through two or more permanent stator magnets producing a repelling force on both sides of the stators. The simplest configuration that meets this requirement is to three magnets angle the direction of its poles such that they are parallel to desired direction of movement. This configuration is shown below in Figure 1 Balanced Repelling Gate Configuration.
Figure 1 Balanced Repelling Gate Configuration
The force area plot of this configuration is show below in Figure 2 Force Area Plot of Repelling Gate. This area plot shows the force exerted on the rotor in direction of motion. A negative force indicates a force in opposition of the desired direction of motion. A positive force indicates a force in the desired direction of motion. For the area plot you can see that the negative forces and positive forces completely balance each other out. The trapezoidal integral on this force curve has a result of 5.5454. This is within the margin of error for the simulation. In a perfect simulation with no error and infinite number of samples one should expect a result of 0 for the trapezoidal integral.
Figure 2 Force Area Plot of Repelling Gate
Now with a base configuration of magnets selected then next step was figuring out how to use steel to significantly reduce the negative force without having a major impact on the positive force. At first I didn’t think I would discover any interesting results. But I eventually created the configuration shown in Figure 3 Gate7 Configuration. This configuration had interesting simulation results. The force area plot for this configuration is shown in Figure 4 Force Area Plot of Gate7.
Figure 3 Gate7 Configuration
Figure 4 Force Area Plot of Gate7
Looking at the force plot you can see the desired effect of reducing the negative force with minimal effect to the positive force is present. The trapezoidal integral tells us the area above the zero axis is significantly larger than the area below. This equates to approximately 22% more force exerted in the positive direction than the negative direction.
In-depth Analysis of the Unbalanced Flux Gate
My thinking behind the design of gate 7 was to see what effect the steel would have if I used the steel as shield on the side of the stators where I wanted to reduce the magnetic flux. From earlier simulations I had learned to not use too much steel. Also the steel that was used for shielding had to be placed up against the stators. My idea was to have the magnetic field from the stators saturate the steel. This would prevent any magnetic domains from being created in the steel that would have the steel and the rotor attract.
I began analyzing magnetic flux line plots of Gate 7 at both the positive and negative peaks. Analysis of the flux line plots lead me to a new hypothesis to which I proceeded to test. My hypothesis is that it is incorrect to think of a material with a relative permeability greater than 1 as a magnetic shield. Instead it is much more appropriate to think of them as conductors of magnetic flux. Magnetic flux will take the path of least resistance. When given the choice of traveling through air or steel, the magnetic flux will travel through the steel in increasingly higher flux densities until either no more magnetic domains can be created in the steel or the steel has already created enough domains to completely carry the magnetic flux to which it is exposed. This is precisely what the B-H curves of materials show us.
The results of testing this hypothesis lead to the creation of gate10. Gate 10 is shown in Figure 5 Gate10 Configurationand its force area plot is shown in Figure 6 Force Area Plot of Gate10.
Figure 5 Gate10 Configuration
Figure 6 Force Area Plot of Gate10
The result of the gate 10 simulation gives evidence to support my hypothesis. Looking at the flux line plots of both the negative and positive force peaks I observed the following effect. The shape and position of the steel in gate10 is causing a significant part of the magnet flux moving the rotor in the –x direction to pass through the steel. In this case part of the N to S flux for the stator magnets is going through the steel. None of the N to S flux of the rotor, N rotor to S stator or N stator to S rotor flux is passing through the steel. By doing this the negative x inducing interaction of the N to S flux of the rotor and the N rotor to S stator flux with the N to S flux of the stator magnets is reduced. The size of the steel is just so that it becomes saturated with the magnetic flux from the stator magnets only. If the steel conducted any of the N to S flux of the rotor or the N rotor to S stator flux then the desired effect would be lessened or become an attractive force for the rotor.
Next I wanted to test the result of moving the stators closer together so the rotor would have a small gap when passing between the stators. The resulting force area plot is show in Figure 7 Force Area Plot of Gate11. The trapezoid integral showed a marked decrease over gate10. I concluded that since I am trying to unbalance the repelling forces on one side of the stators versus the others then it makes little sense in reducing the size of the gap. A smaller gap is actually much more harmful due to several reasons as follows:
• The closer the rotor gets to the steel the more difficult it becomes to fine tune the shape such that saturation comes only the stator magnets.
• Effects from Lenz’s Law will increase with a smaller gap.
• Reducing the gap increases the repelling force on both sides of the stators by equal amounts.
Figure 7 Force Area Plot of Gate11
I managed to improve the gate10 design even more my placing a small amount of steel on the right side of the stators. I found that using the steel to lessen the resistance of S Rotor to N Stator flux showed a larger increase on the positive force versus the increase on the negative force. The force area plot of Gate11 is shown in Figure 8 Force Area Plot of Gate. I
Figure 8 Force Area Plot of Gate12
To sum up how much of a difference the steel has made in the result of the magnetostatic simulations take a look at Figure 9 Force Plot of Baseline Versus Gate . This plot shows the progress the gates have made over the concepts I have investigated thus far. The shape of the steel could probably be further refined to improve the desired effect even more. However, I think this work is best left until the gate design can be explored in 3d magnetostatic FEA.
