Gyroscopic precession

[Kajunbee]

I'm sure most of have seen the demonstration of precession where a spinning wheel remains vertical when only supported by a rope on one side. My question is about the speed of precession around the rope. Most demonstrations I have seen it is relatively slow. From what I've seen there are two things that will increase the rate of precession. Either the wheel slowing down or hanging a counterweight on the other side of wheel. My first question is about the amount of torque generated as the wheel slowly rotates around the rope. If I were to grab the rope where it is attached to wheel axle would it be easy to stop the precession. Or would the gyroscope react to the resistance and try to maintain its rate of precession by increasing torque.
This may be something I have to experiment with on my own but if anyone has any knowledge they can share it would be appreciated.

 

[Kajunbee]

What I'm wondering is whether precession alone can turn a generator. since the motor turning the gyroscopic wheel is not directly turning the generator it would not load down and draw more power.. It should only take minimal power to maintain the rpm of the wheel and power consumption should be relatively constant. I'm just not sure if there is any appreciable amount of torque or rpm that can be achieved.
I did a quick experiment just to see if it might be possible. I mounted a universal joint on the end of one of my pm generators. On the other end of universal I had a short piece of shaft with a 12" plastic cart wheel slid over it. I found that it would indeed turn the generator. I placed a 5.1 ohm resistor across the generator and at the max rate of precession which was maybe 25 rpm I measured about 2 volts. Not much but this was just a quickly thrown together thing. I did not have a motor mounted to maintain the rpm of the wheel either.
Although not conclusive I did learn a couple things. Firstly it seems that the wheel has to be able to freely fall to maintain precession. If you make the universal rigid precession stops. Also the position of the wheel on the axle has seems to effect the torque and precession speed.
Other than spinning tops when I was a kid I don't know that much about gyros. Everything about them seems backwards.

 

[c_mitra]

I strongly suggest you consider the basics: the conservation of angular momentum is central- but I do not understand what you mean by "supported by a rope on one side". If there is any friction OR any external force, the conservation rule will break down. Can you make a sketch? Do you mean the precession of the rotation axis?

 

[Kajunbee]

This a sketch of my setup.

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YouTube- "wheel momentum Walter Lewin " for demonstration of wheel supported by rope. I understand what you are saying about the resistance. I noticed today that if I applied more resistance by hand the wheel would start to fall. If I tried to speed up rotation faster than normal precession the wheel would start to raise higher.
I don't have a motor to maintain rpm so I wasn't able to test if and increase in rpm would offset any resistance added.

 

[BradtheRad]

The generator becomes hard to turn as soon as you attach an electrical load. This slows or stops the gyroscope's precession motion. Then I think the gyroscope reacts by attempting to twist in some direction, which I don't know how to predict.

 

[c_mitra]

I still do not understand where the rope is. But let me get my basics clearer...

I presume the 12" dia wheel is spinning. I also assume that air friction is negligible.

The rotation of the wheel creates an angular momentum which is in the direction of the axis of the wheel (horizontal). As the gravity is perpendicular to the angular momentum, the precession will be around the vertical axis. Your indicators are correct.

Next step begins the crazy part; if the universal joint is frictionless, the precession will continue for ever (correct).

If you attach a load (via the generator), the load will extract energy from the spinning wheel and the wheel will come to a stop. In engineering, this is called regenerative braking.

Spinning wheels have been considered for energy storage. I do not know the current status.

But the rope is still a mystery.

 

[Kajunbee]

There is no rope in my setup. Instead of a rope supporting wheel shaft from ceiling I am supporting wheel shaft from floor with the generator shaft. What I am looking at is precession alone spinning the generator, not the actual rotation of the spinning wheel. The wheel is not permanently fixed to the shaft. The wheel spins but the shaft it's mounted on doesn't.
What I do is spin the wheel up to around 1500 RPM and then set the whole apparatus on the floor like you see in my sketch.
I do realize that there has been research into using flywheels for energy storage. Supposedly NASA had one spin for 20 months straight before it stopped. The flywheel was in a vacuum and had magnetic bearings. The only thing I know about flywheels is if you double the mass you double the amount of energy stored. If you double the rpm you can store 4 times the amount of energy. I'm wondering if this also applys to precession.

