Well ... at least until the next discovery.

(sorry about the delay on this post ... the site was down for quite a while)

Definitions.

-          FCU is the Flight Control Unit (e.g., Pixhawk or APM).

-          VDEP is the Vibration Dampened Electronics Platform where the FCU and other electronics are attached (including a gimbal/camera).

-          Ship attitude is the pitch and roll angle relative to time of the 2-dimensional plane(s) formed by lift from multirotor ships (e.g., the lift-plane formed by the four lifting propellers of a quad).

-          Latency is the delay caused by the time it takes for an attitude change of the ship to reach the FCU, for the FCU to process the change, for the FCU to appropriately command a change in rotor thrust, for the rotors to react, for the rotors and frame to change momentum, and for the attitude of the ship to create a controlled change.

-          Noise is the part of a signal that is random and should be ignored when analyzing ship attitude. Noise is that part of a signal that contains vibrations (up and down movements) that are too high in Hertz for a multirotor response and because these vibrations self-reverse, do not require attitude correction. In fact, correction in many cases would make the ship less stable. Significant causes of vibration noise are:

  • The imbalance of props,
  • The imbalance of motors,
  • Motor mast harmonics or flex (not stiff enough),
  • Propeller harmonics or change in Angle of Attack at different RPM.
  • Prop wash exciting  the rotor spar or VDEP,
  • VDEP harmonics (not stiff enough),
  • External systems (e.g., a camera gimbal that resonates at specific angles or speeds).

-          Attitude Error is the difference between actual ship attitude at time t and the attitude perceived by the FCU at time t. Differences are caused by latency and lack of ship rigidity between the lift-plane and FCU.

-          Damping, in this discussion, is measured by the reduction in the amplitude of noise going to the FCU without causing attitude error and a resulting loss in flight control. A true damper reduces vibration noise by decreasing the amplitude (force) of that vibration (turns part of the energy causing the amplitude into heat or another energy form) but does not increase attitude error. Damping increases the signal to noise ratio between actual ship attitude and the FCU at any given time t.

-          Isolation, in this discussion, is measured by the reduction in the amplitude of noise along with the increase in attitude error. Because it is important that the FCU know the attitude of the multirotor, damping is good and isolation is bad.

Background.  This is the history as I know it.

-          A multirotor weighing more than 300 grams can only respond with significant thrust deltas in the 20 or less Hertz range (see other research I produced testing actual lift response rates on various size ships). Thus vibration noise is typically greater than 5 to 20 Hz, depending on the ship and the FCU is effectively responding to attitude changes occurring at less than 20 Hz.

-          A Pixhawk flight controller is still delivered with optional mounts make of foam.

  • On poorly designed ships (loose), the foam pads help prevent flight run-aways
  • On ships designed well (stiff), the foam pads were proven to increase vibration (increased latency and caused harmonics).

-          To prove the negative impact of dampers on the FCU, I developed the open source Hover Analysis worksheet that:

  • Automatically finds the best hover of an attempted sustained hover flight.
  • Shows vibration levels in x (roll), y (pitch), and z (elevation) axis.
  • Shows the watts required to hover.
  • Shows IMU (gyro and acceleration sensor) health.
  • Suggests the optimal throttle setting.
  • Suggests the optimal roll and pitch balance setting.
  • Shows the impact of damping versus isolation.
  • Invited ship builders/modifiers to take the vibration test. All that did, found that removal of foam, pads, elastic bands, etc. reduced FCU vibration levels and at the same time increase attitude control (reduced isolation).
  • All cases of vibration reduction using elastics that were found to reduce FCU vibration also greatly reduced attitude control (e.g., caused isolation, not good when trying to control ship attitude).

 

An example of the issue with was demonstrated by Keven on one of his ships, shown below. Note the serious inability of the FCU to control the ship with latency caused by tape or moon gel.

Figure 1. Adding Dampers & Isolators Onto A Stiff Frame

-          I was a strong and vocal advocate of:

  • Only using dampers between the ship and camera gimbal but not between the rotor and FCU. The gimbal doesn’t control the ship so it is OK to isolate it. The FCU controls the ship, so it should not be isolated.
  • Hard fixing the FCU to a stiff rotor frame.

 

Then I discovered the Frantz Strut, a fortuitous accident, while trying to prove that dampers have no place on a light, well-engineered ship ... resulting in proving that I was one again … wrong. Oh well J  

Physics of Vibration (Noise):  So what is the Frantz Strut? First, a little physics on vibration control. The following are well known ways to passively control vibration:

1)      Let the vibration wave hit something dense on its way to the FCU, so the dense object will reflect the wave in a manner that allows the reflected wave to cancel other incoming waves. This approach in general does not work on multirotors as a primary approach because adding a denser object between the rotor and FCU adds weight … causing the rotors to work harder … increasing the amplitude of the source vibration wave (and flight times are shortened). But does this really work? If the ends of a rotor spar are relatively fixed, the reflected wave (wave (b) below) is an inverse of the inbound wave (wave (a) below) and can interact with inbound waves of a similar frequencies … partially nullify them (the sum of two inverse identical waves that are overlaid is a cancelled wave (see example t2 in Figure 3); similar to how noise cancelling headphones work, but this is accomplished passively, not actively).

