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23 November 2024 21:57
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Welcome to the gyroscope forum. If you have a question about gyroscopes in general,
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Question |
| Asked by: |
Jesse Smith |
| Subject: |
gimbaled gyro's resistance to movment and conservation of energy |
| Question: |
After reading a good majority of the questions on this forum I have come to realize that most people seem to demand their answers, so I'll try to ask polietly. I have some questions regarding a gyroscope that has been gimbaled so it can only rotate in one plane, perpendicular to the axis of rotation.
1. when the gyro is spinning, and the gimbal is forced to turn at a constant speed, what is the torque or force required to turn the gimbal? is its resistance the same as the couple moment placed on the bearings as in the math page? or is there another equation describing this?
2. with the conservation of energy, what goes in must come out. If a constant torque is required to keep this gimbal spinning (assume frictionless bearings) where does this energy go? does the speed of the flywheel increase? or am I missing somthing? with no friction the temperature stays the same.
I'm interested in gyroscopes as a form of power absorbtion for engine dynometers and also for use in a possible CVT or torque converter.
hopefully these questions are understandable, drop me a line by email if you have any ideas, hints, tips, advice or comments,
Thanks!
Jesse |
| Date: |
10 July 2004
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Answers (Ordered by Date)
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| Answer: |
Nitro Macmad - 10/07/2004 22:17:40
| | | Dear Jesse Smith,
Sorry but this is, of necessity, nastily complex.
I think I understand what you are asking but to make sure can I describe what I think you ask in bike wheel example? Are you describing a bike with the main frame fixed so that the front wheel is off the ground with the rotating bike wheel (gyro) in a front fork that is able to have the handlebars continuously rotated to cause precession that would try to turn (precess) the forks at right angles to the rotation of the handlebars?
If the answer to the above is yes then:-
1. As the wheel is not free on more than one axis it will not display the precession of the force acting to turn the handlebars unless the whole bike frame is allowed to move. This is because the precessional effect of the applied force is itself * precessed by the resistance to free movement presented by the forks inability to move in the precessed plane. (Dear God! I hardly understand all that, now I read it, but it is right - honest) So, while placing a load on the bearings of the fork head, it (the energy required - force as you call it) is small, as any force is precessed all the way round until it effectively goes away (cancels itself out - like negative feedback). The only thing loading this arrangement is, therefore the normal bearing and air resistance.
2. The energy is conserved in the normal way as, if the wheel (gyro) is unable to precess, it is as if the handlebars were turning a simple attached mass instead of a rotating wheel and the normal laws of torque at the handlebars therefore apply. As mentioned above the only thing affecting the speed of the gyro is thus friction whether in the wheel’s bearing or in skin resistance with the air.
Unfortunately, I think that there are probably better means to dump load than by trying to use a gyro both because of the above tendency of a gyro to act like a normal, non precessing, mass (showing all the normal Newtonian tendencies) if it is not free to precess in a particular plane and because if it is free in other planes, it will only precess a theoretical maximum of 90 degrees before it ceases to precess further a torque applied to it because at that point it has aligned its axis with the torque applied to it. This is rather like rotating an eccentric weight to do load dumping - does the job if the device it is fixed to is free (to leap about a bit) but nail it down and it won’t dump energy anymore - tends to bash its bearing to bits, though!
Regards,
NM
PS Sorry if your head hurts now - you might take some comfort in the fact that mine does too.
*Nitros 1st. Law says, “A gyro will precess every damn force that acts on it not just the one that you first thought of”.
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| Answer: |
Jesse Smith - 12/07/2004 17:52:43
| | | ah, I see..... well I'll try to explain my own side more clearly, lol thanks for your effort! I did understand some of what you were saying.
under the behaviour link on this page, go to "in depth" or how a gyroscope works, down the page is a picture of a gimbaled gyroscope. the gyro is allowed to rotate in only 1 plane, OTHER than its own spin about its axle. this is what I'm talking about. with this set up, get the gyro spinning at say 5000 rpm, now the gimbal ring will resist being turned about its gimbal bearings, I'm interested in this resistance. a certain force is required to make it turn at a certain rpm. What is the equation for this force?
or another case. 2 flywheels are placed on the same axle side by side and they rotate in opposite directions. Thus any pressesion is cancled out. correct? this assembly, floating in space will resist being turned about any axis perpindicular to its own spinning axis. it is possible to move this assembly but a force is required, what is this force in terms of the moment of inertia of the flywheels and their rpm?
from this setup I was interested in where the energy goes when this assembly is forced to turn about an axis 90 degress to its axis of spin.
hehe, well I think that makes more sence to me, I'm goin to find a gyro and try some of this stuff myself, but if anyone can help, that would be great!
Thanks!
Jesse
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| Answer: |
sh. yazdani - 18/07/2004 07:58:30
| | | Hi Jesse,
To answer your first question, according my experiments I have conduced, the torque or force required to turn the gimbal is larger (maybe up to 60%) than the couple moment placed on the bearings as in the math page. But I have not any equation for it. If you have any idea against me please tell.
thanks,
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