 

[c_mitra]

I am slowly understanding.

If there is no rotation, there will be no precession. This is a cross product of the angular momentum and the force of gravity.

You now try to extract energy from the precession. How? Attach it like your device. The generator shaft now moves at the precession frequency. That is distinct from the spinning frequency of the wheel.

Consider the generator without a load. The mechanical load (rotor mass) may be ignored for the time being.

The rotor now moves at the precession frequency. Now you attach a load to the generator output. The generator now extracts mechanical energy from the precession of the spinning wheel.

The precession is also associated with an angular momentum. This energy comes from the spinning wheel. The wheel now experiences a friction.

Slowly the spinning wheel will come to rest.

 

[Kajunbee]

That's it. i guess the wheel will come to rest even if it has a motor maintaining its rpm. Gravity will take over and pull the wheel downwards.

 

[c_mitra]

That's it. i guess the wheel will come to rest even if it has a motor maintaining its rpm.

To maintain the RPM of the wheel, you will need to supply energy to compensate for the loss (from all causes).

If you have a motor maintaining its RPM, how it can come to rest??

By the way, universal joint will transmit the rotation of the wheel to the generator and not the precession frequency. Please verify!

In a real gyroscope, a motor maintains the RPM of the spinning wheel to supply the energy lost by friction....

 

[Kajunbee]

If you don't mind go to YouTube and search
" gyroscope precession and nutation ".
The video was made by TOC1955. This will help you fully understand the concept . The motor spins the gyro only and precession would turn the generator.

 

[c_mitra]

... This will help you fully understand the concept . The motor spins the gyro only and precession would turn the generator.

I fully understand the concept. The motor rotor is the gyroscope. It has a wheel attached to increase the moment of inertia.

Now you need to understand the role of the stator. They are coupled together by the magnetic flux. This coupling must be as weak as possible for the proper operation of the gyroscope but cannot be so small that the rotation of the wheel is not maintained.

Ideally the stator must have so small mass (compared to the rotor) such that it does not influence the motion.

Electrical connection must be made with brushes and slip rings and they also add friction. Best to have rotor without brushes.

Remember that coupling between the stator and rotor IS friction. Adding a generator to the precessing rod is also is friction.

Precession is easy to understand. Nutation is more interesting and you need understand perturbation theory. This theory is not new and known for about 100 years (perhaps more).

 

[Kajunbee]

I think I have a better understanding of why precession increases as the wheel slows down. As the wheel slows it loses angular momentum and gravity starts to pull down. Since the wheel and shaft are connected by a universal the wheel moves down in a inward arc towards the generator. When this happens it changes the center of mass and precession increases. The article describes it as being similar to a spinning ice skater who brings her arms in to accelerate rotation.

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Wouldn't there also be angular momentum of the motors rotor to be considered also. The rotor itself would have a gyroscopic effect. Maybe this would offset the mass of the stator somewhat. Still better to minimize the mass of the stator. Very good point and something I did not consider.

 

[FvM]

Precession is easy to understand. Nutation is more interesting and you need understand perturbation theory. This theory is not new and known for about 100 years (perhaps more).

Round about 100 years. Several treatises with detailed analysis of gyroscope movement have been written at the beginning of the last century, a profound German book by Sommerfeld and Klein "Theorie des Kreisels" (theory of the gyroscope), or Crabtree, H. "An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic Motion". Many can be freely downloaded at archive.org or google books.

Precession is represented by a simplified formula in most physic books. It shows the simple inverse relation between gyro rotation speed and precession frequency, also the proportional relation between deflection torque and precession frequency. The exact equations of gyroscope motion are however more complicated, that's why the said books have many hundred pages.

 

[c_mitra]

I think I have a better understanding of why precession increases as the wheel slows down. As the wheel slows it loses angular momentum and gravity starts to pull down..

As the wheel slows down, the precession also slows down. What you are talking about is called nutation. Nutation is the oscillation about the orbit of precession. Mostly this will be a sinusoidal motion but that is often a poor approximation. There are many books and the subject is well studied.

