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Resonance and Harmonics in Woodturning Explained

Discussion in 'Tutorials and Tips' started by Dennis J Gooding, Mar 12, 2020.

  1. Dennis J Gooding

    Dennis J Gooding

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    There seems to be some confusion in some recent postings between the terms “harmonics” and “resonance”, particularly in regard to lathe stability. Let me offer some Engineering Mechanics 101 light on the subject.

    Resonance

    To define “Resonance” in the technical sense, I will first define something that for lack of a better name, I will call a “resonator”. A resonator in mechanics is a system which when activated by a driving force, periodically transforms its stored energy back and forth between kinetic energy and one or more other forms of energy storage such as a stretched spring or a lifted weight. (It is directly analogous to a resonator in electronics, where energy is periodically exchanged between a magnetic field and an electrical charge on a capacitor.)

    A simple example is a pendulum. Given a nudge, the pendulum will swing back and forth, the amplitude of the swing slowly decreasing. The kinetic energy of the pendulum will be at maximum when the pendulum is at the lowest point and the gravitational potential energy will be at maximum at the outer points of the swing. Each of the two quantities will be zero when the other is at maximum.

    A somewhat more complicated example is a weight hanging from a spring. Starting with the system at rest, if the weight is pulled down, energy is introduced into to the system in the form of a stretched spring. At this point, the kinetic energy and the gravitational potential energy are both zero. Now, if the weight is released, it will begin to rise, picking up both kinetic and gravitational energy as it rises. At the top of its rise, all of the system energy will be gravitational potential energy. The kinetic energy will have risen and then fallen to zero again, while the energy in the stretched spring will have decreased smoothly to zero.

    Having defined resonator, we are in a position to define resonance. In each of the cases described above. When given an initial start, the system will continue to cycle at a characteristic frequency, called the resonant frequency, until somehow energy is removed from the system. In the case of a pendulum, the energy loss mechanism would be mainly air friction and friction in the pivot bearing. In the second system, additional losses would occur from the internal friction incurred in stretching the spring. In physical mechanics, this energy loss is characterized by a quantity called the “damping factor”. It is a measure of by what fraction is the amplitude of the oscillation reduced in each successive cycle. If the damping factor is zero, there is no reduction; if it is large, the oscillation dies out rapidly.

    Now consider what would happen if instead of giving the system one nudge and then letting it run, we were to give it similar nudge every time it returned to the same point in the cycle. If the losses in the system were very small (small damping factor), the amplitude of the oscillation would continue to increase until some external factor interceded (e.g., the lathe fell over). This phenomenon, with or without losses, is called “resonance” and is encountered often in woodturning. The work piece, the supporting spindles and other parts of the lathe often form one or more resonant systems, typically of different resonant frequencies. If the rotating work piece is unbalanced, it represents a source of periodic excitation for these resonators.

    The critical issues in each case are: What is the resonant frequency, what is the damping factor, and how firmly is the resonator connected to the source of vibration.

    The damping factor, In addition to determining how strongly the resonating system will respond to periodic excitation at its resonant frequency, determines how sensitive the system is to small differences between the frequency of the excitation and the resonant frequency. If the damping factor is very small, then the excitation frequency must be very close to the resonant frequency to cause much build-up of vibration. If it is large, the exact frequency of excitation will be much less important, but the build-up at the resonant frequency will be much smaller. This explains the situation often encountered in woodturning where as the system is slowly brought up to speed strong vibration occurs and then disappears as the speed increases.

    Harmonics

    Before defining “harmonics” I will define “fundamental” or “fundamental frequency”. In woodturning, this usually is the rotational frequency of the lathe since usually the source of the vibration is an unbalanced or uneven work piece. A “harmonic frequency” is any integer multiple of the fundamental frequency. Under certain conditions some of the vibration energy at the fundamental frequency is converted into vibration components at one or more harmonic frequencies. (More about this later.)