Figure 9 Force Plot of Baseline Versus Gate Configurations
Analysis of Unbalanced Flux in a Linear Track
Next I proceeded to do an analysis of the rotor passing through a series of stators in the gate10 configuration. This configuration is shown in Figure 10 Unbalanced Flux Track Configuration. The spacing of the stator pairs for this configuration was chosen to have minimal interaction of the repelling peaks of the stator pairs. The simulation results of this configuration are shown in Figure 11 Force Area Plot of the Track1 Configuration. The graph shows a very slight negative affect of the stator pairs on upon each other. Each successive positive peak is slightly lessened while each negative peak grows slightly. The trapezoidal integral clearly shows a sum total positive x force.
Figure 10 Unbalanced Flux Track Configuration
Figure 11 Force Area Plot of the Track1 Configuration
I next tested the effect of moving the stator pairs close together. The resulting force plot is shown in Figure 12 Force Area Plot of the Track2 Configuration. Here the negative influence of the stator pairs is much more noticeable. The trapezoidal integral decreased by 48.5%.
Further testing of the linear track should be done. A longer track with more stator pairs should be simulated. At the current time I do not feel this is a very high priority as the linear track serves no practical purpose other than setting a basis for study multiple stator gate interactions.
Figure 12 Force Area Plot of the Track2 Configuration
In summary I would say the gate configuration presented in this document shows much potential. Unbalancing of repelling flux forces in the manner described here might possibly be used to build a permanent magnet motor that has no electrical input. If we use LaFonte balancing with paired armatures, 4 permanent rotor magnets, in an X layout the motor should self start without the need for any electromagnets in the motor. My primary concern is computer simulation versus real world results. My secondary concern is the need for eddy current analysis to get a better idea of Lenz’s Law effects. Beyond that the amount of torque that can be produced from this in a possible motor is questionable. My next step is to move to 3d modeling and magnetostatic FEA simulation. I will write a follow up document after I have completed my 3d analysis of the concepts presented in this document. If the 3d computer simulation results look promising I will have a physical prototype constructed for testing.
Please e-mail me any feedback, questions or ideas you might have. Better yet post on the minatowheel Yahoo group and share your thoughts with all of us there. Best of luck to each and every one of us out there on the quest for free energy!
Update of My Recent Testing Efforts
© Terrence Staton
Thursday June 24, 2004
Here is an update on the tests I have been doing so far. Generally while I am running computer simulations I am also conducting some experiments that I setup up with Legos. I find Legos to be sturdy and fairly precise. I can get accurate results even with small forces. I can often conduct a great many number of experiments in a single night by using them. Here are some of the tests I have conducted over the past few days.
Above is a picture of the Lego train track I often use to conduct linear experiments. I put rotor magnets on cars of varying sizes depending on the test. Then I place stator magnets along the track. This is the setup I use when I test shielding materials. Both stator magnets are repelling the rotor magnet in this picture. I put the shielding around one stator magnet and see how far the car moves towards that magnet. I found that if I didn’t conduct this test before doing other tests with the shielding material I could be wasting my time as the shielding is ineffective.
Right now I don’t have any shielding effective enough to conduct further shielding experiments. Either they don’t absorb enough B or the shape just is not right. Since there is only so much I can do with a Dremel, I am trying to locate a local independently run machine shop so I can get a few pieces of shielding made that should work very well. The shape, size and material of the shielding will be based up some of the simulation results I have conducted thus far. I will use a CAD drawing of the parts to make sure they are accurately fabricated.
Over the past few days I have been exploring possible motor configurations. Next is a picture with one of my motor ideas.
I initial thought this configuration would be a good setup for HJ motor idea that Graham had. I noticed something a bit odd about this setup. Only the left side the stators were set up to repel. On the right side the stators were setup to attract. As can be seen here there is a sticky spot. It is possible that one of the magnets is stronger than the other causing this problem. Also it is possible that the magnets approaching in arc like this creates the sticky spot. My guess is the former. I need to build my own gauss meter to confirm this possibility.
Next I tested a more typical motor configuration.
In this configuration the stator magnets in the 7 and 1 o’clock positions are repelling. The stator magnets in the 4 and 10 o’clock positions are attracting the rotors.
I noticed the exact same sticky and repel spots in this configuration as the previous one. The sticky and repelling spots reversed depending on which rotors were facing different magnets. This leads me to believe that the magnets are indeed imbalanced. I think it is time I go ahead and get a Hal sensor and build my own gauss meter.
Well that is it for now. If anyone else has ideas on what might be going on in the above tests I would like to hear your thoughts the matter.