Precession is the circular motion about the vertical axis. If the angular momentum vector (the axis of rotation) and the force of gravitation (vertical always) are at an angle (not 0 OR 180 deg) there will always be precession because the cross product of the two vectors will be perpendicular to the plane of the two vectors- and will be a circular path around the vertical axis.

The precession of the electron or nucleus in an external magnetic field is similar to the above example. The precession of the orbit of mercury is much more complicated. Perturbation will prevent the orbit of precession to close. Nutation causes the pole star to drift over thousands of year.

By the way, there has been suggestions that we can use wave energy to generate power; the energy associated with the sea waves is associated with the angular momentum of the moon; extracting energy (if the energy is not dissipated otherwise) from the waves will cause moon to slow down!!

 

[Kajunbee]

I did not catch it the first time I read the post. You state that the motor is the gyro and wheel provides extra inertia. I was thinking of the wheel as the gyro and not considering the gyroscopic effect of the motor. Very perceptive of you. I'm having trouble understanding the role magnetic coupling plays in it. I'm thinking your talking about the drive motor. Is it the counter torque effect of the stator trying to spin the rotor that your speaking of. If so I would think think this would be more related to resistance in the system( wind age, bearings etc.)

Since there is basically two gyros ( motor + wheel ) and they will be at different distance from the center axis will they have different precession rates. How will this effect rotation. Will it have a positive or negative effect on precession. I haven't found any information that directly relates to this.

I researched what you said about wave energy. In the process I came across a patent for a gyroscopic wave generator. It uses wave action to maintain rotation of a gyro. which turns a generator.

 

[c_mitra]

I still think there is a problem with the understanding and the language.

The motor rotor and the flywheel together forms one gyroscope. But the stator of the motor (that has the driving coils etc etc) act as friction because there is some magnetic coupling between the two.

The balance wheel of a watch has a very accurate period; but we need to supply energy to make up the loss for the air friction and this coupling causes the friction.

Consider a quartz crystal; it has a very high Q. But you load the crystal with external capacitors so that sufficient energy can be transferred from the driving circuit to make up for the loss.

All the cases, the coupling causes decrease in the Q: the quality factor. As a result, the gyroscope loses its sense of bearing and your watch loses time.

Since there is basically two gyros ( motor + wheel ) and they will be at different distance from the center axis will they have different precession rates

No, you are wrong. The motor rotor and the wheel are together as one rigid body. Together they have one moment of inertial and one angular momentum. It is the angular momentum that precesses.

 

[Kajunbee]

I've been calling it a universal joint but it is actually a swivel joint. It rotates one direction but rigid the other direction. My apologies for the blunder. It it were a true universal I have no idea how it would react.

 

[c_mitra]

It rotates one direction but rigid the other direction

It must allow rotation on the x-axis as well as on the z-axis. Usually z-axis is the vertical one (connected to the generator rotor axis rigidly) and the x-axis is the axis of the spinning wheel (the direction of the angular momentum.

Note that the x-y plane is rotating with the precession frequency of the wheel. In the rotating frame of reference, the centrifugal force disappears (you can focus on the nutation only) but I am not trying to scare you.

The spinning wheel must be mounted on a ball bearing but must be rigid (must not extend).

If it were a flexible universal joint, the generator will spin at the wheel frequency+ precession frequency.

The earth rotates about the sun once a year plus it also rotates about its own axis once a day. Both these two rotations contribute to the sun rise. (No of days/year=no of times it rotates about its own axes + 1)/year

 

[Kajunbee]

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Can you see any reason why this would not work.
In the first photo a double shaft drive motor is mounted on top of the generator so that i only have to have one motor. One end of the motor I'm thinking would have to have a gear box to change the direction of rotation of one of the wheels. If not the wheels would precess in opposite directions and not move. Since the shafts are directly rotating the wheels I would most definitely have to use universal joints. I should be able to get full flexibility of movement though. I'm just not sure how stable it would be.

The second sketch is a top view. Since both wheels are connected by universals do you think the wheels would have a tendency to pivot ahead as in the sketch. I'm open to any and all suggestions.