    Now consider a situation where an unbalanced and perhaps non-round work piece is spinning between centers on the lathe. As the lathe spins, the centrifugal force of the unbalanced component exerts a continuous outward force on the mountings. In the absence of any chatter due to looseness, and assuming that the metal in the lathe is not stressed beyond its yield point, the magnitude of the force acting in any particular direction, say down, will form a perfect sine wave when plotted versus time. That is to say, there are no harmonic components, only the fundamental frequency component. Therefore, in the recurring issue of whether to bolt down the lathe, harmonics are not at factor. Resonances at the fundamental frequency are the primary concern.

    When do harmonics become a factor? As far as I can see, the main cause of harmonic vibration will be turning a non-round work piece, either to true it up or as a step in a multi-axis turning project. In these cases, the cutting tool will not exert a constant force on the work piece all the way around. If you plotted the force in the upward direction versus time you would obtain a distorted sine wave. A distorted sine wave can be resolved into a fundamental component and one or more harmonics. Almost always, the fundamental component would remain far larger than any of the harmonics. Furthermore, the harmonics would only be a factor in stability of the lathe if very aggressive cutting were attempted and one of the harmonics excited a resonance with a very low damping factor. Even then, the problem could be corrected by making a small change in lathe speed.
     
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  2. Tom Albrecht

    Tom Albrecht

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    Thank you Dennis.
    One question: Is your lathe bolted down?
     
  3. Dennis J Gooding

    Dennis J Gooding

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    You are welcome, Tom. No, my lathe is not bolted down, but if I were a production turner of large pieces I am sure it would be. When I replaced a much smaller lathe with a Oneway 2436 20 years ago I felt compelled to challenge it. In a cloud of testosterone, laced from time to time with adrenaline, I turned a couple dozen or so very large bowls, hollow forms, platters and hats. In the process, I managed to work around vibration problems by one means or another without having to bore holes in my new shop floor. These days, I rarely turn a large piece.
     
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  4. Bill Boehme

    Bill Boehme Administrator Staff Member

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    Dennis, thank you for taking the time to define some terms that are frequently used incorrectly. Vibration has been a favorite topic of angst for as long as I have participated in woodturning forums.

    Also known as the "damped natural frequency".

    Even if the wood is round, the force at the cutting edge is alternating from side grain to end grain to side grain to end grain for each revolution of the piece. Interrupted cuts seriously change the harmonic content. The woodturner can also become a contributor to the intensity of harmonics. An example would be a new turner pushing hard with a dull tool to force it to cut.

    FWIW trivia: the fundamental is also the first harmonic (integer multiplier 1).
     
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  5. Emiliano Achaval

    Emiliano Achaval Administrator Staff Member

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    Thank you for taking the time to post such an interesting topic. We are all becoming smarter thanks to you! Aloha
     
  6. Mike Johnson

    Mike Johnson

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    Harmonic is a simple, usually sinusoidal, oscillation at a single frequency. Resonance embraces complex oscillations made up of multiple harmonics. Fourier analysis is used to identify harmonic components of a resonance. The number of harmonics in a resonance is limited by the number of degrees of freedom.

    There have been multiple books written about both Resonance and Harmonics, both of these anomalies can have an impact on physical and biological bodies, extensive studies have been done on various materials and various biological cells Science still has a ways to go before they fully understand how these anomalies work on the molecular level.

    Structural design of engineered components and systems can also be impacted by both harmonic and resonance anomalies, each component can add to or null the effects. A suspension bridge is a good example, the cables suspending the bridge deck can transmit oscillations, vibrations, harmonics into various structural components of the bridge which can resonate at the same frequency and fail like a wine glass reaching a critical frequency.

