I long ago noticed a physical effect whereby mechanical spin is transferred from one object to another when they are connected by a rigid structure but individually free to spin (in loose contact with the structure). One example is the wheel of a bike mounted on the back of a car as it drives on a highway: the bike wheel may be seen to spin. As a separate example, i connected a dc motor with an imbalanced load (such that it created high amplitude vibration) to a series of hollow metal rods. In the end of one of the rods i placed a small (low mass) grinding wheel such that it fit perfectly in the hole and was free to rotate. When the motor was powered, the grinding wheel would turn the same direction (CW or CCW) as the motor, as perceived head-on along the axis. What could cause this?
spin conduction
- Thread starter wolf
- Start date
Can you explain more? Why wouldn't the vibrational energy simply be radiated as sound or heat? I'm sure some of it is, as the second rotating object doesn't have as much energy as the first. I'm looking for the mechanism by which the angular momentum is transferred across a mechanical structure.
RainmanTime
Super Moderator
Can you draw a diagram of the apparatus and post it here?
You seem to have some knowledge about engineering analysis of mechanics, and so I would presume that you know the first step in solving any mechanics problem is:
"Draw a free-body diagram"
Anyone who got their degree in engineering should hear their statics instructor's voice inside their head saying this over and over! /ttiforum/images/graemlins/smile.gif
If you can provide a diagram of the apparatus, I can work with you to draw the free body diagram and develop the equations of motion to help you answer your question.
RMT
You seem to have some knowledge about engineering analysis of mechanics, and so I would presume that you know the first step in solving any mechanics problem is:
"Draw a free-body diagram"
Anyone who got their degree in engineering should hear their statics instructor's voice inside their head saying this over and over! /ttiforum/images/graemlins/smile.gif
If you can provide a diagram of the apparatus, I can work with you to draw the free body diagram and develop the equations of motion to help you answer your question.
RMT
Einstein
Dimensional Traveler
wolf
The mechanism is Newton's Law. For every action there is an equal and opposite reaction. So when the out of balance mass spins, an equal but opposite force changing direction also exists within the solid mechanical structure connected. I've played around with this a lot. It really does enhance your theory making ability to figure this out on your own though.
The mechanism is Newton's Law. For every action there is an equal and opposite reaction. So when the out of balance mass spins, an equal but opposite force changing direction also exists within the solid mechanical structure connected. I've played around with this a lot. It really does enhance your theory making ability to figure this out on your own though.
RainmanTime
Super Moderator
Excellent. Now another question to help us with the free body diagram:
Are any points on this apparatus secured to the surface upon which it sits? If so, denote which points are "grounded". With that question answered we can begin to describe one way to think about the dynamic motion going on.
RMT
Are any points on this apparatus secured to the surface upon which it sits? If so, denote which points are "grounded". With that question answered we can begin to describe one way to think about the dynamic motion going on.
RMT
RainmanTime
Super Moderator
Another question for you with regard to:
Is there any reason to believe that this force is not caused by the aerodynamic forces on the wheel as the car drives through the airmass around it?
RMT
Is there any reason to believe that this force is not caused by the aerodynamic forces on the wheel as the car drives through the airmass around it?
RMT
No.
That's why i gave more than one example. I've also seen the effect occur in a bath tub with a broken valve (that switches between the faucet and shower head); the rush of water vibrating the faucet caused the circular valve to rotate. In another test a hollow tube with a wheel like in the diagram above was placed securely between the strings of a guitar. Playing low frequency notes would cause the wheel to rotate, though it was less reliable than the motor setup pictured above.
I would like to add that, due to the possibility of aerodynamic effects, i placed a cover over the motor in the pictured setup in order to stop any air currents which might result from the imbalanced wheel. The rotation in the second wheel was not changed by this. I chose this setup because it is clearly not caused by aerodynamic forces.
I would also like to note that changing the orientation of the second wheel such that its axis is not parallel to that of the motor did not change its spin direction or speed in the tests i conducted. In other words, if you rotate the second wheel's axis, [omega][2] will rotate by the same amount in the same direction.
I would also like to note that changing the orientation of the second wheel such that its axis is not parallel to that of the motor did not change its spin direction or speed in the tests i conducted. In other words, if you rotate the second wheel's axis, [omega][2] will rotate by the same amount in the same direction.