Figure 2. Reflected Wave

Figure 3: Interaction of a Red and Blue Wave forming a Compound Wave

2)      Find and attach to the node point of the vibrating rotor spar (the node is where the amplitude = 0). A tube when vibrating may have a portion of the vibration (frequency ranges) that causes the bar to oscillate (bend) in full, half, third, quarter (etc.) waves as the vibration excites and permeates through the rotor spar.

Figure 4: Exaggerated Nodes and Harmonics

3)      Find a damper that dampens but does not isolate. Every scientist that I contacted that does damping professionally told me that materials do not exist that can dampen light objects (the FCU only weighs about 40ish grams and less if you remove the covers).

4)      Add mass. Mass is a great dampener and unless the engineer really screws up, does not isolate.  Double the mass and amplitude is cut in half. If the FCU weighs 20 grams and it is bound to a battery weighing 220 grams, then the amplitude of the FCU will be cut by (220 + 20) / 20 or a factor of 12.

Amplitude = -kx / mass

5)      Objects vibrate proportionally to the force acting on them and inversely proportional to the object’s stiffness.

Vibration = Force / Stiffness

 

The Frantz Strut – How It Works:  Enough BS … quit delaying, what is the frackin’ Frantz Strut? The Frantz Strut is a device can weigh less than 20 grams total that takes advantage of all five of the methods that have an a passive impact on vibration (noise to the FCU).

1)      It uses a small but denser (silicone, rubber, or plastic) damper or damper housing between the carbon rod that holds the rotors and the VDEP/FCU.

2)      It firmly attaches a housing to the node point on the rotor spar in order to transmit a minimal portion of the vibration energy.

3)      It embeds the damper inside the housing that dampens the energy between the housing and axle leading to the VDEP/FCU. The damper is such that it can dampen noise (small higher-frequency amplitudes) but transmit even small deltas in ship lower-frequency attitudes with insignificant latency.

4)      It puts the battery weight and non-rotor weight on the VDEP with the FCU so that not only is the mass greater (lower amplitudes) but the damper can now work against a greater load, making the damper material more viable and useful. It should be noted that on really light VDEPs that the damper serves no use (the axle is attached directly to the node points on each rotor spar).

5)      It uses a stiff rotor spar to keep the source magnitude of vibration low and to aide in vibration reflection when noise waves hit a denser damper. Vibration are in the x, y, and z direction, so:

  1. A carbon tube is the most optimal free-span material.
  2. A carbon I-beam is the most optimal side-supported material.

 

The drawing below shows:

-          The rotor

-          The rotor spar (the larger circle; looking down its axis) that is stiff relative to the vibration force.

-          The damper housing (the odd shaped object that contains both circles) that retains a damper and firmly grips or is bonded to the rotor spar at two of the spar’s vibration nodes.

-          The damper is not shown but it is retained by the damper housing, surrounds and is concentric to the VDEP axle in a manner that puts a damping material between the housing and VDEP axle (the small red-dashed circle). The damper is selected so it can respond to x, y, and z vibrations of the energy levels of the rotors and mass of the VDEP.

-          The VDEP axle (the small red dashed circle; looking down its axis) that is fixed to the VDEP. Each axle is suspended by two dampers.

-          The VDEP spans from center to center of both axles (the line coming from the lower left of the drawing, maintaining a space around the rotor spar, and continuing vertically; also see the top-view). The VDEP must maintain a space around the rotor spar in excess of vibration amplitudes and VDEP flight mass movements. Shown below is a 1,27 mm gap (0.050”).

Figure 5: Simplified End-View of the Frantz Strut. 

The Frantz Strut is shown in the Top View (Figure 6) in the two sets of red dashed lines: the fore and aft strut each consisting of 2 housings, 2 dampers, and an axle that is bonded or fixed to the VDEP. The basic design of the ship can be regular, spider, H, coaxial or a variant like below. All that is added (at most) is a damper housing, damper, and axle for a fore and aft strut that is attached to the VDEP.  In the drawing below, the fore spar, aft spar, and crossbar do not touch the VDEP. Only the fore and aft axle hold the VDEP. The axle does not need to be nearly as stiff as the rotor spars. The optimal span of the axle depends on the ship (varies from about 50% to 100% of the motor span), but most ships will find that the optimal span is locating the housings close to the motors.