    High Voltage suspension wires can vibrate and oscillate to the point of failure if subjected to wind loads that hit the right frequency of the "tuned" cable suspended in the air, there are engineered components that can be added to the wires to null these resonant, harmonic forces which prevent the cables from failing. Depending on the materials of the wire, the length of the suspension and the tension on the wire, will determine the wind load needed to resonate the wire, much like a guitar string. The resonant frequency starts the wire vibrating, if the wire reaches a destructive harmonic frequency it can cause failure on the suspension components. The harmonic is like a carrier wave on the wire, if the wire is vibrating at 60 cycles, the 2nd harmonic would be 120 cycles and the 3rd harmonic would be 180 cycles etc. etc.. Certain harmonics can be destructive while other harmonics are not.

    Electrical voltages operate at specific frequencies, these systems can also encounter destructive harmonic voltages that can cause electrical components to heat up, trip breakers, blow fuses, cause capacitors and other electronic components to fail. These destructive forces can migrate anywhere on the system where there is a lower impedance value.

    If we truly understood this anomaly we would most likely know the secrets to levitation.
     
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  7. Dennis J Gooding

    Dennis J Gooding

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    Bill, you are correct about the end grain/side grain phenomenon. I believe it is mostly an issue in getting clean final cuts after everything is in balance. Given that the end grain occurs twice per revolution, one would expect that the second harmonic would be the dominant one. Again, if there is a significant resonance at that frequency, it probably can be evaded by changing the lathe speed slightly. In my discussion, I was concerned mostly with sources of serious vibration in the early stages of truing up a work piece.
    .
     
  8. Dennis J Gooding

    Dennis J Gooding

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    You are welcome Emiliano, and thank you.
     
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  9. Gerald Lawrence

    Gerald Lawrence

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    Mike since you said this I thought about the Tacoma Narrows Bridge. Very famous or infamous bridge failure caught on film. What kind of harmonics were involved there?
    https://www.bing.com/videos/search?...DE7A8755E9011BA35937DE7A8755E9011BA&FORM=VIRE
     
  10. John Torchick

    John Torchick

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    With all the technical talk, my main concern is if the lathe moves when I turn it on. If it moves, then I start all over to balance the piece.
     
  11. odie

    odie

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    Howdy Dennis.......I think you are referencing my recent posts. I appreciate your clarification on the proper use of the terminology. It's a good reference point. This should not be confused with what I was attempting to describe, and my reflection on interacting things happening with lathe tool/human cognizance, and the lathe itself.....These things are difficult for me to communicate in words alone. I may be technically incorrect with my word usage, but the advancements, relevance, and results are real and demonstrable.

    The ONLY thing that really matters, is results.......and if you'd like to compare my turned details to the main stream of wood turning......those results are where it really counts! The actual making of the turned details are not what is different about my work. Anyone can do that......IF they have prepared the surface to accept those details with minimal distortion. The ONLY thing that can do that, is eliminating the need for anything but very fine sanding grits, even on the most difficult woods. The most important result from minimal sanding is a more perfect geometry......and THAT is what allows finely made details to have the appearance of excellence to the eye.....or aesthetic appeal, if you will. The ONLY thing that makes all of this possible, is a refined collaboration between lathe, human brain, human hands......and, the choice/preparation of the lathe tools he uses. The lathe vibrations, no matter how they are described in words, or their origins, need to be controlled, and this is only a small component of the total effort. I suppose it should be stated here that as you remove wood, the vibrations created by the spinning wood, and applied to the lathe, do change as a continual process. :)

    For sure, I do not take your intentions as an affront, but simply as a clarification.......I see it as my problem with word usage, but the semantics intended by my inability to properly express my thoughts, have substance. ;)

    Keep on keepin on, Dennis! :D
    -----odie-----
     
    Last edited: Mar 14, 2020
  12. Dennis J Gooding

    Dennis J Gooding

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    Gerald, Wikipedia has short article on this subject that might interest you. Apparently, the destructive phenomenon involved was assumed initialy to be the sort of resonance I discussed here. However, it was later proven to be an entirely different effect that is referred to as "aerodynamic flutter" Apparently, the problem was not so much that an increasing amount of energy was being periodically changed from kinetic to gravitational and back. Instead, apparently, the flat roadbed was twisting back and forth in such a way that the wind load on the bridge tended to increase the the amount of twist. When twisted one way, the wind would tend to lift the roadbed; when twisted the other, it would tend to depress it.
     