RainmanTime
Super Moderator
Very good.
Both of these effects (your motor apparatus and the vibrating faucet in the shower) are cases of resonant vibrations. Are you aware of this branch of the science of dynamics? We can branch off our discussion into that realm, depending on your answer and your curiosity level.
But back to your motor apparatus: A good engineering analysis begins with the simple and moves to the complex as necessary. We also begin by stating whatever simplifying assumptions we wish to make to do our first round of analysis. For now, let us state the simplifying assumption that we assume all motion of the motor apparatus is constrained to the plane that you have drawn (looking down on the apparatus). Essentially, this simplifying assumption is called the 2 Degree Of Freedom (2-DOF) approximation. The 2 DOFs we consider are the X and Y directions of the plane that defines the apparatus.
Since the motor wheel is unbalanced, the center of mass of the wheel is not on its rotation axis. Rather, it is offset from that axis. One way to view this situation when the wheel is turning is that there is a part of the mass of the wheel that is being "shuttled" from the left to the right side of the spin axis. (It is also moving up and down, but we have assumed 2-DOF so we ignore that up-down motion for this analysis). So model it as a small mass "dm" being moved back and forth a set amount across the spin axis line of the motor. Looking at this mass "dm" moving back and forth we realize that the acceleration profile of "dm" is oscillatory. In other words "dm" accelerates to the left, then decelerates, then accelerates to the right, then decelerates, ad infinitum. So if we were to plot he acceleration signal vs. time we would see a sine wave form for the acceleration. And since Force = mass*acceleration, we can also see that we have an oscillating force acting upon the wheel.... first the force pushes in one direction, and then it pushes in the other direction.
Can you understand this so far? And if so, can you understand how this oscillatory force, created by the constant acceleration of the unbalanced wheel, then is mechanically transferred through the structural arms of the apparatus? The transferrence of this oscillating force through the structure will dissipate some of the energy of the force, such that a resultant smaller force will be exterted on the smaller wheel whose spin axis is inside the copper tube. The force that is felt at the small wheel is also out of phase (somewhat) with the force coming from the unbalanced wheel.
This is what sets up the resonance that is going on. The final rotational velocity of the small wheel is directly related to the structural resonant frequency of the entire apparatus. In fact, this apparatus would be a classical example of an experiment to demonstrate the frequency response analytical technique for characterizing a system's dynamic response. We can talk about that some more, if you wish.
Do you understand, so far?
RMT
Both of these effects (your motor apparatus and the vibrating faucet in the shower) are cases of resonant vibrations. Are you aware of this branch of the science of dynamics? We can branch off our discussion into that realm, depending on your answer and your curiosity level.
But back to your motor apparatus: A good engineering analysis begins with the simple and moves to the complex as necessary. We also begin by stating whatever simplifying assumptions we wish to make to do our first round of analysis. For now, let us state the simplifying assumption that we assume all motion of the motor apparatus is constrained to the plane that you have drawn (looking down on the apparatus). Essentially, this simplifying assumption is called the 2 Degree Of Freedom (2-DOF) approximation. The 2 DOFs we consider are the X and Y directions of the plane that defines the apparatus.
Since the motor wheel is unbalanced, the center of mass of the wheel is not on its rotation axis. Rather, it is offset from that axis. One way to view this situation when the wheel is turning is that there is a part of the mass of the wheel that is being "shuttled" from the left to the right side of the spin axis. (It is also moving up and down, but we have assumed 2-DOF so we ignore that up-down motion for this analysis). So model it as a small mass "dm" being moved back and forth a set amount across the spin axis line of the motor. Looking at this mass "dm" moving back and forth we realize that the acceleration profile of "dm" is oscillatory. In other words "dm" accelerates to the left, then decelerates, then accelerates to the right, then decelerates, ad infinitum. So if we were to plot he acceleration signal vs. time we would see a sine wave form for the acceleration. And since Force = mass*acceleration, we can also see that we have an oscillating force acting upon the wheel.... first the force pushes in one direction, and then it pushes in the other direction.