 

Figure 6: Top View of a Quad with the Frantz Strut

The Frantz Strut – Performance:

-          An FCU will only control objects with any degree of reliability that have vibration noise less than 0.5 gs (gravity equivalents) of force (a measure that is directly proportional to amplitude).

-          A good “score” of vibration noise is between 0.10 and 0.20 gs.

-          When building ships that used hard fixed FCUs on stiff frames to partially isolated FCUs on gel or other isolation method, the best scores derived were between 0.06 to 0.10 gs.

-          The following is one of four ships build (by various folks) tested so far of different size and configurations that all derived a similar scores of between 0.03 to 0.04 gs using the Frantz Strut.

-          Also note that excellent signal to noise ratio proxies were factors of 2 to 5. The ship example below has a signal to noise proxy of nearly 10, easily twice as high as previous bests.

 

Figure 7: Frantz Strut Vibration

In addition, the measure of flight control also scored excellent, even while flying in the man-cave, trying to avoid decks and chairs. I’ll update this picture later after I take time to tune the ship with a "free" hover outside. But, there were people waiting for the test results so …

 

Figure 8: Attitude Control Using the Frantz Strut

How To Build It: “I don’t have the test equipment that you have, so how can I possibly build one?”

It is actually extremely easy as there are only three different parts and two are off the shelf. Your system might not be optimal, but it will have excellent performance and fly just great. The parts list is:

-          Housing for the Damper. It can be made:

  • From
    • Carbon/Balsa sandwich panel (the lightest approach)
    • Printed plastic (ask  if a certain person will share their print file or CAD drawing)
    • CNC’d plastic
  • To fit
    • An H frame (axle is parallel to the fore/aft rotor spars)
    • An X or V or regular frame where the damper retainer is at an angle or can swivel to the axles that can still be perpendicular to the VDEP but at a non-right angle to the spars.

-          Damper is off-the-shelf. Depending on the ship mass (if you don’t have the test equipment, use the Charmin squeeze test).

  • GoPro size for < 400 gram ships
  • Medium size for > 400 gram ships

-          Axle is an off-the-shelf carbon tube that is sized to fit through the center of the damper.

The assembly is:

-          Insert the damper into its damper housing (assemble four).

-          Clamp or bond the housing to the stiff rotor spar at the maximum or optimal span.

  • Two housings fore
  • Two housings aft
  • Max span for many ships will be the ideal location (but not always)

-          Insert the axles through the center of the damper pairs (one pair fore and one pair aft) and either through the VDEP or attached to the VDEP

The entire system will weigh about 15 to 20 grams if made from carbon and less than 45 grams total if the housing is printed from plastic.

I also invite other team members to add their photos and results of the ship they built using the Frantz Strut sharing their unique methods of implementation.

The following shows an aft video of the Frantz Strut working.

https://youtu.be/cHDM2Ql5_aw 

I’ll post photos later.

Developers and Manufacturers of Ships and Ship Parts: This discovery has been made public. You may use it freely use it without royalty. I only ask that you give credit where due. Hopefully as this discovery becomes widely known and proven that this discovery will be recognized and worth advertising as a feature of your commercial ships. From the data above, developers should be able to achieve 80% of the improvement potential of the Frantz Strut.  A significant improvement for most applications.

I will protect data and test methods not disclosed here for how to optimize the design of the Frantz Strut where the remaining 20% of reduction is significant to specific applications by:

-          Minimizing vibration at the VDEP.

-          Maximizing the signal to noise ratio of ship attitude at the FCU in real time.

 

Postscript. Now that ship vibration and the camera gimbal have been optimized, I can finally get back to:

-          Learning FPV (and when legal, long-range FPV)

-          Completing the optimal camera/sensor ship (started last year but distracted by learning to build an optimal gimbal and solving vibrations).

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Lots to study this night :) . Thank's Forrest to share so detailed work.

Great write up, with lots of solid information. The way to go.

Here are some photos of the finished product.

- It becomes clear how all of the mass in the VDEP adds up to allow dampers, which are not good at damping light weights, to actually work

- Also, because the axle goes through the axis of the damper, the damper limits versus exaggerates attitude deltas of the VDEP relative to the attitude of the rotor frame--critical for the FCU to be able to command useful rotor response. If the dampers were turned vertical, the FCU would sway back and forth relative to the rotor frame. Thus the FCU would give unproductive correction commands to the rotors.

- The housing + dampers + axle only weighs 15 grams. This is another problem with damper systems. They add too much weight. So for the ship to fly, it has to give more power that generates more vibration. The damper system needs to be light relative to the lift of the ship.  In this case, it weighs about a quarter of one percent of ship lift.

Below is the top view of ship. You can see a somewhat normal modified H frame (front/aft motor spar with diagonal brace). Then inside that is the Frantz Strut (damper housing that also doubles to hold the ESC, the white damper, and axle). The rotor frame could as easily be an X, V, spider, or other shape.