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  13. Dennis J Gooding

    Dennis J Gooding

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    Actually, Odie my objective was not to censure anyone. I have had the benefit?? of several years of study of this stuff and enough lingering teacher instinct to want to pass some of it along. I was an an electrical engineering student and thought that this stuff was largely a waste of time compared to electronics. Ironically,
    almost everything I learned about electronics is irrelevant now, while I continue to face the effects of physical mechanics every day.

    On another subject, I was interested in some of your vibration measurements using a cell phone. Before writing this Tutorial, I considered using some laboratory type acceleration and position sensors to gather data on some specific examples of vibration amplitude and spectrum. In the end, I decided that the effort required to resurrect the old equipment was not worth it.
     
  14. odie

    odie

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    Hi Dennis.......if you do decide to do some practical technical research on this subject, I'd be very interested in what you come up with. :D

    Actually, I suspect if someone can detect the vibration characteristics, and display them with precision, it could very well be of benefit to other turners.....;)

    Good day, Dennis........:)
    -----odie-----
     
    Last edited: Mar 14, 2020
  15. Clifton C

    Clifton C

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    SOMEONE??? You hurt my feelings :eek::D
    Ok, not "precision"... I'll have to find a way to hook it up to an oscilloscope...

    [​IMG] [​IMG] [​IMG]
     
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  16. odie

    odie

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    Ha,ha......ok, you deserve the credit for your original idea, Clifton.....it's your baby! I've added a few of my own modifications, but you deserve the credit in whole for coming up with the original idea.......I am only a footnote!:D

    Yes......my thoughts are to improve it. I'm not sure just how......maybe Dennis can come up with some ideas of his own. :)......oscilloscope? Whatever fine tunes the output information is ok with me.....we all should butt our nogins together and make the improvements that will bring ideas into practical applications!!!!! o_O

    Keep on keepin' on for you, too, Clifton!;)
    -----odie-----
     
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  17. Bill Boehme

    Bill Boehme Administrator Staff Member

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    Funny that I had the same thoughts when I was an electrical engineering student. When I got to the real world after graduation I discovered what I thought was not something that I would actually use was a mistaken greenhorn idea. Basically my whole career was involved with aircraft and missile guidance and control. Dealing with vibration and other stability issues is a lot more critical if you're flying through the air compared to something that can be anchored to mother Earth.
     
  18. Bernie Hrytzak

    Bernie Hrytzak

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    Two weeks of survey school at the end of 1st year engineering helped me realize Civil engineering was not for me. I went into Mechanical the following year. Spent my career in Automotive Emission Control Component Design for the big 3 and also Honda. Also spent 5 years developing Air bag sensors for the large scale launch of GM airbags in the late 80s. Vibration challenges present in all products I was involved with.
     
  19. Mike Johnson

    Mike Johnson

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    The newer technology used in the industry is a Triaxial sensor which samples vertical, horizontal and axial vibrations from one senor.
    The data is collected from the sensor and the data can then be analyzed to show what is happening with various components in the equipment.
    Various wave forms indicate different types of issues with bearings, gears, belts, pulleys, chain drives, motors etc.
    A proper device is used to record the vibration data and it can be transmitted remotely to a technician that can interpret the data findings.
    This process usually involves opening the vibration data and expanding the time frame of the data to reading the data in milliseconds of time to
    break down the data and determine the various components and sinewave signatures of typical symptoms of mechanical components.
    IMI sensors is one of the large sensor technology companies in the vibration world.
     

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