Can you understand this so far? And if so, can you understand how this oscillatory force, created by the constant acceleration of the unbalanced wheel, then is mechanically transferred through the structural arms of the apparatus? The transferrence of this oscillating force through the structure will dissipate some of the energy of the force, such that a resultant smaller force will be exterted on the smaller wheel whose spin axis is inside the copper tube. The force that is felt at the small wheel is also out of phase (somewhat) with the force coming from the unbalanced wheel.
This is what sets up the resonance that is going on. The final rotational velocity of the small wheel is directly related to the structural resonant frequency of the entire apparatus. In fact, this apparatus would be a classical example of an experiment to demonstrate the frequency response analytical technique for characterizing a system's dynamic response. We can talk about that some more, if you wish.
Do you understand, so far?
RMT
Completely.
At some point i thought maybe the motor was causing spiral transverse surface waves on the cylinders, which then travel to the last tube and "rub" against the second wheel's axle, exerting a tangential force on it by friction. It would be a small force and largely depend on how close the axle is to the interior of the tube. Does that sound right? I'm open to other explanations.
Sounds interesting. Where do we start?
RainmanTime
Super Moderator
Hi again, wolf:
Well, that is one way of describing it, and it is good enough for the imprecision of words over math. Some persnickety science and engineering types might want to question or correct the words "spiral transverse surface waves". But certainly you can even likely see the spiral motion of the unbalanced wheel, so that checks. You can also likely see the apparatus vibrating back and forth, if even a small amount and at a high frequency. But they are really not "surface waves". It is pretty much all rigid body motion. If I am not too lazy today I will save off your diagram and draw some vectors on it to show how the forces are transferred around the apparatus.
Well, we would first start by explaining the concepts of Gain and Phase in oscillatory system dynamics. But first help me to understand if you have any knowledge or familiarity with the concepts of "frequency response" or "gain and phase" or if you know what a Bode Plot is? If you are familiar with any of these, I can tailor my explanation to move quickly. If not (and it is OK if you are not familiar with any of these), then I can start from the basics.
As an introductory thought, your equation which relates Omega2 to Omega1 by a factor "k" is already applying the principle of Gain. "k" is actually the system gain that either amplifies or attenuates the input signal to achieve the amplitude of the output signal. And another thought: The reason your apparatus is such a classical example of frequency response is that the independent variable in the apparatus (the motor speed) deals directly with the frequency parameter that is the fundamental parameter for oscillatory system dynamics.
I'll await your reply before I go into the details of Gain and Phase. But I will say this exercise will give you some initial insight into the world of complex control systems and how we analyze them and design them.
RMT
Well, that is one way of describing it, and it is good enough for the imprecision of words over math. Some persnickety science and engineering types might want to question or correct the words "spiral transverse surface waves". But certainly you can even likely see the spiral motion of the unbalanced wheel, so that checks. You can also likely see the apparatus vibrating back and forth, if even a small amount and at a high frequency. But they are really not "surface waves". It is pretty much all rigid body motion. If I am not too lazy today I will save off your diagram and draw some vectors on it to show how the forces are transferred around the apparatus.
Well, we would first start by explaining the concepts of Gain and Phase in oscillatory system dynamics. But first help me to understand if you have any knowledge or familiarity with the concepts of "frequency response" or "gain and phase" or if you know what a Bode Plot is? If you are familiar with any of these, I can tailor my explanation to move quickly. If not (and it is OK if you are not familiar with any of these), then I can start from the basics.
As an introductory thought, your equation which relates Omega2 to Omega1 by a factor "k" is already applying the principle of Gain. "k" is actually the system gain that either amplifies or attenuates the input signal to achieve the amplitude of the output signal. And another thought: The reason your apparatus is such a classical example of frequency response is that the independent variable in the apparatus (the motor speed) deals directly with the frequency parameter that is the fundamental parameter for oscillatory system dynamics.
I'll await your reply before I go into the details of Gain and Phase. But I will say this exercise will give you some initial insight into the world of complex control systems and how we analyze them and design them.
RMT
ruthless
Rift Surfer
"A Bode magnitude plot is a graph of log magnitude versus frequency, plotted with a log-frequency axis, to show the transfer function or frequency response of a linear, time-invariant system.