Below is a closer look at the fore-starboard side. You can see the housing bonded to the fore-rotor spar that is also holding the ESC, At the aft side of the housing is where the damper is held. Then through the damper goes the axle. And the axle is hard fixed to the VDEP. The VDEP is close to but does not touch the frame. In case of a crash, keeping the VDEP close to the stronger and stiffer frame helps keep load off of the axle that is sized for the VDEP mass but not for a 9x to 50x crash load.


Below is a close-up of the housing. [Note: for those curious about the ESC, it is sealed with electrical sealant, spaced slightly away from all carbon structure to which it is bonded, and there is shrink wrap around the bullets to keep the carbon skin of the damper housing electrically isolated from the rotor power system. The ESC does not touch the VDEP axle.]  There are dabs of adhesive to keep the damper in place.

Then below is a view from the front. One of the only connections between the frame and VDEP are the wires going between the Battery/Pwr Dist Board and the ESCs. The wires are right-sized multi-stranded with soft insulation so they are light and flexible. There is also a loop in the wire between the ESC and VDEP. All of those factors add together to help keep vibrational energy in the wires from transferring to the VDEP. Note: And yes, Jim's famous mint flavored floss to keep wires under control and the ship smelling good.

I'll also try to post photos of the build process.

This is how to build a damper housing from carbon/balsa sandwich panels.

1) two 3mm carbon balsa halves are milled with

   ... a pocket (smaller top hole) to mechanically contain the damper (you really can't bond to them that well)

   ... a hole for the rotor spar that will get bonded to the spar.

2) the damper is then placed into one of the pockets.

3) the side of one of the housing halves is coated with adhesive and the two bonded together, retaining the damper.

4) the housings are bonded to the motor spar (after the null point is located)

5) the fore and aft spar/strut are then joined by side spars

6) one or more crossbars are added (depending on your need for high speed crash worthiness

7) the VDEP with axle is added (not shown)

8) everything is wired up and off you go, nearly vibration free. Shown below is a FPV racer that used the Frantz Strut.

excellent. Way to go.

Really well thought out research and development Forrest.

My experience has also shown that having a bulk of the mass in the isolated / damped section of the copter is optimal for vibration reduction but sometimes suffers from somewhat slower control response.

So I appreciate and understand the potential benefits from extending the damped interface further out on the frame both for improving flight control responsiveness and for modulating main frame vibration frequency at the points of connection to central mass.

It is literally a balancing act.

At first from your description it seemed to me that the somewhat exotic balsa / carbon fiber damper "housing" was important, but now it appears to me that any light and fairly rigid material would work.

Please comment on this.

I am planning on linking to this excellent discussion from my QuadcoptersAreFun web site.

Great job, I definitely think you have produced the current best analysis and solution for this issue.

BTW If you are not already using them ToolsToday now carries polycrystaline diamond bits which will last a lot - lot longer cutting CF in your CNC router.

Best Regards,

Gary

Thanks Gary, and yes, you are absolutely right. Hugues has printed a version and Jim cut a version from plastic. Both of those had the advantage of being screw tightened. Both worked equally well. They just weigh about 20ish grams more. I wish I'd had the other versions for the tests with simple tightening screws to move them along the rotor spar to find the node. On the carbon/balsa ones, I had to glue and then unglue about 20 times.

Thanks for the tip on the bits. Wasn't aware of the website. Really well put together. They even have 1/8" burr type. Perfect. I'll get some.

*-* !

Thank you for sharing this excellent introduction and solution to *vibration on copters*

Time ago, when I found copters interesting an assembled a hexa, I never thought that

there is so much interesting things to learn and to try while having fun (flying and photographing)

Thumbs UUUUUUP!! :)

As requested by Forrest to illustrate its strut application, here a build video where struts were 3D printed for holding a VDEP platform on an X frame:

My vibrations results in kind of rough flying (not even loitering):

Between the music, chicken and tech sharing, that video should get an Oscar!

Hey Bernardo - Sometime share one of your favorite photos taken from your ship. Would be curious.

Chiken are still alive :D

Nice work guys, It's looks important that dampening plate looks much bigger than things over it :) , I'm thinking that, if I can move the hole electronic FPV included, I'm going to have better performance than only dampening the lightweight controller, batteries (2 3s*5.000) perhaps I still prefer downside in case of crash?, with only the electronic and fpv camera it's possible to work? or need the battery too?

mmm....I moved FPV camera (dampened)  from main plate  to parallels with rubbers were I attach the batteries and performs much better, batteries explain things I hope now. (OK, I stop thinking and writing at the same time :O )

I found square tubes to build a cuadplane, It's safe to glue them like the rounded tubes? (sorry the offtopic)

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