The Bode plot is named after Hendrik Wade Bode. It is usually a combination of a Bode magnitude plot and Bode phase plot"
interesting stuff.
The Bode plot is named after Hendrik Wade Bode. It is usually a combination of a Bode magnitude plot and Bode phase plot"
interesting stuff.
RainmanTime
Super Moderator
You got them... good. The fact that you understand these basics will make our discussion productive in short order. And as for:
As ruthless showed with his quote, the Bode Plot is nothing more than a special name given to two strip charts that go together to describe the total frequency response of a dynamical system. Both charts have Log(frequency) as their independent variable. One chart has Gain as the dependent variable (which is defined as 20*Log(Output/Input)), and the other has Phase angle (in Deg) as the dependent variable. It is these charts we refer to when we talk about establishing the "gain margin" and "phase margin" of a dynamical system.
If you happen to have the MS Powerpoint application HERE are a set of charts that I use to introduce frequency response concepts in my ARO 202 course when we begin to talk about aeroelastics. You will see a Bode Plot in one of these charts which also denotes how we determine gain margin and phase margin from them.
Given that the one input parameter of your motor apparatus is the speed (frequency) of the motor, can you begin to understand how your apparatus is a classical frequency response test setup? Can you see that by varying the speed of the motor you can develop a Bode Plot that will characterize the dynamic response of your motor-apparatus-wheel system?
RMT
As ruthless showed with his quote, the Bode Plot is nothing more than a special name given to two strip charts that go together to describe the total frequency response of a dynamical system. Both charts have Log(frequency) as their independent variable. One chart has Gain as the dependent variable (which is defined as 20*Log(Output/Input)), and the other has Phase angle (in Deg) as the dependent variable. It is these charts we refer to when we talk about establishing the "gain margin" and "phase margin" of a dynamical system.
If you happen to have the MS Powerpoint application HERE are a set of charts that I use to introduce frequency response concepts in my ARO 202 course when we begin to talk about aeroelastics. You will see a Bode Plot in one of these charts which also denotes how we determine gain margin and phase margin from them.
Given that the one input parameter of your motor apparatus is the speed (frequency) of the motor, can you begin to understand how your apparatus is a classical frequency response test setup? Can you see that by varying the speed of the motor you can develop a Bode Plot that will characterize the dynamic response of your motor-apparatus-wheel system?
RMT
Interesting. /ttiforum/images/graemlins/smile.gif Now i have some questions.
Is there a way to design a system where the output frequency is different than the input frequency (without using electronics)?
Do you do a Bode plot for each dimension (you talked about simplifying the motor appartus to 2D) or all at once?
Are airplane wings treated as simple cantilevers? How do you excite them at a particular frequency & measure the response (i would guess accelerometers for measurement)?
Resonance is amazing /ttiforum/images/graemlins/smile.gif
Oh, yes, and for my motor setup how would i measure the gain & phase?
Is there a way to design a system where the output frequency is different than the input frequency (without using electronics)?
Do you do a Bode plot for each dimension (you talked about simplifying the motor appartus to 2D) or all at once?
Are airplane wings treated as simple cantilevers? How do you excite them at a particular frequency & measure the response (i would guess accelerometers for measurement)?
Resonance is amazing /ttiforum/images/graemlins/smile.gif
Oh, yes, and for my motor setup how would i measure the gain & phase?
RainmanTime
Super Moderator
Yes. And actually, all REAL systems act this way, because all REAL systems only have a small operating region where their input-to-output relationship is LINEAR. That is the key...linearity vs. non-linearity of the "plant". For example, an airplane (all airplanes) only have a small region where their response is linear. This is, approximately, in the angle of attack range from -10 degrees up to about +14 degrees. Outside of this range, the assumption of linearity of response is not a good assumption. So the maths we use behind frequency response analysis has an assumption that the plant is linear (and time-invariant). If it is NOT linear, the math goes from just being hard to being inordinately difficult.
In the general sense all at once, because both Gain and Phase are scalar measures of the system's dynamics as a whole. However, for aircraft we break down the airplane's dynamics into two planes of response. We analyze Longitudinal-Vertical performance separate from Lateral-Directional by breaking out 2 sets of 3-DOF equations of motion. So the measure of Gain and Phase are measures of whatever portion of the plant that you have decided to model (or test). Did that answer the question to your satisfaction?
Yes, but only in the preliminary design phase because you are not trying to do detailed analysis... only enough analysis to allow you to iterate configuations until you can settle on a "big bones" configuration. Following preliminary design, the wings (and fuselage) are modeled in detail in a finite element structural computing environment (like NASTRAN) where the details of stress and strain can be analyzed and even simulated frequency sweeps run against this model.
This is, perhaps, one of the more fun aspects of my job! /ttiforum/images/graemlins/smile.gif All new airplanes, after the first prototype is built, must go through what is called Ground Resonance Testing/Ground Vibration Testing (GRT/GVT). Aircraft manufacturers have specialized rigs to do this, depending on whether they are just testing the wing or the entire airplane. For the entire airplane GRT/GVT, the whole airplane is secured to a giant "rate table" which can then oscillate in the up-down direction at various frequencies.... so we are literally shaking the airplane through an entire frequency sweep! We will also stop at particular "dwell points" and do several amplitudes at those dwell frequencies. These dwell freqs correspond to the predicted resonance frequencies that the finite element model tells the engineer the structure SHOULD resonate. Obviously, the purpose of the dwell testing is to collect a lot of data around the predicted frequencies for the purpose of validating that the computer model correctly models the real airplane. And yes, you are correct that instrumentation accelerometers are placed at key points on the airplane to measures its response.
It would require some instrumentation (some of which could be pretty expensive). But let me write to you about that after I get home from work... At least I can describe how you would go about it, and one (or more) ways that you could get rough measures.
Later,
RMT
Sounds fun. :D
Do you think there's a way to vibrate a structure such that a unidirectional airflow is created around it? It would involve the interaction of the vibrating surface and the air near it, but i don't know how to analyze it.
Also, since heat is just random motion and vibration of molecules, can a structure be designed to damp all but certain frequencies of vibration caused by heat?
I have thought of building a UAV for fun someday but i haven't yet begun. I found some plans online but i would rather make something original. How difficult would such a project be for one with no aerospace engineering experience?
This is interesting stuff. Thanks for the replies. /ttiforum/images/graemlins/smile.gif
RainmanTime
Super Moderator
No way that I am aware of, and I teach aerodynamics. /ttiforum/images/graemlins/smile.gif The problems with such an idea are twofold:
1) Because air has such a low density (i.e. it is a gas, rather than a liquid) it is not at all effective at transferring momentum from one particle to another in a static airmass. You can demonstrate this just by witnessing how a breeze created by you running past someone dissipates quickly as your distance from them increases.
2) Because a vibration is a standing wave in a structure, it will only impart momentum to air particles adjacent to the structure, and even then only in an "up and down" (perpendicular to the surface) manner. Momentum would need to be imparted to the flow in the direction along the surface instead of perpendicular.
Theoretically, yes, such a thing is possible. But in practice it would be a very difficult thing because not all bodies transfer heat at the same frequency (i.e. different masses with different densities will have different resonance properties for heat transfer). If one were to attempt such a thing, it would certainly require feedback sensors of some sort and a closed-loop control ssytem to pull it off.
Well, that depends on how much general engineering experience you have. You seem to have a good grasp on basic physics and much of the early calculus common to all engineering. If all you have are plans, but no informtion on the aerodynamics of the basic vehicle and the aerodynamics of the moveable control surfaces, it will be quite a task indeed. Not saying it is impossible (and there ARE books out there on aerodynamics, if you are good at self-instruction), but if you take on such an endeavor be prepared for a few accidents...one or more that may be catastrophic! :eek:
Incidentally, one of my goals for my property that I am developing in Colorado is to build and flight test my own UAV design once I can retire from teaching and working for Northrop-Grumman. Here's a pic of my first outbuilding that I just completed construction on last December:
That is a highbay garage door, and behind it will be my assembly shop for building and testing the UAV. I've got 35 acres and plenty of room to get the thing off the ground. /ttiforum/images/graemlins/smile.gif Maybe you can come up to visit and help me with it?
My pleasure. I enjoy teaching and spreading knowledge about my craft! /ttiforum/images/graemlins/smile.gif
RMT